% This file was created with JabRef 2.6.
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@ARTICLE{Aach_T_2000_sp_lap_dtsiaare,
author = {Aach, T. and Kunz, D.},
title = {A lapped directional transform for spectral image analysis and its
application to restoration and enhancement},
journal = j-sp,
year = {2000},
volume = {80},
pages = {2347--2364},
number = {11},
month = {Nov.},
file = {Aach_T_2000_sp_lap_dtsiaare.pdf:Aach_T_2000_sp_lap_dtsiaare.pdf:PDF},
owner = {duvall},
pdf = {Aach_T_2000_sp_lap_dtsiaare.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Abrial_P_2007_j-four-anal-appl_mor_caisapa,
author = {Abrial, P. and Moudden, Y. and Starck, J.-L. and Bobin, J. and Afeyan,
B. and Nguyen, M. K.},
title = {Morphological Component Analysis and Inpainting on the sphere: Application
in Physics and Astrophysics},
journal = j-four-anal-appl,
year = {2007},
volume = {13},
pages = {729--748},
number = {6},
month = {Oct.},
note = {Special issue: "Analysis on the Sphere'"},
file = {Abrial_P_2007_j-four-anal-appl_mor_caisapa.pdf:Abrial_P_2007_j-four-anal-appl_mor_caisapa.pdf:PDF},
owner = {duvall},
timestamp = {2010.10.14}
}
@INPROCEEDINGS{Abry_P_1994_stfts_mul_td,
author = {Abry, P. and Flandrin, P.},
title = {Multiresolution transient detection},
booktitle = p-stfts,
year = {1994},
pages = {225--228},
address = {Philadelphia, PA, USA},
month = {Oct.},
abstract = {Designs and studies the performance of a multiresolution-based transient
detector. The transients the authors are interested in consist of
wide-band, pulse-like, coherent structures in a turbulent flow. To
take advantage of the fast pyramidal wavelet algorithm, an important
point when processing large amounts of experimental data, the detector
makes use of the discrete wavelet transform. The authors show how
the lack of time- invariance drawback of the discrete transform can
be efficiently overcome by using relevant analytic wavelets. They
thus compare this detection technique with one based on a continuous
wavelet transform, as well as with other standard methods and show
that wavelets perform best when the transients are superimposed on
a colored 1/f background noise. This description is very close to
that of turbulence and relevant also in many other situations},
doi = {10.1109/TFSA.1994.467252},
file = {Abry_P_1994_stfts_mul_td.pdf:Abry_P_1994_stfts_mul_td.pdf:PDF},
owner = {duvall},
pdf = {Abry_P_1994_stfts_mul_td.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Adelson_E_1984_j-rca-eng_pyr_mip,
author = {E. H. Adelson and C. H. Anderson and J. R. Bergen and P. J. Burt
and J. M. Ogden},
title = {Pyramid Method in Image Processing},
journal = j-rca-eng,
year = {1984},
volume = {29},
pages = {33--41},
number = {6},
abstract = {The data structure used to represent image information can be critical
to the successful completion of an image processing task. One structure
that has attracted considerable attention is the image pyramid This
consists of a set of lowpass or bandpass copies of an image, each
representing pattern information of a different scale. Here we describe
a variety of pyramid methods that we have developed for image data
compression, enhancement, analysis and graphics.},
file = {Adelson_E_1984_j-rca-eng_pyr_mip.pdf:Adelson_E_1984_j-rca-eng_pyr_mip.pdf:PDF},
owner = {duvall},
pdf = {Adelson_E_1984_j-rca-eng_pyr_mip.pdf},
timestamp = {2009.12.22}
}
@ARTICLE{Allen_J_1977_tassp_sho_tsasmdft,
author = {Allen, J.},
title = {Short-term spectral analysis, synthesis, and modification by discrete
{Fourier} transform},
journal = j-ieee-tassp,
year = {1977},
volume = {25},
pages = {235--238},
number = {3},
month = {Jun.},
abstract = {A theory of short term spectral analysis, synthesis, and modification
is presented with an attempt at pointing out certain practical and
theoretical questions. The methods discussed here are useful in designing
filter banks when the filter bank outputs are to be used for synthesis
after multiplicative modifications are made to the spectrum.},
file = {Allen_J_1977_tassp_sho_tsasmdft.pdf:Allen_J_1977_tassp_sho_tsasmdft.pdf:PDF},
owner = {duvall},
pdf = {Allen_J_1977_tassp_sho_tsasmdft.pdf},
timestamp = {2008.11.26}
}
@INPROCEEDINGS{Andres_E_2002_p-dgci_rid_trdl,
author = {Andres, E. and Carr\'e, P.},
title = {Ridgelet transform based on {R}eveill{\`e}s Discrete Lines},
booktitle = p-dgci,
year = {2002},
volume = {2301},
series = ser-lncs,
pages = {417--427},
month = {Apr.},
abstract = {In this paper we present a new discrete implementation of ridgelet
transforms based on Reveill\`es discrete 2D lines. Ridgelet transforms
are particular invertible wavelet transforms. Our approach uses the
arithmetical thickness parameter of Reveill\`es lines to adapt the
Ridgelet transform to specific applications. We illustrate this with
a denoising and a compression algorithm. The broader aim of this
paper is to show how results of discrete analytical geometry can
be sucessfully used in image analysis.},
owner = {duvall},
timestamp = {2010.02.26}
}
@ARTICLE{Antoine_J_2008_j-ijwmip_con_wtcs,
author = {Antoine, J.-P. and Bogdanova, I. and Vandergheynst, P.},
title = {The continuous wavelet transform on conic sections},
journal = j-ijwmip,
year = {2008},
volume = {6},
pages = {137--156},
number = {2},
abstract = {We review the coherent state (or group-theoretical) construction of
the continuous wavelet transform (CWT) on the two-sphere. Next, we
describe the construction of a CWT on the upper sheet of a two-sheeted
hyperboloid, emphasizing the similarities between the two cases.
Finally, we give some indications on the CWT on a paraboloid and
we introduce a unified approach to the CWT on conic sections.},
doi = {10.1142/S0219691308002288},
keywords = {Continuous wavelet transform; conic sections; two-sphere; two-sheeted
hyperboloid; paraboloid AMSC numbers: 42C15, 42C40, 65T60},
owner = {duvall},
timestamp = {2011.01.05}
}
@ARTICLE{Antoine_J_1993_j-sp_ima_atdcwt,
author = {Antoine, J.-P. and Carrette, P. and Murenzi, R. and Piette, B.},
title = {Image analysis with two-dimensional continuous wavelet transform},
journal = j-sp,
year = {1993},
volume = {31},
pages = {241--272},
number = {3},
month = {Apr.},
file = {Antoine_J_1993_j-sp_ima_atdcwt.pdf:Antoine_J_1993_j-sp_ima_atdcwt.pdf:PDF},
owner = {duvall},
publisher = {Elsevier Science},
timestamp = {2009.11.27}
}
@ARTICLE{Antoine_J_2002_j-acha_wav_sia,
author = {J.-P. Antoine and L. Demanet and L. Jacques and P. Vandergheynst},
title = {Wavelets on the sphere: implementation and approximations},
journal = j-acha,
year = {2002},
volume = {13},
pages = {177--200},
number = {3},
issn = {1063-5203},
abstract = {We continue the analysis of the continuous wavelet transform on the
2-sphere, introduced in a previous paper. After a brief review of
the transform, we define and discuss the notion of directional spherical
wavelet, i.e., wavelets on the sphere that are sensitive to directions.
Then we present a calculation method for data given on a regular
spherical grid . This technique, which uses the FFT, is based on
the invariance of under discrete rotations around the z axis preserving
the [phi] sampling. Next, a numerical criterion is given for controlling
the scale interval where the spherical wavelet transform makes sense,
and examples are given, both academic and realistic. In a second
part, we establish conditions under which the reconstruction formula
holds in strong Lp sense, for 1[less-than-or-equals, slant]p<[infinity].
This opens the door to techniques for approximating functions on
the sphere, by use of an approximate identity, obtained by a suitable
dilation of the mother wavelet.},
doi = {DOI: 10.1016/S1063-5203(02)00507-9},
file = {Antoine_J_2002_j-acha_wav_sia.pdf:Antoine_J_2002_j-acha_wav_sia.pdf:PDF},
keywords = {Continuous wavelet transform; 2-sphere; Directional spherical wavelet;
Approximate identity},
owner = {duvall},
pdf = {Antoine_J_2002_j-acha_wav_sia.pdf},
timestamp = {2009.11.01},
url = {http://www.sciencedirect.com/science/article/B6WB3-474DMCF-3/2/0fe29bdaef0d485c199c1b1218aef397}
}
@ARTICLE{Antoine_J_1999_j-acha_dir_wrcwsdp,
author = {J.-P. Antoine and R. Murenzi and P. Vandergheynst},
title = {Directional Wavelets Revisited: Cauchy Wavelets and Symmetry Detection
in Patterns},
journal = j-acha,
year = {1999},
volume = {6},
pages = {314--345},
number = {3},
issn = {1063-5203},
abstract = {The analysis of oriented features in images requires two-dimensional
directional wavelets. Among these, we study in detail the class of
Cauchy wavelets, which are strictly supported in a (narrow) convex
cone in spatial frequency space. They have excellent angular selectivity,
as shown by a standard calibration test, and they have minimal uncertainty.
In addition, we present a new application of directional wavelets,
namely a technique for determining the symmetries of a given pattern
with respect to rotations and dilation.},
doi = {DOI: 10.1006/acha.1998.0255},
file = {Antoine_J_1999_j-acha_dir_wrcwsdp.pdf:Antoine_J_1999_j-acha_dir_wrcwsdp.pdf:PDF},
owner = {duvall},
pdf = {Antoine_J_1999_j-acha_dir_wrcwsdp.pdf},
timestamp = {2009.11.01},
url = {http://www.sciencedirect.com/science/article/B6WB3-45HR77T-F/2/48f6b27610c784c0a3fcbcf1905d75bb}
}
@BOOK{Antoine_J_2004_book_two_dwr,
title = {{Two-dimensional wavelets and their relatives}},
publisher = {Cambridge University Press},
year = {2004},
author = {Antoine, J.-P. and Murenzi, R. and Vandergheynst, P. and Twareque
Ali, S. },
abstract = {Two-dimensional wavelets offer a number of advantages over discrete
wavelet transforms when processing rapidly varying functions and
signals. In particular, they offer benefits for real-time applications
such as medical imaging, fluid dynamics, shape recognition, image
enhancement and target tracking. This book introduces the reader
to 2-D wavelets via 1-D continuous wavelet transforms, and includes
a long list of useful applications. The authors then describe in
detail the underlying mathematics before moving on to more advanced
topics such as matrix geometry of wavelet analysis, three-dimensional
wavelets and wavelets on a sphere. Throughout the book, practical
applications and illustrative examples are used extensively, ensuring
the book?s value to engineers, physicists and mathematicians alike.
The first of its kind in print dealing with the two - and higher
- dimensional continuous wavelet transforms, with extensive examples
of applications. Gradual introduction of the underlying mathematical
tools, with very few prerequisites, yet leading the reader to the
research frontier. Covers both the continuous and the discrete wavelet
transforms},
file = {Antoine_J_2004_book_two_dwr.pdf:Antoine_J_2004_book_two_dwr.pdf:PDF},
isbn = {9780511227080},
owner = {duvall},
pdf = {Antoine_J_2004_book_two_dwr.pdf},
timestamp = {2009.11.21}
}
@ARTICLE{Antoine_J_2010_j-acha_wav_tmona,
author = {J.-P. Antoine and Ro{\c{s}}ca, D. and Vandergheynst, P.},
title = {Wavelet transform on manifolds: Old and new approaches},
journal = j-acha,
year = {2010},
volume = {28},
pages = {189--202},
number = {2},
note = {Special Issue on Continuous Wavelet Transform in Memory of Jean Morlet,
Part I},
issn = {1063-5203},
abstract = {Given a two-dimensional smooth manifold and a bijective projection
from on a fixed plane (or a subset of that plane), we explore systematically
how a wavelet transform (WT) on may be generated from a plane WT
by the inverse projection . Examples where the projection maps the
whole manifold onto a plane include the two-sphere, the upper sheet
of the two-sheeted hyperboloid and the paraboloid. When no such global
projection is available, the construction may be performed locally,
i.e., around a given point on . We apply this procedure both to the
continuous WT, already treated in the literature, and to the discrete
WT. Finally, we discuss the case of a WT on a graph, for instance,
the graph defined by linking the elements of a discrete set of points
on the manifold.},
doi = {DOI: 10.1016/j.acha.2009.10.002},
file = {Antoine_J_2010_j-acha_wav_tmona.pdf:Antoine_J_2010_j-acha_wav_tmona.pdf:PDF},
keywords = {Continuous wavelet transform; Discrete wavelet transform; Wavelet
transform on manifolds; Projection; Wavelet transform on graphs},
owner = {duvall},
pdf = {Antoine_J_2010_j-acha_wav_tmona.pdf},
timestamp = {2010.02.27},
url = {http://www.sciencedirect.com/science/article/B6WB3-4XF83YM-1/2/f8f4a90ab76eead584134a5741d579ab}
}
@ARTICLE{Antoine_J_1999_j-acha_wav_2sgta,
author = {Antoine, J.-P. and Vandergheynst, P.},
title = {Wavelets on the 2-sphere: A group-theoretical approach},
journal = j-acha,
year = {1999},
volume = {7},
pages = {262--291},
number = {3},
issn = {1063-5203},
doi = {DOI: 10.1006/acha.1999.0272},
file = {Antoine_J_1999_j-acha_wav_2sgta.pdf:Antoine_J_1999_j-acha_wav_2sgta.pdf:PDF},
owner = {duvall},
publisher = {Elsevier},
timestamp = {2011.01.05},
url = {\url{http://www.sciencedirect.com/science/article/B6WB3-45HR76Y-2/2/04d716fb4bd326464c0e65e73911f461}}
}
@ARTICLE{Aujol_J_2005_j-math-imaging-vis_ima_dbvcoc,
author = {Aujol, J.-F. and Aubert, G. and Blanc-Feraud, L. and Chambolle, A.},
title = {Image Decomposition into a Bounded Variation Component and an Oscillating
Component},
journal = j-math-imaging-vis,
year = {2005},
volume = {22},
pages = {71--88},
number = {1},
month = {Jan.},
abstract = {We construct an algorithm to split an image into a sum u + v of a
bounded variation component and a component containing the textures
and the noise. This decomposition is inspired from a recent work
of Y. Meyer. We find this decomposition by minimizing a convex functional
which depends on the two variables u and v, alternately in each variable.
Each minimization is based on a projection algorithm to minimize
the total variation. We carry out the mathematical study of our method.
We present some numerical results. In particular, we show how the
u component can be used in nontextured SAR image restoration.},
doi = {10.1007/s10851-005-4783-8},
file = {Aujol_J_2005_j-math-imaging-vis_ima_dbvcoc.pdf:Aujol_J_2005_j-math-imaging-vis_ima_dbvcoc.pdf:PDF},
keywords = {total variation minimization - BV - texture - restoration - SAR images
- speckle},
owner = {duvall},
timestamp = {2011.04.08}
}
@INCOLLECTION{Auscher_P_1992_in-coll-wav_bl2rrdf,
author = {Auscher, P.},
title = {Wavelet bases for ${L}^2(\mathbb{R})$ with rational dilation factor},
booktitle = {Wavelets and their applications},
publisher = {Jones and Bartlett},
year = {1992},
pages = {439--452},
address = {Boston, MA, USA},
file = {Auscher_P_1992_in-coll-wav_bl2rrdf.pdf:Auscher_P_1992_in-coll-wav_bl2rrdf.pdf:PDF},
owner = {duvall},
pdf = {Auscher_P_1992_in-coll-wav_bl2rrdf.pdf},
timestamp = {2008.11.23}
}
@ARTICLE{Averbuch_A_2006_j-acha_fas_apft,
author = {A. Averbuch and R. R. Coifman and D. L. Donoho and M. Elad and M.
Israeli},
title = {Fast and accurate Polar {Fourier} transform},
journal = j-acha,
year = {2006},
volume = {21},
pages = {145--167},
file = {Averbuch_A_2006_j-acha_fas_apft.pdf:Averbuch_A_2006_j-acha_fas_apft.pdf:PDF},
owner = {duvall},
pdf = {Averbuch_A_2006_j-acha_fas_apft.pdf},
timestamp = {2009.11.27}
}
@ARTICLE{Ayache_A_2001_j-acha_som_mcnocswb,
author = {A. Ayache},
title = {Some Methods for Constructing Nonseparable, Orthonormal, Compactly
Supported Wavelet Bases},
journal = j-acha,
year = {2001},
volume = {10},
pages = {99--111},
number = {1},
issn = {1063-5203},
abstract = {We first show that by combining monodimensional filter banks one can
obtain nonseparable filter banks. We then give necessary conditions
for these filter banks to generate orthonormal and regular wavelets.
Finally, we establish that some of these filter banks lead to arbitrarily
smooth, nonseparable, orthonormal, compactly supported wavelet bases.},
doi = {DOI: 10.1006/acha.2000.0325},
file = {Ayache_A_2001_j-acha_som_mcnocswb.pdf:Ayache_A_2001_j-acha_som_mcnocswb.pdf:PDF},
owner = {duvall},
pdf = {Ayache_A_2001_j-acha_som_mcnocswb.pdf},
timestamp = {2009.11.30},
url = {http://www.sciencedirect.com/science/article/B6WB3-45BT4NK-1B/2/20fcc16958f02d3ae2bc58c0acdd9a6a}
}
@ARTICLE{Babaud_J_1986_tpami_uni_gkssf,
author = {Babaud, J. and Witkin, A. P. and Baudin, M. and Duda, R. O.},
title = {Uniqueness of the {Gaussian} Kernel for Scale-Space Filtering},
journal = j-ieee-tpami,
year = {1986},
volume = {8},
pages = {26--33},
number = {1},
month = {Jan.},
issn = {0162-8828},
abstract = {Scale-space filtering constructs hierarchic symbolic signal descriptions
by transforming the signal into a continuum of versions of the original
signal convolved with a kernal containing a scale or bandwidth parameter.
It is shown that the Gaussian probability density function is the
only kernel in a broad class for which first-order maxima and minima,
respectively, increase and decrease when the bandwidth of the filter
is increased. The consequences of this result are explored when the
signal or its image by a linear differential operator is analyzed
in terms of zero-crossing contours of the transform in scale-space.},
doi = {10.1109/TPAMI.1986.4767749},
file = {Babaud_J_1986_tpami_uni_gkssf.pdf:Babaud_J_1986_tpami_uni_gkssf.pdf:PDF},
owner = {duvall},
pdf = {Babaud_J_1986_tpami_uni_gkssf.pdf},
timestamp = {2009.10.20}
}
@ARTICLE{Bamberger_R_1992_j-ieee-tsp_fil_bdditd,
author = {Bamberger, R. H. and Smith, M. J. T.},
title = {A filter bank for the directional decomposition of images: theory
and design},
journal = j-ieee-tsp,
year = {1992},
volume = {40},
pages = {882--893},
number = {4},
month = {Apr.},
file = {Bamberger_R_1992_j-ieee-tsp_fil_bdditd.pdf:Bamberger_R_1992_j-ieee-tsp_fil_bdditd.pdf:PDF},
keywords = {2-D filter bank directional decomposition directional information
directional reconstruction image decomposition nonrecursive filters
passband recursive filters},
owner = {duvall},
timestamp = {2007.06.15}
}
@ARTICLE{Baussard_A_2004_j-sp_rat_mafwtawsd,
author = {A. Baussard and F. Nicolier and F. Truchetet},
title = {Rational multiresolution analysis and fast wavelet transform: application
to wavelet shrinkage denoising},
journal = j-sp,
year = {2004},
volume = {84},
pages = {1735--1747},
number = {10},
issn = {0165-1684},
abstract = {This paper presents a contribution to rational multiresolution analysis
(MRA). The rational analysis allows a better adaptation of scale
factors to signal components than the dyadic one. The theory of rational
MRA is reviewed and a pyramidal algorithm for fast rational orthogonal
wavelet transform is proposed. Both, the analysis and synthesis parts
of the process are detailed. Examples of scaling and wavelet functions
and associated filters are given. Moreover, dealing with filters
defined in Fourier domain, the implementation of the algorithm in
this domain is described. Then, the study is extended to the 2D separable
case in order to give a more conclusive presentation of the rational
MRA. In order to illustrate the potential of rational analysis for
signal and image processing, some results given by wavelet shrinkage
denoising based on the [`]SURE' thresholding method are presented.},
doi = {DOI: 10.1016/j.sigpro.2004.06.001},
file = {Baussard_A_2004_j-sp_rat_mafwtawsd.pdf:Baussard_A_2004_j-sp_rat_mafwtawsd.pdf:PDF},
keywords = {Pyramidal algorithm; Rational multiresolution analysis; Rational wavelet
transform; Wavelet shrinkage denoising},
owner = {duvall},
pdf = {Baussard_A_2004_j-sp_rat_mafwtawsd.pdf},
timestamp = {2009.07.18},
url = {\url{http://www.sciencedirect.com/science/article/B6V18-4CS4G0S-1/2/90023d217aeef798c7fc727c9b8cd0a6}}
}
@ARTICLE{Bayram_I_2009_j-ieee-tsp_fre_ddordwt,
author = {Bayram, {\.I}. and Selesnick, I. W.},
title = {Frequency-Domain Design of Overcomplete Rational-Dilation Wavelet
Transforms},
journal = j-ieee-tsp,
year = {2009},
volume = {57},
pages = {2957--2972},
number = {8},
month = {Aug.},
issn = {1053-587X},
abstract = {The dyadic wavelet transform is an effective tool for processing piecewise
smooth signals; however, its poor frequency resolution (its low Q-factor)
limits its effectiveness for processing oscillatory signals like
speech, EEG, and vibration measurements, etc. This paper develops
a more flexible family of wavelet transforms for which the frequency
resolution can be varied. The new wavelet transform can attain higher
Q-factors (desirable for processing oscillatory signals) or the same
low Q-factor of the dyadic wavelet transform. The new wavelet transform
is modestly overcomplete and based on rational dilations. Like the
dyadic wavelet transform, it is an easily invertible 'constant-Q'
discrete transform implemented using iterated filter banks and can
likewise be associated with a wavelet frame for L2(R). The wavelet
can be made to resemble a Gabor function and can hence have good
concentration in the time-frequency plane. The construction of the
new wavelet transform depends on the judicious use of both the transform's
redundancy and the flexibility allowed by frequency-domain filter
design.},
doi = {10.1109/TSP.2009.2020756},
file = {Bayram_I_2009_j-ieee-tsp_fre_ddordwt.pdf:Bayram_I_2009_j-ieee-tsp_fre_ddordwt.pdf:PDF},
keywords = {Gabor function;Q-factor;constant-Q discrete transform;dyadic wavelet
transform;frequency-domain filter design;iterated filter banks;oscillatory
signals;overcomplete rational-dilation wavelet transforms;piecewise
smooth signals;rational dilations;channel bank filters;discrete wavelet
transforms;frequency-domain analysis;},
owner = {duvall},
pdf = {Bayram_I_2009_j-ieee-tsp_fre_ddordwt.pdf},
timestamp = {2010.03.04}
}
@ARTICLE{Bayram_I_2008_tsp_dua_tcwpmbt,
author = {Bayram, {\.I}. and Selesnick, I. W.},
title = {On the Dual-Tree Complex Wavelet Packet and ${M}$-Band Transforms},
journal = j-ieee-tsp,
year = {2008},
volume = {56},
pages = {2298--2310},
number = {6},
month = {Jun.},
issn = {1053-587X},
abstract = {The two-band discrete wavelet transform (DWT) provides an octave-band
analysis in the frequency domain, but this might not be ldquooptimalrdquo
for a given signal. The discrete wavelet packet transform (DWPT)
provides a dictionary of bases over which one can search for an optimal
representation (without constraining the analysis to an octave-band
one) for the signal at hand. However, it is well known that both
the DWT and the DWPT are shift-varying. Also, when these transforms
are extended to 2-D and higher dimensions using tensor products,
they do not provide a geometrically oriented analysis. The dual-tree
complex wavelet transform , introduced by Kingsbury, is approximately
shift-invariant and provides directional analysis in 2-D and higher
dimensions. In this paper, we propose a method to implement a dual-tree
complex wavelet packet transform , extending the as the DWPT extends
the DWT. To find the best complex wavelet packet frame for a given
signal, we adapt the basis selection algorithm by Coifman and Wickerhauser,
providing a solution to the basis selection problem for the . Lastly,
we show how to extend the two-band to an -band (provided that ) using
the same method.},
doi = {10.1109/TSP.2007.916129},
file = {Bayram_I_2008_tsp_dua_tcwpmbt.pdf:Bayram_I_2008_tsp_dua_tcwpmbt.pdf:PDF},
keywords = {discrete wavelet transforms, frequency-domain analysis, signal processing,
trees (mathematics)},
owner = {duvall},
pdf = {Bayram_I_2008_tsp_dua_tcwpmbt.pdf},
timestamp = {2009.08.26}
}
@ARTICLE{Belzer_B_1995_tsp_com_lpfeic,
author = {Belzer, B. and Lina, J.-M. and Villasenor, J.},
title = {Complex, linear-phase filters for efficient image coding},
journal = j-ieee-tsp,
year = {1995},
volume = {43},
pages = {2425--2427},
number = {10},
month = {Oct.},
file = {Belzer_B_1995_tsp_com_lpfeic.pdf:Belzer_B_1995_tsp_com_lpfeic.pdf:PDF},
owner = {duvall},
pdf = {Belzer_B_1995_tsp_com_lpfeic.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Bergeaud_F_1996_j-comput-appl-math-birkhauser_mat_paris,
author = {F. Bergeaud and S. Mallat},
title = {Matching pursuit: Adaptive representations of images and sounds},
journal = j-comput-appl-math-birkhauser,
year = {1996},
volume = {15},
pages = {97--109},
number = {2},
owner = {duvall},
timestamp = {2009.11.19}
}
@ARTICLE{Beylkin_G_1996_acha_imp_ofbashw,
author = {Beylkin, G. and Torr{\'e}sani, B.},
title = {Implementation of Operators via Filter Banks: Autocorrelation Shell
and {Hardy} Wavelets},
journal = j-acha,
year = {1996},
volume = {3},
pages = {164--185},
file = {Beylkin_G_1996_acha_imp_ofbashw.pdf:Beylkin_G_1996_acha_imp_ofbashw.pdf:PDF},
keywords = {hilbert transform},
owner = {duvall},
pdf = {Beylkin_G_1996_acha_imp_ofbashw.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Beylkin_G_1994_tfom-tma_tra_hbf,
author = {Beylkin, G. and Torr{\'e}sani, B.},
title = {Transformation de {Hilbert} et Bancs de Filtres},
booktitle = {Colloque temps-fr{\'e}quence, ondelettes et multir{\'e}solution :
th{\'e}orie, mod{\`e}les et applications},
year = {1994},
volume = {25},
pages = {1--4},
address = {Lyon, France},
month = {Mar. 9-11,},
file = {Beylkin_G_1994_tfom-tma_tra_hbf.pdf:Beylkin_G_1994_tfom-tma_tra_hbf.pdf:PDF},
owner = {duvall},
pdf = {Beylkin_G_1994_tfom-tma_tra_hbf.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Bharath_A_2005_tip_ste_cwcaid,
author = {Bharath, A. A. and Ng, J.},
title = {A steerable complex wavelet construction and its application to image
denoising},
journal = j-ieee-tip,
year = {2005},
volume = {14},
pages = {948--959},
number = {7},
month = {Jul.},
issn = {1057-7149},
abstract = {This work addresses the design of a novel complex steerable wavelet
construction, the generation of transform-space feature measurements
associated with corner and edge presence and orientation properties,
and the application of these measurements directly to image denoising.
The decomposition uses pairs of bandpass filters that display symmetry
and antisymmetry about a steerable axis of orientation. While the
angular characterization of the bandpass filters is similar to those
previously described, the radial characteristic is new, as is the
manner of constructing the interpolation functions for steering.
The complex filters have been engineered into a multirate system,
providing a synthesis and analysis subband filtering system with
good reconstruction properties. Although the performance of our proposed
denoising strategy is currently below that of recently reported state-of-the-art
techniques in denoising, it does compare favorably with wavelet coring
approaches employing global thresholds and with an "Oracle" shrinkage
technique, and presents a very promising avenue for exploring structure-based
denoising in the wavelet domain.},
doi = {10.1109/TIP.2005.849295},
file = {Bharath_A_2005_tip_ste_cwcaid.pdf:Bharath_A_2005_tip_ste_cwcaid.pdf:PDF},
pdf = {Bharath_A_2005_tip_ste_cwcaid.pdf},
timestamp = {2009.11.15}
}
@ARTICLE{Blu_T_1998_tsp_new_datborforw,
author = {Blu, T.},
title = {A new design algorithm for two-band orthonormal rational filterbanks
and orthonormal rational wavelets},
journal = j-ieee-tassp,
year = {1998},
volume = {46},
pages = {1494--1504},
number = {6},
month = {Jun.},
abstract = {Abstract We present a new algorithm for the design of orthonormal
two-band rational filter banks. Owing to the connection between iterated
rational filter banks and rational wavelets, this is also a design
algorithm for orthonormal rational wavelets. It is basically a simple
iterative procedure, which explains its exponential convergence and
adaptability under various linear constraints (e,g., regularity).
Although the filters obtained from this algorithm are suboptimally
designed, they show excellent frequency selectivity. After an in-depth
account of the algorithm, we discuss the properties of the rational
wavelets generated by some designed filters. In particular, we stress
the possibility to design ?almost? shift error-free wavelets, which
allows the implementation of a rational wavelet transform},
doi = {10.1109/78.678463},
file = {Blu_T_1998_tsp_new_datborforw.pdf:Blu_T_1998_tsp_new_datborforw.pdf:PDF},
owner = {duvall},
pdf = {Blu_T_1998_tsp_new_datborforw.pdf},
timestamp = {2008.01.09}
}
@ARTICLE{Blu_T_1993_tsp_ite_fbrccdwt,
author = {Blu, T.},
title = {Iterated filter banks with rational rate changes connection with
discrete wavelet transforms},
journal = j-ieee-tassp,
year = {1993},
volume = {41},
pages = {3232--3244},
number = {12},
month = {Dec.},
abstract = {Some properties of two-band filter banks with rational rate changes
(?rational filter banks?) are first reviewed. Focusing then on iterated
rational filter banks, compactly supported limit functions are obtained,
in the same manner as previously done for dyadic schemes, allowing
a characterization of such filter banks. These functions are carefully
studied and the properties they share with the dyadic case are highlighted.
They are experimentally observed to verify a ?shift property? (strictly
verified in the dyadic ease) up to an error which can be made arbitrarily
small when their regularity increases. In this case, the high-pass
outputs of an iterated filter bank can be very close to samples of
a discrete wavelet transform with the same rational dilation factor.
Straightforward extension of the formalism of multiresolution analysis
is also made. Finally, it is shown that if one is ready to put up
with the loss of the shift property, rational iterated filter banks
can be used in the same manner as if they were dyadic filter banks,
with the advantage that rational dilation factors can be chosen closer
to 1},
doi = {10.1109/78.258070},
file = {Blu_T_1993_tsp_ite_fbrccdwt.pdf:Blu_T_1993_tsp_ite_fbrccdwt.pdf:PDF},
owner = {duvall},
pdf = {Blu_T_1993_tsp_ite_fbrccdwt.pdf},
timestamp = {2008.01.09}
}
@INPROCEEDINGS{Blu_T_2000_icassp_fra_swtdi,
author = {Blu, T. and Unser, M.},
title = {The Fractional Spline Wavelet Transform: {D}efinition and Implementation},
booktitle = p-icassp,
year = {2000},
volume = {I},
pages = {512--515},
address = {Istanbul, Turkey},
month = {Jun. 5-9,},
abstract = {We define a new wavelet transform that is based on a recently defined
family of scaling functions: the fractional B-splines. The interest
of this family is that they interpolate between the integer degrees
of polynomial B-splines and that they allow a fractional order of
approximation. The orthogonal fractional spline wavelets essentially
behave as a fractional differentiators. This property seems promising
for the analysis of 1/f^aplha noise that can be whitened by an appropriate
choice of the degree of the spline transform. We present a practical
FFT-based algorithm for the implementation of these fractional wavelet
transforms, and give some examples of processing.},
file = {Blu_T_2000_icassp_fra_swtdi.pdf:Blu_T_2000_icassp_fra_swtdi.pdf:PDF},
owner = {duvall},
pdf = {Blu_T_2000_icassp_fra_swtdi.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Bogdanova_I_2005_j-acha_ste_wfs,
author = {Bogdanova, I. and Vandergheynst, P. and Antoine, J.-P. and Jacques,
L. and Morvidone, M.},
title = {Stereographic wavelet frames on the sphere},
journal = j-acha,
year = {2005},
volume = {19},
pages = {223--252},
number = {2},
month = {Sep.},
owner = {duvall},
timestamp = {2011.01.05}
}
@BOOK{Bracewell_R_1986_book_fou_ta,
title = {The {Fourier} transform and its applications},
publisher = {McGraw-Hill},
year = {1986},
author = {R. N. Bracewell},
address = {New York, NY},
edition = {2nd},
file = {Bracewell_R_1986_book_fou_ta.pdf:Bracewell_R_1986_book_fou_ta.pdf:PDF},
key = {dsp},
owner = {duvall},
pdf = {Bracewell_R_1986_book_fou_ta.pdf},
timestamp = {2009.07.20}
}
@ARTICLE{Bredies_K_2005_j-acha_mat_cms,
author = {Bredies, K. and Lorenz, D. A. and Maass, P.},
title = {Mathematical concepts of multiscale smoothing},
journal = j-acha,
year = {2005},
volume = {19},
pages = {141--161},
number = {2},
issn = {1063-5203},
abstract = {The starting point for this paper is the well-known equivalence between
convolution filtering with a rescaled Gaussian and the solution of
the heat equation. In the first sections we analyze the equivalence
between multiscale convolution filtering, linear smoothing methods
based on continuous wavelet transforms and the solutions of linear
diffusion equations. This means we determine a wavelet [psi], respectively
a convolution filter [phi], which is associated with a given linear
diffusion equation and vice versa. This approach has an extension
to non-linear smoothing techniques. The main result of this paper
is the derivation of a differential equation, whose solution is equivalent
to non-linear multiscale smoothing based on soft shrinkage methods
applied to Fourier or continuous wavelet transforms.},
doi = {DOI: 10.1016/j.acha.2005.02.007},
file = {Bredies_K_2005_j-acha_mat_cms.pdf:Bredies_K_2005_j-acha_mat_cms.pdf:PDF},
keywords = {Image smoothing,Multiscale methods,Wavelet transform,Evolution equations},
owner = {duvall},
pdf = {Bredies_K_2005_j-acha_mat_cms.pdf},
timestamp = {2010.08.28},
url = {http://www.sciencedirect.com/science/article/B6WB3-4G1PKMR-1/2/89406ed97397578cd8b8dada02c8f7af}
}
@BOOK{Breiman_L_1984_book_cla_rt,
title = {Classification and Regression Trees},
publisher = {Wadsworth},
year = {1984},
author = {Breiman, L. and Friedman, J. H. and Olshen, R. A. and Stone, C. J.},
address = {Belmont, CA, USA},
abstract = {The methodology used to construct tree structured rules is the focus
of this monograph. Unlike many other statistical procedures, which
moved from pencil and paper to calculators, this text's use of trees
was unthinkable before computers. Both the practical and theoretical
sides have been developed in the authors' study of tree methods.
Classification and Regression Trees reflects these two sides, covering
the use of trees as a data analysis method, and in a more mathematical
framework, proving some of their fundamental properties.},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Bresenham_J_1998_j-ibm-syst-j_alg_ccdp,
author = {Bresenham, J. E.},
title = {Algorithm for computer control of a digital plotter},
journal = {IBM Syst. J.},
year = {1965},
volume = {4},
pages = {25--30},
number = {1},
file = {Bresenham_J_1998_j-ibm-syst-j_alg_ccdp.pdf:Bresenham_J_1998_j-ibm-syst-j_alg_ccdp.pdf:PDF},
owner = {duvall},
pdf = {Bresenham_J_1998_j-ibm-syst-j_alg_ccdp.pdf},
timestamp = {2009.11.19}
}
@ARTICLE{Bruekers_F_1992_j-ieee-sel-areas-com,
author = {Bruekers, F. A. M. L. and van den Enden, A. W. M.},
title = {New networks for perfect inversion and perfect reconstruction},
journal = j-ieee-sel-areas-com,
year = {1992},
volume = {10},
pages = {129--137},
number = {1},
month = {Jan.},
issn = {0733-8716},
abstract = {The authors present a new network structure that realizes perfect
inversion networks (PINs) and perfect reconstruction networks (PRNs).
In some applications, such as transform source coders, it is important
that the cascade of the forward and the inverse transform give the
identity exactly (perfect inversion), although the coefficients and
the intermediate results are quantized. In subband coders, for example,
the split and merge filter banks should preferably have perfect reconstruction.
It is advantageous if perfect reconstruction can be accomplished
even when the coefficients and the intermediate results are quantized.
The proposed network has a ladderlike shape and a predescribed symmetry
between the forward and inverse network or between the split and
merge bank. In some parts of this ladder network almost any function
is allowed. Due to the prescribed symmetry, the property of perfect
inversion or perfect reconstruction is structurally assured},
doi = {10.1109/49.124464},
file = {Bruekers_F_1992_j-ieee-sel-areas-com.pdf:Bruekers_F_1992_j-ieee-sel-areas-com.pdf:PDF},
keywords = {filter coefficients;forward network;forward transform;inverse network;inverse
transform;ladder network;network structure;perfect inversion networks;perfect
reconstruction networks;split and merge filter banks;subband coders;transform
coding;transform source coders;digital filters;encoding;transforms;},
owner = {duvall},
pdf = {Bruekers_F_1992_j-ieee-sel-areas-com.pdf},
timestamp = {2010.02.24}
}
@BOOK{Bremaud_P_2002_book_mat_pspfwa,
title = {Mathematical principles of signal processing: {Fourier} and wavelet
analysis},
publisher = {Springer-Verlag},
year = {2002},
author = {Br{\'e}maud, P.},
address = {New York, USA},
owner = {duvall},
timestamp = {2007.06.07}
}
@ARTICLE{Burt_P_1983_tcom_lap_pcic,
author = {Burt, P. J. and Adelson, E. H.},
title = {The {Laplacian} Pyramid as a compact image code},
journal = j-ieee-tcom,
year = {1983},
volume = {31},
pages = {532--540},
number = {4},
month = {Apr.},
abstract = {We describe a technique for image encoding in which local operators
of many scales but identical shape serve as the basis functions.
The representation differs from established techniques in that the
code elements are localized in spatial frequency as well as in space.
Pixel-to-pixel correlations are first removed by subtracting a low-pass
filtered copy of the image from the image itself. The result is a
net data compression since the difference, or error, image has low
variance and entropy, and the low-pass filtered image may represented
at reduced sample density. Further data compression is achieved by
quantizing the difference image. These steps are then repeated to
compress the low-pass image iteration of the process at appropriately
expanded scales generates a pyramid data structure. The encoding
process is equivalent to sampling the image with Laplacian operators
of many scales. Thus, the code tends to enhance salient image features.
A further advantage of the present code is that it is well suited
for many image analysis tasks as well as for image compression. Fast
algorithms are described for coding and decoding.},
file = {Burt_P_1983_tcom_lap_pcic.pdf:Burt_P_1983_tcom_lap_pcic.pdf:PDF},
owner = {duvall},
pdf = {Burt_P_1983_tcom_lap_pcic.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Bulow_T_2002_p-dagm_mul_ips,
author = {B{\"u}low, T.},
title = {Multiscale image processing on the sphere},
booktitle = p-dagm,
year = {2002},
series = ser-lncs,
pages = {609--617},
publisher = {Springer},
file = {Bulow_T_2002_p-dagm_mul_ips.pdf:Bulow_T_2002_p-dagm_mul_ips.pdf:PDF},
owner = {duvall},
timestamp = {2011.01.05}
}
@ARTICLE{Bulow_T_2001_j-ieee-tsp_hyp_sneasmc,
author = {B{\"u}low, T. and Sommer, G.},
title = {Hypercomplex signals --- a novel extension of the analytic signal
to the multidimensional case},
journal = j-ieee-tsp,
year = {2001},
volume = {49},
pages = {2844--2852},
number = {11},
month = {Nov.},
issn = {1053-587X},
abstract = {The construction of Gabor's (1946) complex signal-which is also known
as the analytic signal-provides direct access to a real one-dimensional
(1-D) signal's local amplitude and phase. The complex signal is built
from a real signal by adding its Hilbert transform-which is a phase-shifted
version of the signal-as an imaginary part to the signal. Since its
introduction, the complex signal has become an important tool in
signal processing, with applications, for example, in narrowband
communication. Different approaches to an n-D analytic or complex
signal have been proposed in the past. We review these approaches
and propose the hypercomplex signal as a novel extension of the complex
signal to n-D. This extension leads to a new definition of local
phase, which reveals information on the intrinsic dimensionality
of the signal. The different approaches are unified by expressing
all of them as combinations of the signal and its partial and total
Hilbert transforms. Examples that clarify how the approaches differ
in their definitions of local phase and amplitude are shown. An example
is provided for the two-dimensional (2-D) hypercomplex signal, which
shows how the novel phase concept can be used in texture segmentation},
doi = {10.1109/78.960432},
file = {Bulow_T_2001_j-ieee-tsp_hyp_sneasmc.pdf:Bulow_T_2001_j-ieee-tsp_hyp_sneasmc.pdf:PDF},
keywords = {2D hypercomplex signals;Gabor's complex signal;Hilbert transform;analytic
signal;complex signal;multidimensional signal;narrowband communication;partial
Hilbert transform;real 1D signal local amplitude;real 1D signal local
phase;signal processing;texture segmentation;total Hilbert transform;Hilbert
transforms;image segmentation;image texture;multidimensional signal
processing;},
owner = {duvall},
pdf = {Bulow_T_2001_j-ieee-tsp_hyp_sneasmc.pdf},
timestamp = {2010.02.28}
}
@ARTICLE{Cai_T_1999_ann-stat_ada_webtoia,
author = {Cai, T.},
title = {Adaptive Wavelet Estimation: A Block Thresholding And Oracle Inequality
Approach},
journal = j-annals-statistics,
year = {1999},
volume = {27},
pages = {898--924},
abstract = {We study wavelet function estimation via the approach of block thresholding
and ideal adaptation with oracle. Oracle inequalities are derived
and serve as guides for the selection of smoothing parameters. Based
on an oracle inequality and motivated by the data compression and
localization properties of wavelets, an adaptive wavelet estimator
for nonparametric regression is proposed and the optimality of the
procedure is investigated. We show that the estimator achieves simultaneously
three objectives: adaptivity, spatial adaptivity, and computational
efficiency. Specifically, it is proved that the estimator attains
the exact optimal rates of convergence over a range of Besov classes
and the estimator achieves adaptive local minimax rate for estimating
functions at a point. The estimator is easy to implement, at the
computational cost of $O(n)$. Simulation shows that the estimator
has excellent numerical performance relative to more traditional
wavelet estimators.},
file = {Cai_T_1999_ann-stat_ada_webtoia.pdf:Cai_T_1999_ann-stat_ada_webtoia.pdf:PDF},
owner = {duvall},
pdf = {Cai_T_1999_ann-stat_ada_webtoia.pdf},
timestamp = {2007.10.05}
}
@ARTICLE{Candes_E_2004_j-comm-pure-appl-math_new_tfcoropc2s,
author = {E. J. Cand\`es and D. L. Donoho},
title = {New tight frames of curvelets and optimal representations of objects
with piecewise {$\text{C}^2$} singularities},
journal = j-comm-pure-appl-math,
year = {2004},
volume = {57},
pages = {219--266},
number = {2},
keywords = {Curvelet ; Fourier analysis ; Optimality condition ; Convergence rate
; Radon transformation ; Threshold ; Singularity ; Edge ; Wavelets
; Dyadic calculus ; Non linear approximation ; Approximation ;},
owner = {duvall},
timestamp = {2011.01.03}
}
@INPROCEEDINGS{Candes_E_2006_p-int-congress-math_com_s,
author = {E. J. Cand\`{e}s},
title = {Compressive sampling},
booktitle = {Proc. Int. Congr. Mathematicians},
year = {2006},
volume = {3},
pages = {1433--1452},
address = {Madrid, Spain},
abstract = {Conventional wisdom and common practice in acquisition and reconstruction
of
images from frequency data follow the basic principle of the Nyquist
density sampling theory.
This principle states that to reconstruct an image, the number of
Fourier samples we need to
acquire must match the desired resolution of the image, i.e. the number
of pixels in the image.
This paper surveys an emerging theory which goes by the name of ?compressive
sampling? or
?compressed sensing,? and which says that this conventional wisdom
is inaccurate. Perhaps
surprisingly, it is possible to reconstruct images or signals of scientific
interest accurately and
sometimes even exactly from a number of samples which is far smaller
than the desired resolution
of the image/signal, e.g. the number of pixels in the image.
It is believed that compressive sampling has far reaching implications.
For example, it
suggests the possibility of new data acquisition protocols that translate
analog information into
digital form with fewer sensors than what was considered necessary.
This new sampling theory
may come to underlie procedures for sampling and compressing data
simultaneously.
In this short survey, we provide some of the key mathematical insights
underlying this new
theory, and explain some of the interactions between compressive sampling
and other fields such
as statistics, information theory, coding theory, and theoretical
computer science.},
file = {Candes_E_2006_p-int-congress-math_com_s.pdf:Candes_E_2006_p-int-congress-math_com_s.pdf:PDF},
keywords = {Compressive sampling, sparsity, uniform uncertainty principle, underdertermined
systems of linear equations, $l_1$-minimization, linear programming,
signal recovery, error correction.},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Candes_E_2006_siam-mms_fas_dct,
author = {Cand{\`e}s, E. J. and Demanet, L. and Donoho, D. L. and Ying, L.},
title = {Fast discrete curvelet transforms},
journal = j-siam-mms,
year = {2006},
volume = {5},
pages = {861--899},
number = {3},
month = {Mar.},
abstract = {This paper describes two digital implementations of a new mathematical
transform, namely, the second generation curvelet transform in two
and three dimensions. The first digital transformation is based on
unequally spaced fast Fourier transforms, while the second is based
on the wrapping of specially selected Fourier samples. The two implementations
essentially differ by the choice of spatial grid used to translate
curvelets at each scale and angle. Both digital transformations return
a table of digital curvelet coefficients indexed by a scale parameter,
an orientation parameter, and a spatial location parameter. And both
implementations are fast in the sense that they run in O(n^2 \log
n) flops for n by n Cartesian arrays; in addition, they are also
invertible, with rapid inversion algorithms of about the same complexity.
Our digital transformations improve upon earlier implementations?based
upon the first generation of curvelets?in the sense that they are
conceptually simpler, faster, and far less redundant. The software
CurveLab, which implements both transforms presented in this paper,
is available at http://www.curvelet.org.},
doi = {10.1137/05064182X},
file = {Candes_E_2006_siam-mms_fas_dct.pdf:Candes_E_2006_siam-mms_fas_dct.pdf:PDF},
keywords = {two-dimensional and three-dimensional curvelet transforms; fast Fourier
transforms; unequally spaced fast Fourier transforms; smooth partitioning;
interpolation; digital shear; filtering; wrapping},
owner = {duvall},
pdf = {Candes_E_2006_siam-mms_fas_dct.pdf},
timestamp = {2007.06.07}
}
@INCOLLECTION{Candes_E_1999_curves-surfaces_cur_senroe,
author = {Cand{\`e}s, E. J. and Donoho, D. L.},
title = {Curvelets --- a surprisingly effective nonadaptive representation
for objects with edges},
booktitle = {Curves and Surfaces},
publisher = {Vanderbilt University Press},
year = {1999},
editor = {C. Rabut, A. Cohen and L. L. Schumaker},
pages = {105--120},
address = {Nashville, TN, USA},
abstract = {It is widely believed that to efficiently represent an otherwise smooth
object with discontinuities along edges, one must use an adaptive
representation that in some sense 'tracks' the shape of the discontinuity
set. This folk-belief --- some would say folk-theorem --- is incorrect.
At the very least, the possible quantitative advantage of such adaptation
is vastly smaller than commonly believed. We have recently constructed
a tight frame of curvelets which provides stable, efficient, and
near-optimal representation of otherwise smooth objects having discontinuities
along smooth curves. By applying naive thresholding to the curvelet
transform of such an object, one can form m-term approximations with
rate of L2 approximation rivaling the rate obtainable by complex
adaptive schemes which attempt to `track' the discontinuity set.
In this article we explain the basic issues of efficient m-term approximation,
the construction of efficient adaptive representation, the construction
of the curvelet frame, and a crude analysis of the performance of
curvelet schemes.},
file = {Candes_E_1999_curves-surfaces_cur_senroe.pdf:Candes_E_1999_curves-surfaces_cur_senroe.pdf:PDF},
owner = {duvall},
pdf = {Candes_E_1999_curves-surfaces_cur_senroe.pdf},
timestamp = {2007.06.15}
}
@ARTICLE{Candes_E_2003_j-acha_con_ct1rws,
author = {E. J. Cand{\`e}s and D. L. Donoho},
title = {Continuous curvelet transform: I. Resolution of the wavefront set},
journal = j-acha,
year = {2003},
volume = {19},
pages = {162--197},
file = {Candes_E_2003_j-acha_con_ct1rws.pdf:Candes_E_2003_j-acha_con_ct1rws.pdf:PDF},
owner = {duvall},
pdf = {Candes_E_2003_j-acha_con_ct1rws.pdf},
timestamp = {2010.02.21}
}
@ARTICLE{Candes_E_2003_j-acha_con_ct2df,
author = {E. J. Cand{\`e}s and D. L. Donoho},
title = {Continuous curvelet transform: {II}. Discretization and frames},
journal = j-acha,
year = {2003},
volume = {19},
pages = {198--222},
file = {Candes_E_2003_j-acha_con_ct2df.pdf:Candes_E_2003_j-acha_con_ct2df.pdf:PDF},
owner = {duvall},
pdf = {Candes_E_2003_j-acha_con_ct2df.pdf},
timestamp = {2010.02.21}
}
@ARTICLE{Candes_E_2003_j-comm-pure-appl-math_new_tfcoropc2s,
author = {Cand{\`e}s, E. J. and Donoho, D. L.},
title = {New tight frames of curvelets and optimal representations of objects
with piecewise $\mathcal{C}^2$ singularities},
journal = j-comm-pure-appl-math,
year = {2003},
volume = {57},
pages = {219--266},
number = {2},
abstract = {This paper introduces new tight frames of curvelets to address the
problem of finding optimally sparse representations of objects with
discontinuities along piecewise C2 edges. Conceptually, the curvelet
transform is a multiscale pyramid with many directions and positions
at each length scale, and needle-shaped elements at fine scales.
These elements have many useful geometric multiscale features that
set them apart from classical multiscale representations such as
wavelets. For instance, curvelets obey a parabolic scaling relation
which says that at scale 2-j, each element has an envelope that is
aligned along a ridge of length 2-j/2 and width 2-j. We prove that
curvelets provide an essentially optimal representation of typical
objects f that are C2 except for discontinuities along piecewise
C2 curves. Such representations are nearly as sparse as if f were
not singular and turn out to be far more sparse than the wavelet
decomposition of the object. For instance, the n-term partial reconstruction
fCn obtained by selecting the n largest terms in the curvelet series
obeys ?f - fCn?2L2 ? C . n-2 . (log n)3, n ? ?. This rate of convergence
holds uniformly over a class of functions that are C2 except for
discontinuities along piecewise C2 curves and is essentially optimal.
In comparison, the squared error of n-term wavelet approximations
only converges as n-1 as n ? ?, which is considerably worse than
the optimal behavior.},
file = {Candes_E_2003_j-comm-pure-appl-math_new_tfcoropc2s.pdf:Candes_E_2003_j-comm-pure-appl-math_new_tfcoropc2s.pdf:PDF},
keywords = {Curvelet ; Fourier analysis ; Optimality condition ; Convergence rate
; Radon transformation ; Threshold ; Singularity ; Edge ; Wavelets
; Dyadic calculus ; Non linear approximation ; Approximation ;},
owner = {duvall},
pdf = {Candes_E_2003_j-comm-pure-appl-math_new_tfcoropc2s.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Candes_E_1999_phil-trans-r-soc-lond_rid_khdi,
author = {Cand{\`e}s, E. J. and Donoho, D. L.},
title = {Ridgelets: a key to higher-dimensional intermittency?},
journal = {Phil. Trans. R. Soc. Lond. A},
year = {1999},
volume = {357},
pages = {2495--2509},
owner = {duvall},
timestamp = {2007.06.15}
}
@ARTICLE{Casazza_P_2000_tjm_art_ft,
author = {Casazza, P. G.},
title = {The art of frame theory},
journal = {Taiwanese J. of Math.},
year = {2000},
volume = {15},
pages = {129--201},
number = {4},
file = {Casazza_P_2000_tjm_art_ft.pdf:Casazza_P_2000_tjm_art_ft.pdf:PDF},
owner = {duvall},
pdf = {Casazza_P_2000_tjm_art_ft.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Cayon_L_2000_j-mon-not-roy-astron-soc_iso_wptepscmbm,
author = {Cay\'on, L. and Sanz, J. L. and Barreiro, R. B. and Mart\'inez-Gonz\'alez,
E. and Vielva, P. and Toffolatti, L. and Silk, J. and Diego, J. M.
and Arg\"ueso, F.},
title = {Isotropic wavelets: a powerful tool to extract point sources from
cosmic microwave background maps},
journal = j-mon-not-roy-astron-soc,
year = {2000},
volume = {315},
pages = {757--761},
number = {4},
month = {Jul.},
abstract = {It is the aim of this paper to introduce the use of isotropic wavelets
to detect and determine the flux of point sources appearing in cosmic
microwave background (CMB) maps. The most suitable wavelet to detect
point sources filtered with a Gaussian beam is the 'Mexican Hat'.
An analytical expression of the wavelet coefficient obtained in the
presence of a point source is provided and used in the detection
and flux estimation methods presented. For illustration the method
is applied to two simulations (assuming Planck mission characteristics)
dominated by CMB (100 GHz) and dust (857 GHz), as these will be the
two signals dominating at low and high frequencies respectively in
the Planck channels. We are able to detect bright sources above 1.58
Jy at 857 GHz (82 per cent of all sources) and above 0.36 Jy at 100
GHz (100 per cent of all), with errors in the flux estimation below
25 per cent. The main advantage of this method is that nothing has
to be assumed about the underlying field, i.e. about the nature and
properties of the signal plus noise present in the maps. This is
not the case in the detection method presented by Tegmark & Oliveira-Costa.
Both methods are compared, producing similar results.},
doi = {10.1046/j.1365-8711.2000.03462.x},
owner = {duvall},
timestamp = {2010.10.14},
url = {\url{http://dx.doi.org/10.1046/j.1365-8711.2000.03462.x}}
}
@ARTICLE{Chambolle_A_2001_j-ieee-tip_int_tiwsnisss,
author = {Chambolle, A. and Lucier, B. J.},
title = {Interpreting translation-invariant wavelet shrinkage as a new image
smoothing scale space},
journal = j-ieee-tip,
year = {2001},
volume = {10},
pages = {993--1000},
number = {7},
month = {Jul.},
issn = {1057-7149},
abstract = {Coifman and Donoho (1995) suggested translation-invariant wavelet
shrinkage as a way to remove noise from images. Basically, their
technique applies wavelet shrinkage to a two-dimensional (2-D) version
of the semi-discrete wavelet representation of Mallat and Zhong (1992),
Coifman and Donoho also showed how the method could be implemented
in O(Nlog N) operations, where there are N pixels. In this paper,
we provide a mathematical framework for iterated translation-invariant
wavelet shrinkage, and show, using a theorem of Kato and Masuda (1978),
that with orthogonal wavelets it is equivalent to gradient descent
in L 2(I) along the semi-norm for the Besov space B1 1(L1(I)), which,
in turn, can be interpreted as a new nonlinear wavelet-based image
smoothing scale space. Unlike many other scale spaces, the characterization
is not in terms of a nonlinear partial differential equation},
doi = {10.1109/83.931093},
file = {Chambolle_A_2001_j-ieee-tip_int_tiwsnisss.pdf:Chambolle_A_2001_j-ieee-tip_int_tiwsnisss.pdf:PDF},
keywords = {Besov space;image smoothing scale space;iterated translation-invariant
wavelet shrinkage;noise;nonlinear wavelet-based image smoothing scale
space;orthogonal wavelets;semi-discrete wavelet representation;semi-norm;translation-invariant
wavelet shrinkage;gradient methods;image representation;interference
suppression;noise;smoothing methods;wavelet transforms;},
owner = {duvall},
timestamp = {2010.11.24}
}
@INPROCEEDINGS{Chan_W_2004_icassp_dir_hwmsap,
author = {Chan, W. and Choi, H. and Baraniuk, R. G.},
title = {Directional hypercomplex wavelets for multidimensional signal analysis
and processing},
booktitle = p-icassp,
year = {2004},
volume = {3},
pages = {996--999},
month = {May},
abstract = {We extend the wavelet transform to handle multidimensional signals
that are smooth save for singularities along lower-dimensional manifolds.
We first generalize the complex wavelet transform to higher dimensions
using a multidimensional Hilbert transform. Then, using the resulting
hypercomplex wavelet transform (HWT) as a building block, we construct
new classes of nearly shift-invariant wavelet frames that are oriented
along lower-dimensional subspaces. The HWT can be computed efficiently
using a 1D dual-tree complex wavelet transform along each signal
axis. We demonstrate how the HWT can be used for fast line detection
in 3D.},
doi = {10.1109/ICASSP.2004.1326715},
file = {Chan_W_2004_icassp_dir_hwmsap.pdf:Chan_W_2004_icassp_dir_hwmsap.pdf:PDF},
owner = {duvall},
pdf = {Chan_W_2004_icassp_dir_hwmsap.pdf},
timestamp = {2007.06.05}
}
@ARTICLE{Chandrasekaran_V_2009_j-ieee-tit_rep_cmpfs,
author = {Chandrasekaran, V. and Wakin, M. B. and Baron, D. and Baraniuk, R.
G.},
title = {Representation and Compression of Multidimensional Piecewise Functions
Using Surflets},
journal = j-ieee-tit,
year = {2009},
volume = {55},
pages = {374--400},
number = {1},
month = {Jan.},
issn = {0018-9448},
abstract = {We study the representation, approximation, and compression of functions
in M dimensions that consist of constant or smooth regions separated
by smooth (M-1)-dimensional discontinuities. Examples include images
containing edges, video sequences of moving objects, and seismic
data containing geological horizons. For both function classes, we
derive the optimal asymptotic approximation and compression rates
based on Kolmogorov metric entropy. For piecewise constant functions,
we develop a multiresolution predictive coder that achieves the optimal
rate-distortion performance; for piecewise smooth functions, our
coder has near-optimal rate-distortion performance. Our coder for
piecewise constant functions employs surflets, a new multiscale geometric
tiling consisting of M-dimensional piecewise constant atoms containing
polynomial discontinuities. Our coder for piecewise smooth functions
uses surfprints, which wed surflets to wavelets for piecewise smooth
approximation. Both of these schemes achieve the optimal asymptotic
approximation performance. Key features of our algorithms are that
they carefully control the potential growth in surflet parameters
at higher smoothness and do not require explicit estimation of the
discontinuity. We also extend our results to the corresponding discrete
function spaces for sampled data. We provide asymptotic performance
results for both discrete function spaces and relate this asymptotic
performance to the sampling rate and smoothness orders of the underlying
functions and discontinuities. For approximation of discrete data,
we propose a new scale-adaptive dictionary that contains few elements
at coarse and fine scales, but many elements at medium scales. Simulation
results on synthetic signals provide a comparison between surflet-based
coders and previously studied approximation schemes based on wedgelets
and wavelets.},
doi = {10.1109/TIT.2008.2008153},
file = {Chandrasekaran_V_2009_j-ieee-tit_rep_cmpfs.pdf:Chandrasekaran_V_2009_j-ieee-tit_rep_cmpfs.pdf:PDF},
keywords = {asymptotic approximation;discrete data approximation;images edges;moving
objects;multidimensional piecewise functions compression;multidimensional
piecewise functions representation;multiresolution predictive coder;multiscale
geometric tiling;piecewise smooth approximation;piecewise smooth
functions;polynomial discontinuities;seismic data;video sequences;approximation
theory;data compression;polynomials;},
owner = {duvall},
timestamp = {2011.04.12}
}
@ARTICLE{Chang_C_2007_tip_dir_adwtic,
author = {C.-L. Chang and Girod, B.},
title = {Direction-Adaptive Discrete Wavelet Transform for Image Compression},
journal = j-ieee-tip,
year = {2007},
volume = {16},
pages = {1289--1302},
number = {5},
month = may,
issn = {1057-7149},
abstract = {We propose a direction-adaptive DWT (DA-DWT) that locally adapts the
filtering directions to image content based on directional lifting.
With the adaptive transform, energy compaction is improved for sharp
image features. A mathematical analysis based on an anisotropic statistical
image model is presented to quantify the theoretical gain achieved
by adapting the filtering directions. The analysis indicates that
the proposed DA-DWT is more effective than other lifting-based approaches.
Experimental results report a gain of up to 2.5 dB in PSNR over the
conventional DWT for typical test images. Subjectively, the reconstruction
from the DA-DWT better represents the structure in the image and
is visually more pleasing},
doi = {10.1109/TIP.2007.894242},
file = {Chang_C_2007_tip_dir_adwtic.pdf:Chang_C_2007_tip_dir_adwtic.pdf:PDF},
owner = {duvall},
pdf = {Chang_C_2007_tip_dir_adwtic.pdf},
timestamp = {2009.12.06}
}
@ARTICLE{Chappelier_V_2006_tip_ori_wticd,
author = {Chappelier, V. and Guillemot, C.},
title = {Oriented Wavelet Transform for Image Compression and Denoising},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {2892--2903},
number = {10},
month = {Oct.},
issn = {1057-7149},
abstract = {In this paper, we introduce a new transform for image processing,
based on wavelets and the lifting paradigm. The lifting steps of
a unidimensional wavelet are applied along a local orientation defined
on a quincunx sampling grid. To maximize energy compaction, the orientation
minimizing the prediction error is chosen adaptively. A fine-grained
multiscale analysis is provided by iterating the decomposition on
the low-frequency band. In the context of image compression, the
multiresolution orientation map is coded using a quad tree. The rate
allocation between the orientation map and wavelet coefficients is
jointly optimized in a rate-distortion sense. For image denoising,
a Markov model is used to extract the orientations from the noisy
image. As long as the map is sufficiently homogeneous, interesting
properties of the original wavelet are preserved such as regularity
and orthogonality. Perfect reconstruction is ensured by the reversibility
of the lifting scheme. The mutual information between the wavelet
coefficients is studied and compared to the one observed with a separable
wavelet transform. The rate-distortion performance of this new transform
is evaluated for image coding using state-of-the-art subband coders.
Its performance in a denoising application is also assessed against
the performance obtained with other transforms or denoising methods},
doi = {10.1109/TIP.2006.877526},
file = {Chappelier_V_2006_tip_ori_wticd.pdf:Chappelier_V_2006_tip_ori_wticd.pdf:PDF},
keywords = {Markov processes, data compression, image coding, image denoising,
image reconstruction, image resolution, image sampling, transform
coding, tree codes, wavelet transforms},
owner = {duvall},
pdf = {Chappelier_V_2006_tip_ori_wticd.pdf},
timestamp = {2009.12.06}
}
@ARTICLE{Chaudhury_K_2010_j-ieee-tsp_shi_dtcwt,
author = {K. N. Chaudhury and M. Unser},
title = {On the Shiftability of Dual-Tree Complex Wavelet Transforms},
journal = j-ieee-tsp,
year = {2010},
volume = {58},
pages = {221--232},
number = {1},
month = {Jan.},
abstract = {The dual-tree complex wavelet transform (DT-CWT) is known to exhibit
better shift-invariance than the conventional discrete wavelet transform.
We propose an amplitude-phase representation of the DT-CWT which,
among other things, offers a direct explanation for the improvement
in the shift-invariance. The representation is based on the shifting
action of the group of fractional Hilbert transform (fHT) operators,
which extends the notion of arbitrary phase-shifts from sinusoids
to finite-energy signals (wavelets in particular). In particular,
we characterize the shiftability of the DT-CWT in terms of the shifting
property of the fHTs. At the heart of the representation are certain
fundamental invariances of the fHT group, namely that of translation,
dilation, and norm, which play a decisive role in establishing the
key properties of the transform. It turns out that these fundamental
invariances are exclusive to this group. Next, by introducing a generalization
of the Bedrosian theorem for the fHT operator, we derive an explicitly
understanding of the shifting action of the fHT for the particular
family of wavelets obtained through the modulation of lowpass functions
(e.g., the Shannon and Gabor wavelet). This, in effect, links the
corresponding dual-tree transform with the framework of windowed-Fourier
analysis. Finally, we extend these ideas to the multidimensional
setting by introducing a directional extension of the fHT, the fractional
directional Hilbert transform. In particular, we derive a signal
representation involving the superposition of direction-selective
wavelets with appropriate phase-shifts, which helps explain the improved
shift-invariance of the transform along certain preferential directions.},
file = {Chaudhury_K_2010_j-ieee-tsp_shi_dtcwt.pdf:Chaudhury_K_2010_j-ieee-tsp_shi_dtcwt.pdf:PDF},
owner = {duvall},
pdf = {Chaudhury_K_2010_j-ieee-tsp_shi_dtcwt.pdf},
timestamp = {2010.02.27}
}
@ARTICLE{Chaudhury_K_2009_j-ieee-tsp_con_htpwbglt,
author = {Chaudhury, K. N. and Unser, M.},
title = {Construction of {Hilbert} Transform Pairs of Wavelet Bases and {Gabor}-Like
Transforms},
journal = j-ieee-tsp,
year = {2009},
volume = {57},
pages = {3411--3425},
number = {9},
month = {Sep.},
abstract = {We propose a novel method for constructing Hilbert transform (HT)
pairs of wavelet bases based on a fundamental approximation-theoretic
characterization of scaling functions?the B-spline factorization
theorem. In particular, starting from well-localized scaling functions,
we construct HT pairs of biorthogonal wavelet bases of L2(?) by relating
the corresponding wavelet filters via a discrete form of the continuous
HT filter. As a concrete application of this methodology, we identify
HT pairs of spline wavelets of a specific flavor, which are then
combined to realize a family of complex wavelets that resemble the
optimally-localized Gabor function for sufficiently large orders.
Analytic wavelets, derived from the complexification of HT wavelet
pairs, exhibit a one-sided spectrum. Based on the tensor-product
of such analytic wavelets, and, in effect, by appropriately combining
four separable biorthogonal wavelet bases of L2(?2), we then discuss
a methodology for constructing 2D directional-selective complex wavelets.
In particular, analogous to the HT correspondence between the components
of the 1D counterpart, we relate the real and imaginary components
of these complex wavelets using a multi-dimensional extension of
the HT?the directional HT. Next, we construct a family of complex
spline wavelets that resemble the directional Gabor functions proposed
by Daugman. Finally, we present an efficient FFT-based filterbank
algorithm for implementing the associated complex wavelet transform.},
file = {Chaudhury_K_2009_j-ieee-tsp_con_htpwbglt.pdf:Chaudhury_K_2009_j-ieee-tsp_con_htpwbglt.pdf:PDF},
owner = {duvall},
pdf = {Chaudhury_K_2009_j-ieee-tsp_con_htpwbglt.pdf},
timestamp = {2009.07.20}
}
@INPROCEEDINGS{Chaudhury_K_2009_p-spie-wasip_gab_wafht,
author = {Chaudhury, K. N. and Unser, M.},
title = {{G}abor Wavelet Analysis and the Fractional {H}ilbert Transform},
booktitle = p-spie-wasip,
year = {2009},
volume = {7446},
pages = {74460T-1--74460T-7},
address = {San Diego CA, USA},
month = {Aug. 2-6,},
abstract = {We propose an amplitude-phase representation of the dual-tree complex
wavelet transform (DT-CWT) which provides an intuitive interpretation
of the associated complex wavelet coefficients. The representation,
in particular, is based on the shifting action of the group of fractional
Hilbert transforms (fHT) which allow us to extend the notion of arbitrary
phase-shifts beyond pure sinusoids. We explicitly characterize this
shifting action for a particular family of Gabor-like wavelets which,
in effect, links the corresponding dual-tree transform with the framework
of windowed-Fourier analysis. We then extend these ideas to the bivariate
DT-CWT based on certain directional extensions of the fHT. In particular,
we derive a signal representation involving the superposition of
direction-selective wavelets affected with appropriate phase-shifts.},
timestamp = {2011.01.07}
}
@ARTICLE{Chaux_C_2008_j-ieee-tsp_non_sbemid,
author = {Chaux, C. and Duval, L. and Benazza-Benyahia, A. and Pesquet, J.-C.},
title = {A nonlinear {Stein} based estimator for multichannel image denoising},
journal = j-ieee-tsp,
year = {2008},
volume = {56},
pages = {3855--3870},
number = {8},
month = {Aug.},
issn = {1053-587X},
abstract = {The use of multicomponent images has become widespread with the improvement
of multisensor systems having increased spatial and spectral resolutions.
However, the observed images are often corrupted by an additive Gaussian
noise. In this paper, we are interested in multichannel image denoising
based on a multiscale representation of the images. A multivariate
statistical approach is adopted to take into account both the spatial
and the inter-component correlations existing between the different
wavelet subbands. More precisely, we propose a new parametric nonlinear
estimator which generalizes many reported denoising methods. The
derivation of the optimal parameters is achieved by applying Stein's
principle in the multivariate case. Experiments performed on multispectral
remote sensing images clearly indicate that our method outperforms
conventional wavelet denoising techniques},
doi = {10.1109/TSP.2008.921757},
owner = {duvall},
timestamp = {2006.10.26}
}
@ARTICLE{Chaux_C_2006_tip_ima_adtmbwt,
author = {Chaux, C. and Duval, L. and Pesquet, J.-C.},
title = {Image analysis using a dual-tree ${M}$-band wavelet transform},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {2397--2412},
number = {8},
month = {Aug.},
owner = {duvall},
timestamp = {2006.04.27}
}
@ARTICLE{Chen_S_1998_j-siam-sci-comp_ato_dbp,
author = {S. S. Chen and D. L. Donoho and M. A. Saunders},
title = {Atomic Decomposition by Basis Pursuit},
journal = j-siam-sci-comp,
year = {1998},
volume = {20},
pages = {33--61},
number = {1},
abstract = {The time-frequency and time-scale communities have recently developed
a large number of overcomplete waveform dictionaries --- stationary
wavelets, wavelet packets, cosine packets, chirplets, and warplets,
to name a few. Decomposition into overcomplete systems is not unique,
and several methods for decomposition have been proposed, including
the method of frames (MOF), Matching pursuit (MP), and, for special
dictionaries, the best orthogonal basis (BOB). Basis Pursuit (BP)
is a principle for decomposing a signal into an "optimal" superposition
of dictionary elements, where optimal means having the smallest l1
norm of coefficients among all such decompositions. We give examples
exhibiting several advantages over MOF, MP, and BOB, including better
sparsity and superresolution. BP has interesting relations to ideas
in areas as diverse as ill-posed problems, in abstract harmonic analysis,
total variation denoising, and multiscale edge denoising. BP in highly
overcomplete dictionaries leads to large-scale optimization problems.
With signals of length 8192 and a wavelet packet dictionary, one
gets an equivalent linear program of size 8192 by 212,992. Such problems
can be attacked successfully only because of recent advances in linear
programming by interior-point methods. We obtain reasonable success
with a primal-dual logarithmic barrier method and conjugate-gradient
solver.},
file = {Chen_S_1998_j-siam-sci-comp_ato_dbp.pdf:Chen_S_1998_j-siam-sci-comp_ato_dbp.pdf:PDF},
keywords = {overcomplete signal representation, interior-point methods for linear
programming, total variation denoising, multiscale edges, denoising,
time-frequency analysis, time-scale analysis, $\ell^1$ norm optimization,
matching pursuit, wavelets, wavelet packets, cosine packets,; interior-point
methods for linear programming; total variation denoising; multiscale
edges},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Christensen_O_2001_j-bull-amer-math-soc_fra_rbdgwe,
author = {O. Christensen},
title = {Frames, {Riesz} bases, and discrete {Gabor}/wavelet expansions},
journal = j-bull-amer-math-soc,
year = {2001},
volume = {38},
pages = {273--291},
abstract = {This paper is a survey of research in discrete expansions over the
last 10 years, mainly of functions in $L^2(\mathbb R)$. The concept
of an orthonormal basis $\{f_n\}$, allowing every function $f \in
L^2(\mathbb R)$ to be written $f=\sum c_nf_n$for suitable coefficients
$\{c_n\}$, is well understood. In separable Hilbert spaces, a generalization
known as frames exists, which still allows such a representation.
However, the coefficients $\{c_n\}$ are not necessarily unique. We
discuss the relationship between frames and Riesz bases, a subject
where several new results have been proved over the last 10 years.
Another central topic is the study of frames with additional structure,
most important Gabor frames (consisting of modulated and translated
versions of a single function) and wavelets (translated and dilated
versions of one function). Along the way, we discuss some possible
directions for future research.},
file = {Christensen_O_2001_j-bull-amer-math-soc_fra_rbdgwe.pdf:Christensen_O_2001_j-bull-amer-math-soc_fra_rbdgwe.pdf:PDF},
owner = {duvall},
pdf = {Christensen_O_2001_j-bull-amer-math-soc_fra_rbdgwe.pdf},
timestamp = {2010.02.13}
}
@ARTICLE{Chui_C_2002_p-acha_com_stsfmvm,
author = {C. K. Chui and W. He and J. St\"ockler},
title = {Compactly supported tight and sibling frames with maximum vanishing
moments},
journal = j-acha,
year = {2002},
volume = {13},
pages = {224--262},
number = {3},
issn = {1063-5203},
abstract = {The notion of vanishing-moment recovery (VMR) functions is introduced
in this paper for the construction of compactly supported tight frames
with two generators having the maximum order of vanishing moments
as determined by the given refinable function, such as the mth order
cardinal B-spline Nm. Tight frames are also extended to #sibling##frames#
to allow additional properties, such as symmetry (or antisymmetry),
minimum support, shift-invariance, and inter-orthogonality. For Nm,
it turns out that symmetry can be achieved for even m and antisymmetry
for odd m, that minimum support and shift-invariance can be attained
by considering the frame generators with two-scale symbols 2-m(1-z)m
and 2-mz(1-z)m, and that inter-orthogonality is always achievable,
but sometimes at the sacrifice of symmetry. The results in this paper
are valid for all compactly supported refinable functions that are
reasonably smooth, such as piecewise Lip[alpha] for some [alpha]>0,
as long as the corresponding two-scale Laurent polynomial symbols
vanish at z=-1. Furthermore, the methods developed here can be extended
to the more general setting, such as arbitrary integer scaling factors,
multi-wavelets, and certainly biframes (i.e., allowing the dual frames
to be associated with a different refinable function).},
doi = {DOI: 10.1016/S1063-5203(02)00510-9},
file = {Chui_C_2002_p-acha_com_stsfmvm.pdf:Chui_C_2002_p-acha_com_stsfmvm.pdf:PDF},
keywords = {Sibling frame; Tight frame; Unitary extension; Vanishing moment recovery;
Inter-orthogonality; Matrix factorization},
owner = {duvall},
timestamp = {2011.03.27},
url = {http://www.sciencedirect.com/science/article/B6WB3-474DMCF-6/2/db9dc4c2133b1959e78efa4e3db881ff}
}
@ARTICLE{Claypoole_R_2003_tip_non_wticl,
author = {Claypoole, R. L. and Davis, G. M. and Sweldens, W. and Baraniuk,
R. G.},
title = {Nonlinear wavelet transforms for image coding via lifting},
journal = j-ieee-tip,
year = {2003},
volume = {12},
pages = {1449--1459},
number = {12},
month = {Dec.},
issn = {1057-7149},
abstract = {We investigate central issues such as invertibility, stability, synchronization,
and frequency characteristics for nonlinear wavelet transforms built
using the lifting framework. The nonlinearity comes from adaptively
choosing between a class of linear predictors within the lifting
framework. We also describe how earlier families of nonlinear filter
banks can be extended through the use of prediction functions operating
on a causal neighborhood of pixels. Preliminary compression results
for model and real-world images demonstrate the promise of our techniques.},
doi = {10.1109/TIP.2003.817237},
file = {Claypoole_R_2003_tip_non_wticl.pdf:Claypoole_R_2003_tip_non_wticl.pdf:PDF},
keywords = {adaptive signal processing, channel bank filters, data compression,
image coding, nonlinear filters, prediction theory, synchronisation,
transform coding, wavelet transforms},
owner = {duvall},
pdf = {Claypoole_R_2003_tip_non_wticl.pdf},
timestamp = {2009.10.14}
}
@ARTICLE{Clonda_D_2004_sp_com_dwpsim,
author = {Clonda, D. and Lina, J.-M. and Goulard, B.},
title = {Complex {Daubechies} wavelets: properties and statistical image modelling},
journal = j-sp,
year = {2004},
volume = {84},
pages = {1--23},
number = {1},
month = {Jan.},
abstract = {This article presents the construction and various properties of complex
Daubechies wavelets with a special emphasis on symmetric solutions.
Such solutions exhibit interesting relationships between the real
and imaginary components of the complex scaling function and the
complex wavelet. We present those properties in the context of image
processing. Within the framework of statistical modelling, we focus
on the redundant description of real images given by the complex
multiresolution representation. A hierarchical Markovian Graphical
model is then explored. We present an Expectation Maximization algorithm
for optimizing the model with observational complex wavelet data.
This model is then applied to image estimation and texture classification.
In both applications, we demonstrate the benefit brought by the Markovian
hypothesis and the performance of the real images's complex multiscale
representation.},
file = {Clonda_D_2004_sp_com_dwpsim.pdf:Clonda_D_2004_sp_com_dwpsim.pdf:PDF},
owner = {duvall},
pdf = {Clonda_D_2004_sp_com_dwpsim.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Cohen_A_1992_j-comm-acm_bio_bcsw,
author = {Cohen, A. and Daubechies, I. and Feauveau, J.-C.},
title = {Biorthogonal bases of compactly supported wavelets},
journal = j-comm-acm,
year = {1992},
volume = {45},
pages = {485--560},
number = {5},
abstract = {Orthonormal bases of compactly supported wavelet bases correspond
to subband coding schemes with exact reconstruction in which the
analysis and synthesis filters coincide. We show here that under
fairly general conditions, exact reconstruction schemes with synthesis
filters different from the analysis filters give rise to two dual
Riesz bases of compactly supported wavelets. We give necessary and
sufficient conditions for biorthogonality of the corresponding scaling
functions, and we present a sufficient conditions for the decay of
their Fourier transforms. We study the regularity of these biorthogonal
bases. We provide several families of examples, all symmetric (corresponding
to ldquolinear phaserdquo filters). In particular we can construct
symmetric biorthogonal wavelet bases with arbitraily high preassigned
regularity; we also show how to construct symmetric biorthogonal
wavelet bases ldquocloserdquo to a (nonsymmetric) orthonormal basis.},
doi = {10.1002/cpa.3160450502},
owner = {duvall},
timestamp = {2007.06.15}
}
@INCOLLECTION{Cohen_A_1998_incoll_non_ssmawp,
author = {A. Cohen and N. Dyn},
title = {Nonstationary subdivision schemes, multiresolution analysis, and
wavelet packets},
booktitle = {Signal and image representation in combined spaces},
publisher = {Academic Press},
year = {1998},
editor = {Y. Zeevi and R. Coifman},
volume = {7},
series = {Wavelet analysis and its applications},
pages = {189--200},
abstract = {Nonstationary subdivision schemes consist of recursive refinements
of an initial sparse sequence with the use of masks that may vary
from one scale to the next finer one. We show that such schemes can
be used to construct C[infinity] compactly supported orthonormal
scaling functions, wavelets, and wavelet-packets with better control
on the frequency localization.},
doi = {DOI: 10.1016/S1874-608X(98)80008-3},
issn = {1874-608X},
owner = {duvall},
timestamp = {2011.01.07},
url = {http://www.sciencedirect.com/science/article/B8H44-4NVH5KF-8/2/5db5af84ac9c81a4c62f218ff48996e2}
}
@ARTICLE{Cohen_A_2011_PREPRINT_ada_mabat,
author = {A. Cohen and N. Dyn and F. Hecht and J.-M. Mirebeau},
title = {Adaptive multiresolution analysis based on anisotropic triangulations},
journal = j-math-comput,
year = {2011},
note = {Preprint, submitted, \url{http://arxiv.org/abs/1101.1512}},
abstract = {A simple greedy refinement procedure for the generation of data-adapted
triangulations is proposed and studied. Given a function of two variables,
the algorithm produces a hierarchy of triangulations and piecewise
polynomial approximations on these triangulations. The refinement
procedure consists in bisecting a triangle T in a direction which
is chosen so as to minimize the local approximation error in some
prescribed norm between the approximated function and its piecewise
polynomial approximation after T is bisected.
The hierarchical structure allows us to derive various approximation
tools such as multiresolution analysis, wavelet bases, adaptive triangulations
based either on greedy or optimal CART trees, as well as a simple
encoding of the corresponding triangulations. We give a general proof
of convergence in the Lp norm of all these approximations.
Numerical tests performed in the case of piecewise linear approximation
of functions with analytic expressions or of numerical images illustrate
the fact that the refinement procedure generates triangles with an
optimal aspect ratio (which is dictated by the local Hessian of of
the approximated function in case of C2 functions).},
file = {Cohen_A_2011_PREPRINT_ada_mabat.pdf:Cohen_A_2011_PREPRINT_ada_mabat.pdf:PDF},
owner = {duvall},
pdf = {Cohen_A_2010_j-math-comput_ada_mabat.pdf},
timestamp = {2010.02.16}
}
@INCOLLECTION{Cohen_A_2002_inbook_non-ssaip,
author = {A. Cohen and B. Matei},
title = {Nonlinear subdivision schemes: applications to image processing},
booktitle = {Tutorials on Multiresolution in Geometric Modelling},
publisher = {Springer Verlag},
year = {2002},
editor = {A. Iske and E. Quak and Floater, M. S.},
pages = {93--97},
address = {Munich Univ. Technol., Germany},
note = {Europ. summer school on principles of multiresolution in geometric
modelling},
abstract = {The authors discuss some refinement rules for subdivision subschemes,
which are of interest because of their relation to multiresolution
analysis and wavelets bases, making them suitable for signal, hence
image, processing. The refinements include linear refinement by polynomial
reconstruction, nonlinear refinement by essentially non-oscillatory
stencil selection, and nonlinear refinement by using stencil selection
and subcell resolution.},
file = {Cohen_A_2002_inbook_non-ssaip.pdf:Cohen_A_2002_inbook_non-ssaip.pdf:PDF},
keywords = {image processing; subdivision subschemes; wavelets; linear refinement;
nonlinear refinement; stencil selection; subcell resolution},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Cohen_A_1999_j-am-j-math_non_lasbvr2,
author = {Cohen, A. and de Vore, R. and Petrushev, P. and Xu, H.},
title = {Non linear approximation and the space ${BV}(\mathbb{R}^2)$},
journal = j-am-j-math,
year = {1999},
volume = {121},
pages = {587--628},
owner = {duvall},
timestamp = {2010.01.12}
}
@ARTICLE{Cohen_I_1997_j-sp_ort_sialtd,
author = {I. Cohen and S. Raz and D. Malah},
title = {Orthonormal shift-invariant adaptive local trigonometric decomposition},
journal = j-sp,
year = {1997},
volume = {57},
pages = {43--64},
number = {1},
issn = {0165-1684},
abstract = {In this paper, an extended library of smooth local trigonometric bases
is defined, and an appropriate fast #best-basis# search algorithm
is introduced. When compared with the standard local cosine decomposition
(LCD), the proposed algorithm is advantageous in three respects.
First, it leads to a best-basis expansion that is shift-invariant.
Second, the resulting representation is characterized by a lower
information cost. Third, the polarity of the folding operator is
adapted to the parity properties of the segmented signal at the end-points.
The shift invariance stems from an adaptive relative shift of expansions
in distinct resolution levels. We show that at any resolution level
l it suffices to examine and select one of two relative shift options
-- a zero shift or a 2-l-1 shift. A variable folding operator, whose
polarity is locally adapted to the parity properties of the signal,
further enhances the representation. The computational complexity
is manageable and comparable to that of the LCD.},
doi = {DOI: 10.1016/S0165-1684(96)00185-5},
file = {Cohen_I_1997_j-sp_ort_sialtd.pdf:Cohen_I_1997_j-sp_ort_sialtd.pdf:PDF},
keywords = {Shift-invariant; Best-basis; Time frequency; Lapped transform; Algorithm},
owner = {duvall},
timestamp = {2011.04.08},
url = {http://www.sciencedirect.com/science/article/B6V18-3SNV3JD-J/2/2e2fae13ff56a03e02d2aecad76a61b2}
}
@INCOLLECTION{Coifman_R_1995_was_tra_id,
author = {Coifman, R. and Donoho, D.},
title = {Translation-invariant de-noising},
booktitle = {Wavelets and Statistics},
publisher = {Springer},
year = {1995},
editor = {Antoniadis, A. and Oppenheim, G.},
volume = {103},
series = {Lecture Notes in Statistics},
pages = {125--150},
address = {New York, NY, USA},
owner = {duvall},
timestamp = {2007.11.06}
}
@ARTICLE{Coifman_R_2006_j-acha_diff_w,
author = {Coifman, R. R. and Maggioni, M.},
title = {Diffusion wavelets},
journal = j-acha,
year = {2006},
volume = {21},
pages = {53--94},
number = {1},
issn = {1063-5203},
abstract = {Our goal in this paper is to show that many of the tools of signal
processing, adapted Fourier and wavelet analysis can be naturally
lifted to the setting of digital data clouds, graphs, and manifolds.
We use diffusion as a smoothing and scaling tool to enable coarse
graining and multiscale analysis. Given a diffusion operator T on
a manifold or a graph, with large powers of low rank, we present
a general multiresolution construction for efficiently computing,
representing and compressing Tt. This allows a direct multiscale
computation, to high precision, of functions of the operator, notably
the associated Green's function, in compressed form, and their fast
application. Classes of operators for which these computations are
fast include certain diffusion-like operators, in any dimension,
on manifolds, graphs, and in non-homogeneous media. We use ideas
related to the Fast Multipole Methods and to the wavelet analysis
of Calderón-Zygmund and pseudo-differential operators, to numerically
enforce the emergence of a natural hierarchical coarse graining of
a manifold, graph or data set. For example for a body of text documents
the construction leads to a directory structure at different levels
of generalization. The dyadic powers of an operator can be used to
induce a multiresolution analysis, as in classical Littlewood-Paley
and wavelet theory: we construct, with efficient and stable algorithms,
bases of orthonormal scaling functions and wavelets associated to
this multiresolution analysis, together with the corresponding downsampling
operators, and use them to compress the corresponding powers of the
operator. While most of our discussion deals with symmetric operators
and relates to localization to spectral bands, the symmetry of the
operators and their spectral theory need not be considered, as the
main assumption is reduction of the numerical ranks as we take powers
of the operator.},
doi = {DOI: 10.1016/j.acha.2006.04.004},
file = {Coifman_R_2006_j-acha_diff_w.pdf:Coifman_R_2006_j-acha_diff_w.pdf:PDF},
keywords = {Multiresolution; Multiscale analysis; Wavelets; Wavelets on manifolds;
Wavelets on graphs; Diffusion semigroups; Laplace?Beltrami operator;
Fast Multipole Method; Matrix compression; Spectral graph theory},
owner = {duvall},
timestamp = {2011.04.08},
url = {http://www.sciencedirect.com/science/article/B6WB3-4K4PSX2-2/2/383131de381044772c31895fa7488ce3}
}
@ARTICLE{Coifman_R_1992_tit_ent_babbs,
author = {Coifman, R. R. and Wickerhauser, M. V.},
title = {Entropy-based algorithms for best-basis selection},
journal = j-ieee-tit,
year = {1992},
volume = {38},
pages = {713--718},
number = {2},
month = {Mar.},
file = {Coifman_R_1992_tit_ent_babbs.pdf:Coifman_R_1992_tit_ent_babbs.pdf:PDF},
owner = {duvall},
pdf = {Coifman_R_1992_tit_ent_babbs.pdf},
timestamp = {2007.06.07}
}
@INCOLLECTION{Combettes_P_2010_incoll_pro_smsp,
author = {Combettes, P. L. and Pesquet, J.-C.},
title = {Proximal splitting methods in signal processing},
booktitle = {Fixed-point algorithms for inverse problems in science and engineering},
publisher = {Springer Verlag},
year = {2010},
editor = {H. H. Bauschke and R. Burachik and P. L. Combettes and V. Elser and
D. R. Luke and H. Wolkowicz},
abstract = {The proximity operator of a convex function is a natural extension
of the notion of a projection operator onto a convex set. This tool,
which plays a central role in the analysis and the numerical solution
of convex optimization problems, has recently been introduced in
the arena of inverse problems and, especially, in signal processing,
where it has become increasingly important. In this paper, we review
the basic properties of proximity operators which are relevant to
signal processing and present optimization methods based on these
operators. These proximal splitting methods are shown to capture
and extend several well-known algorithms in a unify- ing framework.
Applications of proximal methods in signal recovery and synthesis
are discussed.},
file = {Combettes_P_2010_incoll_pro_smsp.pdf:Combettes_P_2010_incoll_pro_smsp.pdf:PDF},
keywords = {Alternating-direction method of multipliers, backward-backward al-
gorithm, convex optimization, denoising, Douglas-Rachford algorithm,
forward- backward algorithm, frame, Landweber method, iterative thresholding,
parallel computing, Peaceman-Rachford algorithm, proximal algorithm,
restoration and re- construction, sparsity, splitting.},
owner = {duvall},
timestamp = {2010.11.11}
}
@ARTICLE{Combettes_P_2005_siam-mms_sig_rpfbs,
author = {Combettes, P. L. and Wajs, V. R.},
title = {Signal recovery by proximal forward-backward splitting},
journal = j-siam-mms,
year = {2005},
volume = {4},
pages = {1168--1200},
number = {4},
month = {Nov.},
abstract = {We show that various inverse problems in signal recovery can be formulated
as the generic problem of minimizing the sum of two convex functions
with certain regularity properties. This formulation makes it possible
to derive existence, uniqueness, characterization, and stability
results in a unified and standardized fashion for a large class of
apparently disparate problems. Recent results on monotone operator
splitting methods are applied to establish the convergence of a forward-backward
algorithm to solve the generic problem. In turn, we recover, extend,
and provide a simplified analysis for a variety of existing iterative
methods. Applications to geometry/texture image decomposition schemes
are also discussed. A novelty of our framework is to use extensively
the notion of a proximity operator, which was introduced by Moreau
in the 1960s.},
file = {Combettes_P_2005_siam-mms_sig_rpfbs.pdf:Combettes_P_2005_siam-mms_sig_rpfbs.pdf:PDF},
owner = {duvall},
pdf = {Combettes_P_2005_siam-mms_sig_rpfbs.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Coulombe_S_1996_p-icassp_mul_walafirfd,
author = {Coulombe, S. and Dubois, E.},
title = {Multidimensional windows over arbitrary lattices and their application
to {FIR} filter design},
booktitle = p-icassp,
year = {1996},
volume = {4},
pages = {2383--2386},
address = {Atlanta, GA, USA},
month = may,
abstract = {This paper presents some applications to FIR filter design of multi-D
windows over arbitrary lattices and with arbitrary center of spatial
symmetry. First, classic windows (such as Hamming, Blackman, etc.)
are extended to windows over 1D and multi-D lattices with arbitrary
spatial symmetry centers (which multirate applications sometimes
require). Then the problem of obtaining a target frequency response
with a good transition band from an ideal frequency response (made
of a passband having constant gain and a stopband for which the gain
is zero) is studied. A method to obtain a described target response
using multi-D windows with application to the design of FIR filters
is presented. Finally, a procedure for designing multi-D FIR filters
by windowing is explained},
doi = {10.1109/ICASSP.1996.547762},
file = {Coulombe_S_1996_p-icassp_mul_walafirfd.pdf:Coulombe_S_1996_p-icassp_mul_walafirfd.pdf:PDF},
keywords = {FIR filters, band-pass filters, band-stop filters, frequency response,
lattice filters, multidimensional digital filters},
owner = {duvall},
pdf = {Coulombe_S_1996_p-icassp_mul_walafirfd.pdf},
timestamp = {2009.12.06}
}
@ARTICLE{Cunha_A_2006_tip_non_cttda,
author = {Cunha, A. L. and Zhou, J. and Do, M. N.},
title = {The nonsubsampled contourlet transform: theory, design, and applications},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {3089--3101},
number = {10},
month = {Oct.},
abstract = {In this paper, we develop the nonsubsampled contourlet transform (NSCT)
and study its applications. The construction proposed in this paper
is based on a nonsubsampled pyramid structure and nonsubsampled directional
filter banks. The result is a flexible multiscale, multidirection,
and shift-invariant image decomposition that can be efficiently implemented
via the \`a trous algorithm. At the core of the proposed scheme is
the nonseparable two-channel nonsubsampled filter bank (NSFB). We
exploit the less stringent design condition of the NSFB to design
filters that lead to a NSCT with better frequency selectivity and
regularity when compared to the contourlet transform. We propose
a design framework based on the mapping approach, that allows for
a fast implementation based on a lifting or ladder structure, and
only uses one-dimensional filtering in some cases. In addition, our
design ensures that the corresponding frame elements are regular,
symmetric, and the frame is close to a tight one. We assess the performance
of the NSCT in image denoising and enhancement applications. In both
applications the NSCT compares favorably to other existing methods
in the literature.},
doi = {10.1109/TIP.2006.877507},
file = {Cunha_A_2006_tip_non_cttda.pdf:Cunha_A_2006_tip_non_cttda.pdf:PDF},
owner = {duvall},
pdf = {Cunha_A_2006_tip_non_cttda.pdf},
timestamp = {2008.11.27}
}
@INCOLLECTION{Daragon_X_2003_incoll_dis_f,
author = {X. Daragon and M. Couprie and G. Bertrand},
title = {Discrete Frontiers},
booktitle = {Discrete geometry for computer imagery},
publisher = {Springer Verlag},
year = {2003},
volume = {2886},
series = {LNCS},
pages = {236--245},
file = {Daragon_X_2003_incoll_dis_f.pdf:Daragon_X_2003_incoll_dis_f.pdf:PDF},
pdf = {Daragon_X_2003_incoll_dis_f.pdf},
timestamp = {2009.07.11}
}
@BOOK{Daubechies_I_1992_book_ten_lw,
title = {Ten Lectures on Wavelets},
publisher = {CBMS-NSF, SIAM Lecture Series},
year = {1992},
author = {Daubechies, I.},
address = {Philadelphia, PA, USA},
file = {Daubechies_I_1992_book_ten_lw.pdf:Daubechies_I_1992_book_ten_lw.pdf:PDF},
owner = {duvall},
pdf = {Daubechies_I_1992_book_ten_lw.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Daubechies_I_2010_j-comm-pure-appl-math_ite_rwlsmsr,
author = {I. Daubechies and R. DeVore and Fornasier, M. and S. G{\"u}nt{\"u}rk},
title = {Iteratively re-weighted least squares minimization for sparse recovery},
journal = j-comm-pure-appl-math,
year = {2010},
volume = {63},
pages = {1--38},
file = {Daubechies_I_2010_j-comm-pure-appl-math_ite_rwlsmsr.pdf:Daubechies_I_2010_j-comm-pure-appl-math_ite_rwlsmsr.pdf:PDF},
owner = {duvall},
pdf = {Daubechies_I_2010_j-comm-pure-appl-math_ite_rwlsmsr.pdf},
timestamp = {2010.01.13}
}
@ARTICLE{Daubechies_I_2003_j-acha_fra_mrabcwf,
author = {Daubechies, I. and Han, B. and Ron, A. and Shen, Z.},
title = {Framelets: {MRA}-based constructions of wavelet frames},
journal = j-acha,
year = {2003},
volume = {14},
pages = {1--46},
number = {1},
issn = {1063-5203},
abstract = {We discuss wavelet frames constructed via multiresolution analysis
(MRA), with emphasis on tight wavelet frames. In particular, we establish
general principles and specific algorithms for constructing framelets
and tight framelets, and we show how they can be used for systematic
constructions of spline, pseudo-spline tight frames, and symmetric
bi-frames with short supports and high approximation orders. Several
explicit examples are discussed. The connection of these frames with
multiresolution analysis guarantees the existence of fast implementation
algorithms, which we discuss briefly as well.},
doi = {DOI: 10.1016/S1063-5203(02)00511-0},
file = {Daubechies_I_2003_j-acha_fra_mrabcwf.pdf:Daubechies_I_2003_j-acha_fra_mrabcwf.pdf:PDF},
keywords = {Unitary extension principle; Oblique extension principle; Framelets;
Pseudo-splines; Frames; Tight frames; Fast frame transform; Multiresolution
analysis; Wavelets},
owner = {duvall},
pdf = {Daubechies_I_2003_j-acha_fra_mrabcwf.pdf},
timestamp = {2009.06.19},
url = {http://www.sciencedirect.com/science/article/B6WB3-47G3R6F-1/2/8f6f85efc54408c99a53768f71fb7c4b}
}
@ARTICLE{Daubechies_I_1998_j-four-anal-appl_fac_wtls,
author = {I. Daubechies and W. Sweldens},
title = {Factoring Wavelet Transforms into Lifting Steps},
journal = j-four-anal-appl,
year = {1998},
volume = {4},
pages = {245--267},
number = {3},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Daugman_J_1980_j-vis-res_two_dsacrfp,
author = {J. Daugman},
title = {Two-dimensional spectral analysis of cortical receptive field profile},
journal = j-vis-res,
year = {1980},
volume = {20},
pages = {847--856},
owner = {duvall},
timestamp = {2010.02.26}
}
@ARTICLE{Daugman_J_1985_j-opt-soc-am-a_unc_rrssfootvcf,
author = {Daugman, J. G.},
title = {Uncertainty relation for resolution in space, spatial frequency,
and orientation optimized by twodimensional visual cortical filters},
journal = j-opt-soc-am-a,
year = {1985},
volume = {2},
pages = {1160--1169},
number = {7},
owner = {duvall},
timestamp = {2009.11.01}
}
@INCOLLECTION{Davis_G_1998_incoll_wav_bico,
author = {Davis, G. and Nosratinia, A.},
title = {Wavelet-Based Image Coding: An Overview},
booktitle = {Applied and Computational Control, Signals, and Circuits},
publisher = {Birkh{\"a}user},
year = {1998},
editor = {B. N. Datta},
volume = {1},
chapter = {8},
pages = {369--434},
abstract = {This paper presents an overview of wavelet-based image coding. We
develop the basics of image coding with a discussion of vector quantization.
We motivate the use of transform coding in practical settings, and
describe the properties of various decorrelating transforms. We motivate
the use of the wavelet transform in coding using rate-distortion
considerations as well as approximation-theoretic considerations.
Finally, we give an overview of current coders in the literature.},
file = {Davis_G_1998_j-app-comp-cont-signal-circ_wav_bico.pdf:Davis_G_1998_j-app-comp-cont-signal-circ_wav_bico.pdf:PDF},
owner = {duvall},
timestamp = {2010.02.13}
}
@BOOK{Deans_S_1983_book_rad_tsa,
title = {The {Radon} transform and some of its applications},
publisher = {John Wiley \& Sons},
year = {1983},
author = {Deans, S. R.},
address = {New York},
owner = {duvall},
timestamp = {2010.01.11}
}
@ARTICLE{Dekel_S_2005_j-siam-j-numer-anal_ada_mabspgw,
author = {Dekel, S. and Leviatan, D.},
title = {Adaptive Multivariate Approximation Using Binary Space Partitions
and Geometric Wavelets},
journal = j-siam-j-numer-anal,
year = {2005},
volume = {43},
pages = {707--732},
number = {2},
issn = {0036-1429},
address = {Philadelphia, PA, USA},
doi = {http://dx.doi.org/10.1137/040604649},
file = {Dekel_S_2005_j-siam-j-numer-anal_ada_mabspgw.pdf:Dekel_S_2005_j-siam-j-numer-anal_ada_mabspgw.pdf:PDF},
keywords = {Binary Space Partitions, Geometric Wavelets, Piecewise polynomial
approximation, Nonlinear approximation, Adaptive multivariate approximation.},
owner = {duvall},
pdf = {Dekel_S_2005_j-siam-j-numer-anal_ada_mabspgw.pdf},
publisher = {Society for Industrial and Applied Mathematics},
timestamp = {2010.02.16}
}
@INPROCEEDINGS{Demanet_L_2003_p-spie-wasip_gab_ws,
author = {Demanet, L. and Vandergheynst, P.},
title = {Gabor wavelets on the sphere},
booktitle = p-spie-wasip,
year = {2003},
editor = {{Unser}, M.~A. and {Aldroubi}, A. and {Laine}, A.~F.},
volume = {5207},
pages = {208--215},
address = {San Diego, CA, USA},
month = {Aug. 4-8,},
abstract = {We propose the construction of directional - or Gabor - continuous
wavelets on the sphere. We provide a criterion to measure their angular
selectivity. We finally discuss implementation issues and potential
applications. The code for the spherical wavelet transform is available
in the YAWTB Matlab Toolbox, \urlhttp://www.yawtb.be.tf},
file = {Demanet_L_2003_p-spie-wasip_gab_ws.pdf:Demanet_L_2003_p-spie-wasip_gab_ws.pdf:PDF},
owner = {duvall},
timestamp = {2011.01.05}
}
@ARTICLE{Demanet_L_2007_j-acha_wav_asop,
author = {L. Demanet and L. Ying},
title = {Wave atoms and sparsity of oscillatory patterns},
journal = j-acha,
year = {2007},
volume = {23},
pages = {368--387},
number = {3},
issn = {1063-5203},
abstract = {We introduce #wave##atoms# as a variant of 2D wavelet packets obeying
the parabolic scaling wavelength~(diameter)2. We prove that warped
oscillatory functions, a toy model for texture, have a significantly
sparser expansion in wave atoms than in other fixed standard representations
like wavelets, Gabor atoms, or curvelets. We propose a novel algorithm
for a tight frame of wave atoms with redundancy two, directly in
the frequency plane, by the #wrapping# technique. We also propose
variants of the basic transform for applications in image processing,
including an orthonormal basis, and a shift-invariant tight frame
with redundancy four. Sparsity and denoising experiments on both
seismic and fingerprint images demonstrate the potential of the tool
introduced.},
doi = {DOI: 10.1016/j.acha.2007.03.003},
file = {Demanet_L_2007_j-acha_wav_asop.pdf:Demanet_L_2007_j-acha_wav_asop.pdf:PDF},
keywords = {Wave atoms; Image processing; Texture; Oscillatory; Warping; Diffeomorphism},
owner = {duvall},
pdf = {Demanet_L_2007_j-acha_wav_asop.pdf},
timestamp = {2009.11.01},
url = {http://www.sciencedirect.com/science/article/B6WB3-4NG3TG4-2/2/f454d2df448c7f929cb1b55c1a9c4f8c}
}
@ARTICLE{Demaret_L_2006_j-sp_ima_clsat,
author = {L. Demaret and N. Dyn and A. Iske},
title = {Image compression by linear splines over adaptive triangulations},
journal = j-sp,
year = {2006},
volume = {86},
pages = {1604--1616},
number = {7},
issn = {0165-1684},
abstract = {This paper proposes a new method for image compression. The method
is based on the approximation of an image, regarded as a function,
by a linear spline over an adapted triangulation, , which is the
Delaunay triangulation of a small set Y of significant pixels. The
linear spline minimizes the distance to the image, measured by the
mean square error, among all linear splines over . The significant
pixels in Y are selected by an adaptive thinning algorithm, which
recursively removes less significant pixels in a greedy way, using
a sophisticated criterion for measuring the significance of a pixel.
The proposed compression method combines the approximation scheme
with a customized scattered data coding scheme. We compare our compression
method with JPEG2000 on two geometric images and on three popular
test cases of real images.},
doi = {DOI: 10.1016/j.sigpro.2005.09.003},
file = {Demaret_L_2006_j-sp_ima_clsat.pdf:Demaret_L_2006_j-sp_ima_clsat.pdf:PDF},
keywords = {Image compression; Adaptive thinning; Linear splines; Delaunay triangulations;
Scattered data coding},
owner = {duvall},
pdf = {Demaret_L_2006_j-sp_ima_clsat.pdf},
timestamp = {2009.11.25},
url = {http://www.sciencedirect.com/science/article/B6V18-4H6XNBP-1/2/9e038cbd48b235537548054efdbb1491}
}
@TECHREPORT{Deriche_R_1993_tr_rec_igd,
author = {Deriche, R.},
title = {Recursively implementing the {Gaussian} and its derivative},
institution = {INRIA},
year = {1993},
month = {Apr.},
file = {:Deriche_R_1993_tr_rec_igd.pdf:PDF},
owner = {duvall},
pdf = {Deriche_R_1993_tr_rec_igd.pdf},
timestamp = {2008.06.14}
}
@ARTICLE{Distasi_R_1997_j-ieee-tcom_ima_cbttc,
author = {Distasi, R. and Nappi, M. and Vitulano, S.},
title = {Image compression by {B}-tree triangular coding},
journal = j-ieee-tcom,
year = {1997},
volume = {45},
pages = {1095--1100},
number = {9},
month = {Sep.},
issn = {0090-6778},
abstract = {This paper describes an algorithm for still image compression called
B-tree triangular coding (BTTC). The coding scheme is based on the
recursive decomposition of the image domain into right-angled triangles
arranged in a binary tree. The method is attractive because of its
fast encoding, O(n log n), and decoding, Theta;(n), where n is the
number of pixels, and because it is easy to implement and to parallelize.
Experimental studies indicate that BTTC produces images of satisfactory
quality from a subjective and objective point of view, One advantage
of BTTC over JPEG is its shorter execution time},
doi = {10.1109/26.623074},
file = {Distasi_R_1997_j-ieee-tcom_ima_cbttc.pdf:Distasi_R_1997_j-ieee-tcom_ima_cbttc.pdf:PDF},
keywords = {B-tree triangular coding;binary tree;execution time;image compression;image
domain;quality;recursive decomposition;right-angled triangles;still
image compression;data compression;image coding;trees (mathematics);},
owner = {duvall},
pdf = {Distasi_R_1997_j-ieee-tcom_ima_cbttc.pdf},
timestamp = {2010.02.15}
}
@INCOLLECTION{Do_M_2003_incoll_con,
author = {Do, M. N. and Vetterli, M.},
title = {Contourlets},
booktitle = {Beyond Wavelets},
publisher = {Academic Press},
year = {2003},
editor = {G. V. Welland},
file = {Do_M_2003_incoll_con.pdf:Do_M_2003_incoll_con.pdf:PDF},
owner = {duvall},
pdf = {Do_M_2003_incoll_con.pdf},
timestamp = {2009.07.14}
}
@ARTICLE{Do_M_2005_tip_con_tedmir,
author = {Do, M. N. and Vetterli, M.},
title = {The contourlet transform: an efficient directional multiresolution
image representation},
journal = j-ieee-tip,
year = {2005},
volume = {14},
pages = {2091--2106},
number = {12},
month = {Dec.},
file = {Do_M_2005_tip_con_tedmir.pdf:Do_M_2005_tip_con_tedmir.pdf:PDF},
owner = {duvall},
pdf = {Do_M_2005_tip_con_tedmir.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Do_M_2003_j-ieee-tsp_fra_p,
author = {Do, M. N. and Vetterli, M.},
title = {Framing pyramids},
journal = j-ieee-tsp,
year = {2003},
volume = {51},
pages = {2329--2342},
number = {9},
month = {Sep.},
issn = {1053-587X},
abstract = { Burt and Adelson (1983) introduced the Laplacian pyramid (LP) as
a multiresolution representation for images. We study the LP using
the frame theory, and this reveals that the usual reconstruction
is suboptimal. We show that the LP with orthogonal filters is a tight
frame, and thus, the optimal linear reconstruction using the dual
frame operator has a simple structure that is symmetric with the
forward transform. In more general cases, we propose an efficient
filterbank (FB) for the reconstruction of the LP using projection
that leads to a proved improvement over the usual method in the presence
of noise. Setting up the LP as an oversampled FB, we offer a complete
parameterization of all synthesis FBs that provide perfect reconstruction
for the LP. Finally, we consider the situation where the LP scheme
is iterated and derive the continuous-domain frames associated with
the LP.},
doi = {10.1109/TSP.2003.815389},
file = {Do_M_2003_j-ieee-tsp_fra_p.pdf:Do_M_2003_j-ieee-tsp_fra_p.pdf:PDF},
keywords = { Laplacian pyramid; continuous-domain frames; dual frame operator;
forward transform; frame theory; framing pyramids; multiresolution
image representation; noise; optimal linear reconstruction; orthogonal
filters; oversampled filterbank; perfect reconstruction; suboptimal
image reconstruction; tight frame; Laplace transforms; channel bank
filters; filtering theory; image reconstruction; image representation;
image resolution; image sampling;},
owner = {duvall},
pdf = {Do_M_2003_j-ieee-tsp_fra_p.pdf},
timestamp = {2010.08.28}
}
@ARTICLE{Do_M_2003_tip_fin_rtir,
author = {Do, M. N. and Vetterli, M.},
title = {The Finite Ridgelet Transform for Image Representation},
journal = j-ieee-tip,
year = {2003},
volume = {12},
pages = {16--28},
number = {1},
month = {Jan.},
owner = {duvall},
timestamp = {2009.07.14}
}
@ARTICLE{Donoho_D_1999_j-annals-statistics_wed_nmee,
author = {Donoho, D. L.},
title = {Wedgelets: nearly minimax estimation of edges},
journal = j-annals-statistics,
year = {1999},
volume = {27},
pages = {859--897},
number = {3},
abstract = {We study a simple ?horizon model? for the problem of recovering an
image from noisy data; in this model the image has an edge with $\alpha$-H\"older
regularity. Adopting the viewpoint of computational harmonic analysis,
we develop an overcomplete collection of atoms called wedgelets,
dyadically organized indicator functions with a variety of locations,
scales and orientations. The wedgelet representation provides nearly
optimal representations of objects in the horizon model, as measured
by minimax description length. We show how to rapidly compute a wedgelet
approximation to noisy data by finding a special edgelet-decorated
recursive partition which minimizes a complexity-penalized sum of
squares. This estimate, using sufficient subpixel resolution, achieves
nearly the minimax mean-squared error in the horizon model. In fact,
the method is adaptive in the sense that it achieves nearly the minimax
risk for any value of the unknown degree of regularity of the horizon,
$1 \leq \alpha \leq 2$. Wedgelet analysis and denoising may be used
successfully outside the horizon model. We study images modelled
as indicators of star-shaped sets with smooth boundaries and show
that complexity-penalized wedgelet partitioning achieves nearly the
minimax risk in that setting also.},
file = {Donoho_D_1999_j-annals-statistics_wed_nmee.pdf:Donoho_D_1999_j-annals-statistics_wed_nmee.pdf:PDF},
keywords = {Minimax estimation; edges; edgels; edgelets; fast algorithms; complexity
penalized estimates; recursive partitioning; subpixel resolution;
oracle inequalities},
owner = {duvall},
pdf = {Donoho_D_1999_j-annals-statistics_wed_nmee.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Donoho_D_1999_j-pnas_tig_fkprprosddsrn,
author = {Donoho, D. L.},
title = {Tight frames of k-plane ridgelets and the problem of representing
objects that are smooth away from d-dimensional singularities in
$\mathbb{R}^n$},
journal = j-pnas,
year = {1999},
volume = {96},
pages = {1828--1833},
number = {5},
eprint = {http://www.pnas.org/content/96/5/1828.full.pdf+html},
file = {Donoho_D_1999_j-pnas_tig_fkprprosddsrn.pdf:Donoho_D_1999_j-pnas_tig_fkprprosddsrn.pdf:PDF},
pdf = {Donoho_D_1999_j-pnas_tig_fkprprosddsrn.pdf},
timestamp = {2009.11.15},
url = {http://www.pnas.org/content/96/5/1828.abstract}
}
@ARTICLE{Donoho_D_1997_j-annals-statistics-car_bobc,
author = {D. L. Donoho},
title = {{CART} and best-ortho-basis: A connection},
journal = j-annals-statistics,
year = {1997},
volume = {25},
pages = {1870--1911},
number = {5},
doi = {doi:10.1214/aos/1069362377},
file = {Donoho_D_1997_j-annals-statistics-car_bobc.pdf:Donoho_D_1997_j-annals-statistics-car_bobc.pdf:PDF},
keywords = {Wavelets; anisotropic smoothness; anisotropic Haar basis; best orthogonal
basis; minimax estimation; spatial adaptation; oracle inequalities},
owner = {duvall},
timestamp = {2011.01.03},
url = {\url{http://projecteuclid.org/euclid.aos/1069362377}}
}
@ARTICLE{Donoho_D_2006_j-ieee-tit_sta_rsorpn,
author = {D. L. Donoho and M. Elad and Temlyakov, V. N.},
title = {Stable recovery of sparse overcomplete representations in the presence
of noise},
journal = j-ieee-tit,
year = {2006},
volume = {52},
pages = {6--18},
number = {1},
month = {Jan.},
issn = {0018-9448},
abstract = { Overcomplete representations are attracting interest in signal processing
theory, particularly due to their potential to generate sparse representations
of signals. However, in general, the problem of finding sparse representations
must be unstable in the presence of noise. This paper establishes
the possibility of stable recovery under a combination of sufficient
sparsity and favorable structure of the overcomplete system. Considering
an ideal underlying signal that has a sufficiently sparse representation,
it is assumed that only a noisy version of it can be observed. Assuming
further that the overcomplete system is incoherent, it is shown that
the optimally sparse approximation to the noisy data differs from
the optimally sparse decomposition of the ideal noiseless signal
by at most a constant multiple of the noise level. As this optimal-sparsity
method requires heavy (combinatorial) computational effort, approximation
algorithms are considered. It is shown that similar stability is
also available using the basis and the matching pursuit algorithms.
Furthermore, it is shown that these methods result in sparse approximation
of the noisy data that contains only terms also appearing in the
unique sparsest representation of the ideal noiseless sparse signal.},
doi = {10.1109/TIT.2005.860430},
file = {Donoho_D_2006_j-ieee-tit_sta_rsorpn.pdf:Donoho_D_2006_j-ieee-tit_sta_rsorpn.pdf:PDF},
keywords = { Kruskal rank; greedy approximation algorithm; incoherent dictionary;
matching pursuit; noisy data; optimal sparse decomposition; signal
processing theory; sparse overcomplete representation; stable recovery;
stepwise regression; superresolution signal; approximation theory;
iterative methods; signal denoising; signal representation; time-frequency
analysis;},
owner = {duvall},
timestamp = {2011.01.03}
}
@INCOLLECTION{Donoho_D_2003_incoll_dig_rtbtrf,
author = {Donoho, D. L. and Flesia, A. G.},
title = {Digital ridgelet transform based on true ridge functions},
booktitle = {Beyond Wavelets},
publisher = {Academic Press},
year = {2003},
editor = {G. Wellands},
volume = {10},
series = {Studies in Computational Mathematics},
pages = {1--30},
doi = {DOI: 10.1016/S1570-579X(03)80029-0},
file = {Donoho_D_2003_incoll_dig_rtbtrf.pdf:Donoho_D_2003_incoll_dig_rtbtrf.pdf:PDF},
issn = {1570-579X},
owner = {duvall},
timestamp = {2010.12.06},
url = {http://www.sciencedirect.com/science/article/B8GXW-4NW0SWP-2/2/c641f3555a4b704754addeae0cdf1dd0}
}
@ARTICLE{Driscoll_J_1994_j-adv-appl-math_com_ftc2s,
author = {J. R. Driscoll and D. M. Healy},
title = {Computing {F}ourier Transforms and Convolutions on the 2-Sphere},
journal = j-adv-appl-math,
year = {1994},
volume = {15},
pages = {202--250},
number = {2},
month = {Jun.},
abstract = {This paper considers the problem of efficient computation of the spherical
harmonic expansion, or Fourier transform, of functions defined on
the two dimensional sphere, S2. The resulting algorithms are applied
to the efficient computation of convolutions of functions on the
sphere. We begin by proving convolution theorems generalizing well
known and useful results from the abelian case. These convolution
theorems are then used to develop a sampling theorem on the sphere.
which reduces the calculation of Fourier transforms and convolutions
of band-limited functions to discrete computations. We show how to
perform these efficiently, starting with an O(n(log n)2) time algorithm
for computing the Legendre transform of a function defined on the
interval [-1,1] sampled at n points there. Theoretical and experimental
results on the effects of finite precision arithmetic are presented.
The Legendre transform algorithm is then generalized to obtain an
algorithm for the Fourier transform, requiring O(n(log n)2) time,
and an algorithm for its inverse in O(n1.5) time, where n is the
number of points on the sphere at which the function is sampled.
This improves the naive O(n2) bound, which is the best previously
known. These transforms give an O(n1.5) algorithm for convolving
two functions on the sphere.},
date-added = {2009-10-17 16:23:14 +0200},
date-modified = {2009-10-21 15:58:08 +0200},
doi = {DOI: 10.1006/aama.1994.1008},
file = {Driscoll_J_1994_j-adv-appl-math_com_ftc2s.pdf:Driscoll_J_1994_j-adv-appl-math_com_ftc2s.pdf:PDF},
owner = {duvall},
rating = {0},
timestamp = {2011.01.05},
uri = {papers://C319F6DA-DBA8-4257-A9FA-3BDE437CA713/Paper/p66},
url = {\url{http://www.sciencedirect.com/science/article/B6W9D-45P0H0G-B/2/44060d9d048f53ab56ccc47adf07d705}}
}
@ARTICLE{Duffin_R_1952_tams_cla_nhfs,
author = {Duffin, R. and Schaeffer, A.},
title = {A class of non-harmonic {Fourier} series},
journal = {Trans. Amer. Math. Soc.},
year = {1952},
volume = {72},
pages = {341--366},
owner = {duvall},
timestamp = {2007.06.07}
}
@ARTICLE{Durand_S_2007_acha_m_bfndw,
author = {Durand, S.},
title = {{$M$}-band filtering and nonredundant directional wavelets},
journal = j-acha,
year = {2007},
volume = {22},
pages = {124--139},
doi = {doi:10.1016/j.acha.2006.05.006},
file = {Durand_S_2007_acha_m_bfndw.pdf:Durand_S_2007_acha_m_bfndw.pdf:PDF},
owner = {duvall},
pdf = {Durand_S_2007_acha_m_bfndw.pdf},
timestamp = {2007.07.06}
}
@MISC{Duval_L_2005_url_wits,
author = {Duval, L.},
title = {{WITS: Where Is The \emph{Star}let?}},
note = {{\url{http://www.laurent-duval.eu/siva-wits-where-is-the-starlet.html}}},
owner = {duvall},
timestamp = {2011.01.05}
}
@ARTICLE{Dyn_N_1987_j-comput-aided-geomet-desfou_pisccd,
author = {N. Dyn and J. A. Gregory and D. Levin},
title = {A four-point interpolatory subdivision scheme for curve design},
journal = j-comput-aided-geomet-des,
year = {1987},
volume = {4},
pages = {257--268},
keywords = {lifting, sweldens},
owner = {duvall},
timestamp = {2010.02.24}
}
@INPROCEEDINGS{Efros_A_2001_p-acm-siggraph_ima_qtst,
author = {A. A. Efros and W. T. Freeman},
title = {Image Quilting for Texture Synthesis and Transfer},
booktitle = p-acm-siggraph,
year = {2001},
pages = {341--346},
month = {Aug. 12-17},
abstract = {We present a simple image-based method of generating novel visual
appearance in which a new image is synthesized by stitching together
small patches of existing images. We call this process image quilting.
First, we use quilting as a fast and very simple texture synthesis
algorithm which produces surprisingly good results for a wide range
of textures. Second, we extend the algorithm to perform texture transfer
--- rendering an object with a texture taken from a different object.
More generally, we demonstrate how an image can be re-rendered in
the style of a different image. The method works directly on the
images and does not require 3D information.},
file = {Efros_A_2001_p-acm-siggraph_ima_qtst.pdf:Efros_A_2001_p-acm-siggraph_ima_qtst.pdf:PDF},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Egger_1995_j-proc-ieee_hig_cicamsd,
author = {Egger, O. and Li, W. and Kunt, M.},
title = {High compression image coding using an adaptive morphological subband
decomposition},
journal = j-proc-ieee,
year = {1995},
volume = {83},
pages = {272--287},
number = {2},
month = {Feb.},
issn = {0018-9219},
abstract = {A morphological subband decomposition with perfect reconstruction
is proposed. Critical subsampling is achieved. The reconstructed
images using this decomposition do not suffer from any ringing effect.
In order to avoid poor texture representation by the morphological
filters an adaptive subband decomposition is introduced. It chooses
linear filters on textured regions and morphological filters otherwise.
A simple and efficient texture detection criterion is proposed and
applied to the adaptive decomposition. Comparisons to other coding
techniques such as JPEG and linear subband coding show that the proposed
scheme performs significantly better both in terms of PSNR and visual
quality},
doi = {10.1109/5.364462},
file = {Egger_1995_j-proc-ieee_hig_cicamsd.pdf:Egger_1995_j-proc-ieee_hig_cicamsd.pdf:PDF},
keywords = {JPEG coding;PSNR;adaptive morphological subband decomposition;image
coding;image compression;linear filters;linear subband coding;morphological
filters;perfect reconstruction;subsampling;texture detection criterion;texture
representation;textured regions;visual quality;adaptive filters;adaptive
signal detection;adaptive signal processing;filtering theory;image
coding;image reconstruction;image sampling;image texture;mathematical
morphology;},
owner = {duvall},
timestamp = {2010.11.12}
}
@INCOLLECTION{Fadili_J_2009_incoll_cur_r,
author = {Fadili, J. M. and Starck, J.-L.},
title = {Curvelets and ridgelets},
booktitle = {Encyclopedia of Complexity and Systems Science},
publisher = {Springer, New York},
year = {2009},
volume = {3},
pages = {1718--1738},
file = {Fadili_J_2009_incoll_cur_r.pdf:Fadili_J_2009_incoll_cur_r.pdf:PDF},
owner = {duvall},
pdf = {Fadili_J_2009_incoll_cur_r.pdf},
timestamp = {2010.08.28}
}
@ARTICLE{Faugere_J_1998_tsp_des_rnbwgbt,
author = {Faug{\`e}re, J.-C. and Moreau de Saint-Martin, F. and Rouillier,
F.},
title = {Design of Regular Nonseparable Bidimensional Wavelets Using {Gr{\"o}bner}
Basis Techniques},
journal = j-ieee-tsp,
year = {1998},
volume = {46},
pages = {845--856},
number = {4},
month = {Apr.},
abstract = {The design of two-dimensional (2-D) filter banks yielding orthogonality
and linear-phase filters and generating regular wavelet bases is
a difficult task involving the algebraic properties of multivariate
polynomials. Using cascade forms implies dealing with nonlinear optimization.
We turn the issue of optimizing the orthogonal linear-phase cascade
from Kovacevic and Vetterli (1992) into a polynomial problem and
solve it using Grobner basis techniques and computer algebra. This
leads to a complete description of maximally flat wavelets among
the orthogonal linear-phase family proposed by Kovacevic and Vetterli.
We obtain up to five degrees of flatness for a $16\times 16$ filter
bank, whose Sobolev exponent is 2.11, making this wavelet the most
regular orthogonal linear-phase nonseparable wavelet to the authors'
knowledge,},
doi = {10.1109/78.668541},
file = {Faugere_J_1998_tsp_des_rnbwgbt.pdf:Faugere_J_1998_tsp_des_rnbwgbt.pdf:PDF},
owner = {duvall},
pdf = {Faugere_J_1998_tsp_des_rnbwgbt.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Feauveau_J_1990_ts_ana_mfrs2,
author = {Feauveau, J. C.},
title = {Analyse multir{\'e}solution pour les images avec un facteur de r{\'e}solution
$\sqrt{2}$},
journal = j-trait-signal,
year = {1990},
volume = {7},
pages = {117--128},
number = {2},
abstract = {Recently, an algorithm for multiresolution signal analysis, based
on tvavelet theory las been proposed by S. Mallat. The basic idea
is to capture signifďcant d\'etails in the signal through the analysis
ai successive scales . Mallat's algorithm uses a scaling factor of
2 between two successive scales . The aim of this paper is to develop
a theory and an algorith n for image processing, with a scaling factor
of $\sqrt(2)$ . This will allow for sinipler resulis interpretation
and doubled sharpness of analysis . The theory is illustrated on
both artificial and natural images, where our algorithm proves efficient
for non-oriented contour detection . R\'ecemment, un algorithme d'analyse
multir\'esolution a \'et\'e propos\'e par S. Mallat . Cet algorithme
a pour but d'extraire les caract\'eristiques d'un signal en l'analysant
\`a diverses \'echelles, un facteur de r\'esolution 2 reliant deux
\'echelles cons\'ecutives . Nous d\'eveloppons ici un cadre th\'eorique
et un algorithme d\'edi\'e au traitement d'images, avec un facteur
de r\'esolution qui double la finesse d'analyse . Une autre caract\'eristique
essentielle de cet algorithme est d'\^etre non s\'electif \`a l'orientation
comme le montre les images sur lesquelles il a \'et\'e test\'e .},
file = {Feauveau_J_1990_ts_ana_mfrs2.pdf:Feauveau_J_1990_ts_ana_mfrs2.pdf:PDF},
keywords = {Orthogonal rnultiresolution analysis, wavelets, resolution factor
sqrt(2), zero crossings, non-ariented process},
owner = {duvall},
pdf = {Feauveau_J_1990_ts_ana_mfrs2.pdf},
timestamp = {2009.07.14}
}
@TECHREPORT{Felsberg_M_2002_tr_low_lipsm,
author = {Felsberg, M.},
title = {Low-Level Image Processing with the Structure Multivector},
institution = {Christian-Albrechts-Universit\"at},
year = {2002},
number = {Bericht Nr. 0203},
address = {Kiel, Germany},
month = {Mar. 15,},
abstract = {The present thesis deals with two-dimensional signal processing for
computer vision. The main topic is the development of a sophisticated
generalization of the one-dimensional analytic signal to two dimensions.
Motivated by the fundamental property of the latter, the invariance
? equivariance constraint, and by its relation to complex analysis
and potential theory, a two-dimensional approach is derived. This
method is called the monogenic signal and it is based on the Riesz
transform instead of the Hilbert transform. By means of this linear
approach it is possible to estimate the local orientation and the
local phase of signals which are projections of one-dimensional functions
to two dimensions. For general two-dimensional signals, however,
the monogenic signal has to be further extended, yielding the structure
multivector. The latter approach combines the ideas of the structure
tensor and the quaternionic analytic signal. A rich feature set can
be extracted from the structure multivector, which contains measures
for local amplitudes, the local anisotropy, the local orientation,
and two local phases. Both, the monogenic signal and the structure
multivector are combined with an appropriate scale-space approach,
resulting in generalized quadrature filters. Same as the monogenic
signal, the applied scalespace approach is derived from the three-dimensional
Laplace equation instead of the diffusion equation. Hence, the two-dimensional
generalization of the analytic signal turns out to provide a whole
new framework for low-level vision. Several applications are presented
to show the efficiency and power of the theoretic considerations.
Among these are methods for orientation estimation, edge and corner
detection, stereo correspondence and disparity estimation, and adaptive
smoothing.},
file = {Felsberg_M_2002_tr_low_lipsm.pdf:Felsberg_M_2002_tr_low_lipsm.pdf:PDF},
owner = {duvall},
pdf = {Felsberg_M_2002_tr_low_lipsm.pdf},
timestamp = {2009.07.12}
}
@ARTICLE{Fernandes_F_2005_tip_mul_mbcwt,
author = {Fernandes, F. C. A. and van Spaendonck, R. L. C. and Burrus, C. S.},
title = {Multidimensional, Mapping-Based Complex Wavelet Transforms},
journal = j-ieee-tip,
year = {2005},
volume = {14},
pages = {110--124},
number = {1},
month = {Jan.},
abstract = {Although the discrete wavelet transform (DWT) is a powerful tool for
signal and image processing, it has three serious disadvantages:
shift sensitivity, poor directionality, and lack of phase information.
To overcome these disadvantages, we introduce multidimensional, mapping-based,
complex wavelet transforms that consist of a mapping onto a complex
function space followed by a DWT of the complex mapping. Unlike other
popular transforms that also mitigate DWT shortcomings, the decoupled
implementation of our transforms has two important advantages. First,
the controllable redundancy of the mapping stage offers a balance
between degree of shift sensitivity and transform redundancy. This
allows us to create a directional, nonredundant, complex wavelet
transform with potential benefits for image coding systems. To the
best of our knowledge, no other complex wavelet transform is simultaneously
directional and nonredundant. The second advantage of our approach
is the flexibility to use any DWT in the transform implementation.
As an example, we exploit this flexibility to create the complex
double-density DWT: a shift-insensitive, directional, complex wavelet
transform with a low redundancy of (3 1) (2 1) in dimensions. No
other transform achieves all these properties at a lower redundancy,
to the best of our knowledge. By exploiting the advantages of our
multidimensional, mapping-based complex wavelet transforms in seismic
signal-processing applications, we have demonstrated state-of-the-art
results.},
file = {Fernandes_F_2005_tip_mul_mbcwt.pdf:Fernandes_F_2005_tip_mul_mbcwt.pdf:PDF},
owner = {duvall},
pdf = {Fernandes_F_2005_tip_mul_mbcwt.pdf},
timestamp = {2009.07.12}
}
@ARTICLE{Fernandes_F_2003_tsp_new_fcwt,
author = {Fernandes, F. C. A. and van Spaendonck, R. L. C. and Burrus, C. S.},
title = {A new framework for complex wavelet transforms},
journal = j-ieee-tsp,
year = {2003},
volume = {51},
pages = {1825--1837},
number = {7},
month = {Jul.},
abstract = {Although the discrete wavelet transform (DWT) is a powerful tool for
signal and image processing, it has three serious disadvantages:
shift sensitivity, poor directionality, and lack of phase information.
To overcome these disadvantages, we introduce two-stage mapping-based
complex wavelet transforms that consist of a mapping onto a complex
function space followed by a DWT of the complex mapping. Unlike other
popular transforms that also mitigate DWT shortcomings, the decoupled
implementation of our transforms has two important advantages. First,
the controllable redundancy of the mapping stage offers a balance
between degree of shift sensitivity and transform redundancy. This
allows us to create a directional, non-redundant, complex wavelet
transform with potential benefits for image coding systems. To the
best of our knowledge, no other complex wavelet transform is simultaneously
directional and non-redundant. The second advantage of our approach
is the flexibility to use any DWT in the transform implementation.
As an example, we can exploit this flexibility to create the complex
double-density DWT (CDDWT): a shift-insensitive, directional, complex
wavelet transform with a low redundancy of (3/sup m/-1/2/sup m/-1)
in m dimensions. To the best of our knowledge, no other transform
achieves all these properties at a lower redundancy.},
doi = {10.1109/TSP.2003.812841},
file = {Fernandes_F_2003_tsp_new_fcwt.pdf:Fernandes_F_2003_tsp_new_fcwt.pdf:PDF},
owner = {duvall},
pdf = {Fernandes_F_2003_tsp_new_fcwt.pdf},
timestamp = {2007.06.21}
}
@INPROCEEDINGS{Fernandes_F_2001_p-icip_dir_silrwt,
author = {Fernandes, F. C. A. and van Spaendonck, R. L. C. and Burrus, C. S.},
title = {A directional, shift insensitive, low-redundancy, wavelet transform},
booktitle = p-icip,
year = {2001},
volume = {1},
pages = {618--621},
address = {Thessaloniki, Greece},
month = {Oct.},
abstract = {Shift sensitivity and poor directionality, two major disadvantages
of the discrete wavelet transform, have previously been circumvented
either by using highly redundant, non-separable wavelet transforms
or by using restrictive designs to obtain a pair of wavelet trees
with a transform-domain redundancy of 4.0 in 2D. We demonstrate that
excellent shift-invariance properties and directional selectivity
may be obtained with a transform-domain redundancy of only 2.67 in
2D. We achieve this by projecting the wavelet coefficients from Selesnick's
(see Wavelet Applications VII, Proceedings of SPIE, 2000) shift-
insensitive, double-density wavelet transform so as to separate approximately
the positive and negative frequencies, thereby increasing directionality.
Subsequent decimation and a novel inverse projection maintain the
low redundancy while ensuring perfect reconstruction. Although our
transform generates complex-valued coefficients that provide valuable
phase information, it may be implemented with a fast algorithm that
uses only real arithmetic. To demonstrate the efficacy of our new
transform, we show that it achieves state-of-the-art performance
in a seismic image-processing application},
doi = {10.1109/ICIP.2001.959121},
file = {Fernandes_F_2001_p-icip_dir_silrwt.pdf:Fernandes_F_2001_p-icip_dir_silrwt.pdf:PDF},
owner = {duvall},
pdf = {Fernandes_F_2001_p-icip_dir_silrwt.pdf},
timestamp = {2009.10.20}
}
@INPROCEEDINGS{Fernandes_F_2004_icassp_non_rlpsodcw,
author = {Fernandes, F. C. A. and Wakin, M. and Baraniuk, R.},
title = {Non-Redundant, Linear-Phase, Semi-Orthogonal, Directional Complex
Wavelets},
booktitle = p-icassp,
year = {2004},
address = {Montr{\'e}al, Qu{\'e}bec, Canada},
month = {May},
file = {Fernandes_F_2004_icassp_non_rlpsodcw.pdf:Fernandes_F_2004_icassp_non_rlpsodcw.pdf:PDF},
owner = {duvall},
pdf = {Fernandes_F_2004_icassp_non_rlpsodcw.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{FiguerasIVentura_R_2006_tip_low_rficrr,
author = {Figueras i Ventura, R. and Vandergheynst, P. and Frossard, P.},
title = {Low rate and flexible image coding with redundant representations},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {726--739},
number = {3},
month = {Mar.},
file = {FiguerasIVentura_R_2006_tip_low_rficrr.pdf:FiguerasIVentura_R_2006_tip_low_rficrr.pdf:PDF},
owner = {duvall},
pdf = {FiguerasIVentura_R_2006_tip_low_rficrr.pdf},
timestamp = {2007.06.07}
}
@TECHREPORT{Florack_L_1998_tr_top_sssi,
author = {Florack, L. and Kuijper, A.},
title = {The Topological Structure of Scale-Space Images},
institution = {NL},
year = {1998},
abstract = {We investigate the “deep structure” of a scale-space image. The emphasis
is on topology, i.e. we concentrate on critical points—points with
vanishing gradient --- and top-points --- critical points with degenerate
Hessian --- and monitor their displacements, respectively generic
morsifications in scale-space. Relevant parts of catastrophe theory
in the context of the scale-space paradigm are briefly reviewed,
and subsequently rewritten into coordinate independent form. This
enables one to implement topological descriptors using a conveniently
defined coordinate system.},
file = {Florack_L_1998_tr_top_sssi.pdf:Florack_L_1998_tr_top_sssi.pdf:PDF},
owner = {duvall},
pdf = {Florack_L_1998_tr_top_sssi.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Forster_B_2008_j-acha_shi_isrcf,
author = {Forster, B. and Blu, T. and Van De Ville, D. and Unser, M.},
title = {Shift-invariant spaces from rotation-covariant functions},
journal = j-acha,
year = {2008},
volume = {25},
pages = {240--265},
number = {2},
month = {Sep.},
doi = {10.1016/j.acha.2007.11.002},
file = {Forster_B_2008_j-acha_shi_isrcf.pdf:Forster_B_2008_j-acha_shi_isrcf.pdf:PDF},
keywords = {Complex wavelets; Riesz basis; Two-scale relation; Multiresolution;
Scaling functions; Shift-invariant spaces; Rotation covariance},
owner = {duvall},
publisher = {Elsevier},
timestamp = {2010.01.13},
url = {http://bigwww.epfl.ch/publications/forster0801.ps, http://bigwww.epfl.ch/publications/forster0801.html}
}
@ARTICLE{Freeden_W_2003_j-rev-mat-complutense_sur_wmga,
author = {W. Freeden and T. Maier and S. Zimmermann},
title = {A Survey on Wavelet Methods for (geo)applications},
journal = j-rev-mat-complutense,
year = {2003},
volume = {16},
pages = {277--310},
number = {1},
abstract = {Wavelets originated in 1980's for the analysis of (seismic) signals
and have seen an explosion of applications. However, almost all the
material is based on wavelets over Euclidean spaces. This paper deals
with an approach to the theory and algorithmic aspects of wavelets
in a general separable Hilbert space framework. As examples Legendre
wavelets on the interval $[-1,1]$ and scalar and vector spherical
wavelets on the unit sphere are discussed in more detail.},
date-added = {2009-10-17 16:23:14 +0200},
date-modified = {2009-10-21 15:58:08 +0200},
file = {Freeden_W_2003_j-rev-mat-complutense_sur_wmga.pdf:Freeden_W_2003_j-rev-mat-complutense_sur_wmga.pdf:PDF},
keywords = {Wavelet theory, scalar multiscale approximation, vectorial multiscale
approximation, pyramid scheme, geoapplications.},
owner = {duvall},
rating = {0},
timestamp = {2011.01.05},
uri = {papers://C319F6DA-DBA8-4257-A9FA-3BDE437CA713/Paper/p297}
}
@ARTICLE{Freeden_W_1996_j-adv-appl-math_sph_wtd,
author = {W. Freeden and U. Windheuser},
title = {Spherical Wavelet Transform and its Discretization},
journal = j-adv-appl-math,
year = {1996},
volume = {5},
pages = {51--94},
number = {1},
abstract = {A continuous version of spherical multiresolution is described, starting
from continuous wavelet transform on the sphere. Scale discretization
enables us to construct spherical counterparts to wavelet packets
and scale discrete wavelets. The essential tool is the theory of
singular integrals on the sphere. It is shown that singular integral
operators forming a semigroup of contraction operators of class (C0)
(like Abel-Poisson or Gau -Weierstra operators) lead in a canonical
way to (pyramidal) algorithms.},
date-added = {2009-10-17 16:23:14 +0200},
date-modified = {2009-10-21 15:58:09 +0200},
owner = {duvall},
rating = {0},
timestamp = {2011.01.05},
uri = {papers://C319F6DA-DBA8-4257-A9FA-3BDE437CA713/Paper/p22}
}
@PHDTHESIS{Freeman_W_1992_phd_ste_flais,
author = {Freeman, W. T.},
title = {Steerable Filters and Local Analysis of Image Structure},
school = {Massachusetts Institute of Technology},
year = {1992},
abstract = {Two paradigms for visual analysis are {\em top-down}, starting from
high-level models or information about the image, and {\em bottom-up},
where little is assumed about the image or objects in it. We explore
a local, bottom-up approach to image analysis. We develop operators
to identify and classify image junctions, which contain important
visual cues for identifying occlusion, transparency, and surface
bends. Like the human visual system, we begin with the application
of linear filters which are oriented in all possible directions.
We develop an efficient way to create an oriented filter of arbitrary
orientation by describing it as a linear combination of {\em basis
filters}. This approach to oriented filtering, which we call {\em
steerable filters}, offers advantages for analysis as well as computation.
We design a variety of steerable filters, including steerable quadrature
pairs, which measure local energy. We show applications of these
filters in orientation and texture analysis, and image representation
and enhancement. We develop methods based on steerable filters to
study structures such as contours and junctions. We describe how
to post-filter the energy measures in order to more efficiently analyze
structures with multiple orientations. We introduce a new detector
for contours, based on energy local maxima. We analyze contour phases
at energy local maxima, and compare the results with the prediction
of a simple model. Using these tools, we analyze junctions. Based
on local oriented filters, we develop simple mechanisms which respond
selectively to ``T'', ``L'', and ``X'' junctions. The T and X junctions
may indicate occlusion and transparency, respectively. These mechanism
show that detectors for important, low-level visual cues can be built
out of oriented filters and energy measures, which resemble responses
found in the visual cortex. We present a second approach to junction
detection based on salient contours. We combine our contour detector
with the structural saliency algorithm of Shashua and Ullman, which
finds visually salient contours. To improve its descriptive power,
we include a competitive mechanism in the algorithm. From the local
configuration of saliencies, we form simple detectors which respond
to cues for occlusion, transparency and surface bending. Using the
saliency values and curve linking information, we can propagate this
information along image contours. For both algorithms, we show successful
results on simple synthetic and natural images. We show results for
more complicated scenes and discuss the methods do not work, and
why. Each algorithm uses only local calculations applied in parallel
throughout the image, and assumes little prior information about
the objects it expects to see.},
file = {Freeman_W_1992_phd_ste_flais.pdf:Freeman_W_1992_phd_ste_flais.pdf:PDF},
owner = {duvall},
pdf = {Freeman_W_1992_phd_ste_flais.pdf},
timestamp = {2009.10.14}
}
@ARTICLE{Freeman_W_1991_tpami_des_usf,
author = {Freeman, W. T. and Adelson, E. H.},
title = {The design and use of steerable filters},
journal = j-ieee-tpami,
year = {1991},
volume = {13},
pages = {891--906},
number = {9},
month = {Sep.},
abstract = {Oriented filters are useful in many early vision and image processing
tasks. One often needs to apply the same filter, rotated to different
angles under adaptive control, or wishes to calculate the filter
response at various orientations. We present an efficient architecture
to synthesize filters of arbitrary orientations from linear combinations
of basis filters, allowing one to adaptively ``steer'' a filter to
any orientation, and to determine analytically the filter output
as a function of orientation. Steerable filters may be designed in
quadrature pairs to allow adaptive control over phase as well as
orientation. We show how to design and steer the filters, and present
examples of their use in several tasks: the analysis of orientation
and phase, angularly adaptive filtering, edge detection, and shape-from-shading.
One can also build a self-similar steerable pyramid representation
which may be used to implement a steerable ``wavelet'' decomposition.
The same concepts can be generalized to the design of 3-D steerable
filters, which should be useful in the analysis of image sequences
and volumetric data.},
file = {Freeman_W_1991_tpami_des_usf.pdf:Freeman_W_1991_tpami_des_usf.pdf:PDF;Freeman_W_1991_tpami_des_usf-preprint.pdf:Freeman_W_1991_tpami_des_usf-preprint.pdf:PDF},
owner = {duvall},
pdf = {Freeman_W_1991_tpami_des_usf.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Freeman_W_1990_p-iccv_ste_feviawd,
author = {Freeman, W. T. and Adelson, E. H.},
title = {Steerable Filters for Early Vision, Image Analysis and Wavelet Decomposition},
booktitle = p-iccv,
year = {1990},
pages = {406--415},
file = {Freeman_W_1990_p-iccv_ste_feviawd.pdf:Freeman_W_1990_p-iccv_ste_feviawd.pdf:PDF},
owner = {duvall},
pdf = {Freeman_W_1990_p-iccv_ste_feviawd.pdf},
timestamp = {2009.10.14}
}
@ARTICLE{Friedrich_F_2007_j-siam-sci-comp_eff_mcpdarwa,
author = {F. Friedrich and L. Demaret and H. Fuhr and K. Wicker},
title = {Efficient Moment Computation over Polygonal Domains with an Application
to Rapid Wedgelet Approximation},
journal = j-siam-sci-comp,
year = {2007},
volume = {29},
pages = {842--863},
number = {2},
owner = {duvall},
timestamp = {2011.01.03}
}
@INCOLLECTION{Fuhr_H_2006_incoll_bey_wnirp,
author = {H. F{\"u}hr and L. Demaret and F. Friedrich},
title = {Beyond wavelets: New image representation paradigms},
booktitle = {Document and Image Compression},
publisher = {CRC Press},
year = {2006},
editor = {M. Barni},
file = {Fuhr_H_2006_incoll_bey_wnirp.pdf:Fuhr_H_2006_incoll_bey_wnirp.pdf:PDF},
owner = {duvall},
pdf = {Fuhr_H_2006_incoll_bey_wnirp.pdf},
timestamp = {2009.10.20}
}
@ARTICLE{Gabor_D_1946_j-iee_the_c,
author = {Gabor, D.},
title = {Theory of Communication},
journal = j-iee,
year = {1946},
volume = {93},
pages = {429--457},
number = {26},
note = {Part. III},
abstract = {The purpose of these studies is an inquiry into the essence of the
"information" conveyed by channels of communication, and the application
of the result of this inquiry to the practical problem of optimum
utilization of frequency bands. In Part 1, a new method of analysing
signals is presented in which time and frequency play symmetrical
parts, and which contains "time analysis" and "frequency analysis"
as special cases. It is shown that the information conveyed by a
frequency band in a given time-interval can be analysed in various
ways into the same number of elementary "quanta of information,"
each quantum conveying one numerical datum. In Part 2, this method
is applied to the analysis of hearing sensations. It is shown on
the basis of existing experimental material that in the band between
60 an 1000 c/s the human ear can discriminate very nearly every second
datum of information, and that this efficiency of nearly 50 percent
is independent of the duration of the signals in a remarkably wide
interval. This fact, which cannot be explained by any mechanism in
the inner ear, suggests a new phenomenon in nerve conduction. At
frequencies above 1000 c/s the efficiency of discrimination falls
off sharply, proving that sound reproductions which are far from
faithful may be perceived by the ear as perfect, and that "condensed"
methods of transmission and reproduction with improved waveband economy
are possible in principle. In Part 3, suggestions are discussed for
compresse transmission and reproduction of speech or music, and the
first experimental results obtained with one of these methods are
described.},
file = {Gabor_D_1946_j-iee_the_c.pdf:Gabor_D_1946_j-iee_the_c.pdf:PDF},
keywords = {time analysis, frequency analysis, Fourier Analysis,},
owner = {duvall},
pdf = {Gabor_D_1946_j-iee_the_c.pdf},
timestamp = {2009.11.01}
}
@INPROCEEDINGS{Gagnon_L_1995_p-embs_sha_edmcsdw,
author = {Gagnon, L. and Lina, J.-M. and Goulard, B.},
title = {Sharpening Enhancement of Digitized Mammograms with Complex Symmetric
{Daubechies} Wavelets},
booktitle = {Proc. EMBS},
year = {1995},
abstract = {Some complex symmetric Daubechies wavelets provide a natural way to
calculate zero- crossings because of a hidden "Laplacian operator"
in the imaginary part of the scaling function. We propose a simple
multiscale sharpening enhancement algorithm based on this property.
The algorithm is tested on low-contrast digitized mammograms.},
file = {Gagnon_L_1995_p-embs_sha_edmcsdw.pdf:Gagnon_L_1995_p-embs_sha_edmcsdw.pdf:PDF},
keywords = {Image processing, wavelets, mammograms.},
owner = {duvall},
pdf = {Gagnon_L_1995_p-embs_sha_edmcsdw.pdf},
timestamp = {2009.07.12}
}
@ARTICLE{Gauthier_J_2009_tsp_opt_socfb,
author = {Gauthier, J. and Duval, L. and Pesquet, J.-C.},
title = {Optimization of Synthesis Oversampled Complex Filter Banks},
journal = j-ieee-tsp,
year = {2009},
volume = {57},
pages = {3827--3843},
number = {10},
month = {Oct.},
issn = {1053-587X},
abstract = {An important issue with oversampled FIR analysis filter banks (FBs)
is to determine inverse synthesis FBs, when they exist. Given any
complex oversampled FIR analysis FB, we first provide an algorithm
to determine whether there exists an inverse FIR synthesis system.
We also provide a method to ensure the Hermitian symmetry property
on the synthesis side, which is serviceable to processing real-valued
signals. As an invertible analysis scheme corresponds to a redundant
decomposition, there is no unique inverse FB. Given a particular
solution, we parameterize the whole family of inverses through a
null space projection. The resulting reduced parameter set simplifies
design procedures, since the perfect reconstruction constrained optimization
problem is recast as an unconstrained optimization problem. The design
of optimized synthesis FBs based on time or frequency localization
criteria is then investigated, using a simple yet efficient gradient
algorithm.},
doi = {10.1109/TSP.2009.2023947},
file = {Gauthier_J_2009_tsp_opt_socfb.pdf:Gauthier_J_2009_tsp_opt_socfb.pdf:PDF;Gauthier_J_2009_tsp_opt_socfb-published.pdf:Gauthier_J_2009_tsp_opt_socfb-published.pdf:PDF},
keywords = {Data mining Discrete Fourier transforms Finite impulse response filter
IEEE Optimization Oversampled filter banks Polynomials Probability
density function filter design frequency localization inversion lapped
transforms modulated filter banks optimization time localization},
owner = {duvall},
pdf = {Gauthier_J_2009_tsp_opt_socfb-published.pdf},
timestamp = {2009.06.11}
}
@ARTICLE{Gerek_O_2000_j-ieee-tip_ada_psdsic,
author = {O. N. Gerek and A. E. Cetin},
title = {Adaptive Polyphase Subband Decomposition Structures for Image Compression},
journal = j-ieee-tip,
year = {2000},
volume = {9},
pages = {1649--1660},
number = {10},
month = {Oct.},
issn = {1057-7149},
abstract = {Subband decomposition techniques have been extensively used for data
coding and analysis. In most filter banks, the goal is to obtain
subsampled signals corresponding to different spectral regions of
the original data. However, this approach leads to various artifacts
in images having spatially varying characteristics, such as images
containing text, subtitles, or sharp edges. In this paper, adaptive
filter banks with perfect reconstruction property are presented for
such images. The filters of the decomposition structure which can
be either linear or nonlinear vary according to the nature of the
signal. This leads to improved image compression ratios. Simulation
examples are presented},
doi = {10.1109/83.869176},
file = {Gerek_O_2000_j-ieee-tip_ada_psdsic.pdf:Gerek_O_2000_j-ieee-tip_ada_psdsic.pdf:PDF},
keywords = {adaptive filter banks;adaptive polyphase subband decomposition structures;adaptive
prediction filters;data analysis;data coding;image artifacts;image
compression ratios;linear filters;nonlinear filters;perfect reconstruction
property;sharp edges;simulation;spatially varying characteristics;spectral
regions;subsampled signals;subtitles;text;adaptive filters;adaptive
signal processing;channel bank filters;data compression;filtering
theory;image coding;image reconstruction;image sampling;prediction
theory;},
owner = {duvall},
timestamp = {2011.04.08}
}
@BOOK{Golomb_S_1994_book_pol,
title = {Polyominoes},
publisher = {Princeton University Press},
year = {1994},
author = {Golomb, S.},
address = {Princeton},
edition = {2nd},
file = {Golomb_S_1994_book_pol.djvu:Golomb_S_1994_book_pol.djvu:Djvu},
isbn = {0691024448},
owner = {duvall},
timestamp = {2010.02.26}
}
@ARTICLE{Gopinath_R_2005_tsp_pha_f,
author = {Gopinath, R. A.},
title = {Phaselets of Framelets},
journal = j-ieee-tsp,
year = {2005},
volume = {53},
pages = {1794--1806},
number = {5},
month = {May},
owner = {duvall},
timestamp = {2007.06.21}
}
@ARTICLE{Gopinath_R_2003_tsp_pha_tirnsiwt,
author = {Gopinath, R. A.},
title = {The phaselet transform --- an integral redundancy nearly shift-invariant
wavelet transform},
journal = j-ieee-tsp,
year = {2003},
volume = {51},
pages = {1792--1805},
number = {7},
month = {Jul.},
file = {Gopinath_R_2003_tsp_pha_tirnsiwt.pdf:Gopinath_R_2003_tsp_pha_tirnsiwt.pdf:PDF},
owner = {duvall},
pdf = {Gopinath_R_2003_tsp_pha_tirnsiwt.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Goutsias_J_2000_j-ieee-tip_non_msds1mp,
author = {Goutsias, J. and Heijmans, H. J. A. M.},
title = {Nonlinear multiresolution signal decomposition schemes. I. {Morphological
pyramids}},
journal = j-ieee-tip,
year = {2000},
volume = {9},
pages = {1862--1876},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {Interest in multiresolution techniques for signal processing and analysis
is increasing steadily. An important instance of such a technique
is the so-called pyramid decomposition scheme. This paper presents
a general theory for constructing linear as well as nonlinear pyramid
decomposition schemes for signal analysis and synthesis. The proposed
theory is based on the following ingredients: 1) the pyramid consists
of a (finite or infinite) number of levels such that the information
content decreases toward higher levels and 2) each step toward a
higher level is implemented by an (information-reducing) analysis
operator, whereas each step toward a lower level is implemented by
an (information-preserving) synthesis operator. One basic assumption
is necessary: synthesis followed by analysis yields the identity
operator, meaning that no information is lost by these two consecutive
steps. Several examples of pyramid decomposition schemes are shown
to be instances of the proposed theory: a particular class of linear
pyramids, morphological skeleton decompositions, the morphological
Haar pyramid, median pyramids, etc. Furthermore, the paper makes
a distinction between single-scale and multiscale decomposition schemes,
i.e., schemes without or with sample reduction. Finally, the proposed
theory provides the foundation of a general approach to constructing
nonlinear wavelet decomposition schemes and filter banks},
doi = {10.1109/83.877209},
file = {Goutsias_J_2000_j-ieee-tip_non_msds1mp.pdf:Goutsias_J_2000_j-ieee-tip_non_msds1mp.pdf:PDF},
keywords = {filter banks;identity operator;images;information content;information-preserving
synthesis operator;information-reducing analysis operator;linear
pyramids;median pyramids;morphological Haar pyramid;morphological
pyramids;morphological skeleton decompositions;multiresolution techniques;multiscale
decomposition;nonlinear multiresolution signal decomposition schemes;nonlinear
wavelet decomposition schemes;pyramid decomposition scheme;sample
reduction;signal analysis;signal processing;single-scale decomposition;channel
bank filters;image resolution;mathematical morphology;mathematical
operators;transforms;},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Gouze_A_2004_j-ieee-tip_des_samlslc,
author = {Gouze, A. and Antonini, M. and Barlaud, M. and Macq, B.},
title = {Design of signal-adapted multidimensional lifting scheme for lossy
coding},
journal = j-ieee-tip,
year = {2004},
volume = {13},
pages = {1589--1603},
number = {12},
month = {Dec.},
issn = {1057-7149},
abstract = {This paper proposes a new method for the design of lifting filters
to compute a multidimensional nonseparable wavelet transform. Our
approach is stated in the general case, and is illustrated for the
2-D separable and for the quincunx images. Results are shown for
the JPEG2000 database and for satellite images acquired on a quincunx
sampling grid. The design of efficient quincunx filters is a difficult
challenge which has already been addressed for specific cases. Our
approach enables the design of less expensive filters adapted to
the signal statistics to enhance the compression efficiency in a
more general case. It is based on a two-step lifting scheme and joins
the lifting theory with Wiener's optimization. The prediction step
is designed in order to minimize the variance of the signal, and
the update step is designed in order to minimize a reconstruction
error. Application for lossy compression shows the performances of
the method.},
doi = {10.1109/TIP.2004.837556},
file = {Gouze_A_2004_j-ieee-tip_des_samlslc.pdf:Gouze_A_2004_j-ieee-tip_des_samlslc.pdf:PDF},
keywords = {biorthogonal wavelet transforms;image compression;image reconstruction;lifting
filters;lossy coding;nonseparable filtering;optimization;quincunx
images;satellite images;signal statistics;signal-adapted multidimensional
lifting scheme;channel coding;data compression;filtering theory;image
coding;image reconstruction;image sampling;multidimensional signal
processing;optimisation;prediction theory;statistics;telecommunication
channels;wavelet transforms;Algorithms;Artificial Intelligence;Computer
Graphics;Computer Simulation;Data Compression;Feedback;Hypermedia;Image
Enhancement;Image Interpretation, Computer-Assisted;Numerical Analysis,
Computer-Assisted;Reproducibility of Results;Sensitivity and Specificity;Signal
Processing, Computer-Assisted;},
owner = {duvall},
timestamp = {2010.11.12}
}
@MISC{Grossmann_A_1984_misc_dec_fwcsrt,
author = {A. Grossman and J. Morlet},
title = {Decompositions of Functions into Wavelets of Constant Shape, and
Related Transforms},
year = {1984},
note = {"Mathematics and Physics, Lectures on recent results", L. Streit,
ed., World Scientific Publishing Co., Singapore},
file = {Grossmann_A_1984_misc_dec_fwcsrt.pdf:Grossmann_A_1984_misc_dec_fwcsrt.pdf:PDF},
key = {wlet},
owner = {duvall},
pages = {135-165},
pdf = {Grossmann_A_1984_misc_dec_fwcsrt.pdf},
timestamp = {2009.03.21}
}
@ARTICLE{Guilloux_F_2009_j-acha_pra_wds,
author = {F. Guilloux and G. Fa{\"y} and J.-F. Cardoso},
title = {Practical wavelet design on the sphere},
journal = j-acha,
year = {2009},
volume = {26},
pages = {143--160},
number = {2},
issn = {1063-5203},
abstract = {This paper considers the design of isotropic analysis functions on
the sphere which are perfectly limited in the spectral domain and
optimally localized in the spatial domain. This is motivated by the
need of localized analysis tools in domains where the data is lying
on the sphere, e.g. the science of the Cosmic Microwave Background.
Our construction is derived from the localized frames introduced
by F. Narcowich et al. [F. Narcowich, P. Petrushev, J. Ward, Localized
tight frames on spheres, SIAM J. Math. Anal. 38 (2) (2006) 574-594].
The analysis frames are optimized for given applications and compared
numerically using various criteria.},
doi = {DOI: 10.1016/j.acha.2008.03.003},
file = {Guilloux_F_2009_j-acha_pra_wds.pdf:Guilloux_F_2009_j-acha_pra_wds.pdf:PDF},
keywords = {Wavelet frames; Wavelets on the sphere; Needlets; Slepian concentration
problem; Prolate spheroidal wave functions; Cosmic microwave background
analysis},
owner = {duvall},
pdf = {Guilloux_F_2009_j-acha_pra_wds.pdf},
timestamp = {2009.11.01},
url = {http://www.sciencedirect.com/science/article/B6WB3-4S62RSR-1/2/4efc6cf368a88710d74e68d414783415}
}
@ARTICLE{Guo_K_2007_j-siam-math-anal_opt_smrs,
author = {K. Guo and D. Labate},
title = {Optimally Sparse Multidimensional Representation using Shearlets},
journal = j-siam-math-anal,
year = {2007},
volume = {39},
pages = {298--318},
file = {Guo_K_2007_j-siam-math-anal_opt_smrs.pdf:Guo_K_2007_j-siam-math-anal_opt_smrs.pdf:PDF},
owner = {duvall},
pdf = {Guo_K_2007_j-siam-math-anal_opt_smrs.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Haar_A_1910_ma_zur_tofs,
author = {Haar, A.},
title = {Zur {Theory der orthogalen Funktionen Systeme}},
journal = j-math-annalen,
year = {1910},
volume = {69},
pages = {331--371},
file = {Haar_A_1910_ma_zur_tofs.pdf:Haar_A_1910_ma_zur_tofs.pdf:PDF;:Haar_A_1910_ma_zur_tofs.ps:PostScript},
owner = {duvall},
pdf = {Haar_A_1910_ma_zur_tofs.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Hahn_S_1992_proc-ieee_mul_cssos,
author = {Hahn, S. L.},
title = {Multidimensional complex signals with single-orthant spectra},
journal = j-proc-ieee,
year = {1992},
volume = {80},
pages = {1287--1300},
number = {8},
month = {Aug.},
abstract = {An extension of the notion of the analytical signal to multidimensional
signals is presented. The real and imaginary parts of this signal
are a linear combination of the original signal and of its complete
and partial Hilbert transforms. Its Fourier image exists only in
one orthant of the multidimensional frequency space. The orthant
is a half-axis in one dimension, a quadrant in two dimensions, an
octant in three dimensions, etc. A multidimensional complex signal
makes it possible to introduce the definitions of instantaneous amplitude,
instantaneous phase, and partial instantaneous complex frequencies
(partial derivatives of the instantaneous phase) and to formulate
a modulation theory of a multidimensional harmonic carrier. The 2-D
equivalent of 1-D single-sideband modulation is defined and called
single quadrant modulation. It is shown that the multidimensional
complex signal with a signal orthant spectrum may be defined as a
convolution of the real signal with the multidimensional complex
delta distribution},
doi = {10.1109/5.158601},
file = {Hahn_S_1992_proc-ieee_mul_cssos.pdf:Hahn_S_1992_proc-ieee_mul_cssos.pdf:PDF},
owner = {duvall},
pdf = {Hahn_S_1992_proc-ieee_mul_cssos.pdf},
timestamp = {2007.06.20}
}
@ARTICLE{Hammond_2011_j-acha_wav_gsgt,
author = {D. K. Hammond and P. Vandergheynst and R. Gribonval},
title = {Wavelets on graphs via spectral graph theory},
journal = j-acha,
year = {2011},
volume = {30},
pages = {129--150},
number = {2},
month = {Mar.},
abstract = {We propose a novel method for constructing wavelet transforms of functions
defined on the vertices of an arbitrary finite weighted graph. Our
approach is based on defining scaling using the graph analogue of
the Fourier domain, namely the spectral decomposition of the discrete
graph Laplacian L. Given a wavelet generating kernel g and a scale
parameter t, we define the scaled wavelet operator Ttg = g(tL). The
spectral graph wavelets are then formed by localizing this operator
by applying it to an indicator function. Subject to an admissibility
condition on g, this procedure defines an invertible transform. We
explore the localization properties of the wavelets in the limit
of fine scales. Additionally, we present a fast Chebyshev polynomial
approximation algorithm for computing the transform that avoids the
need for diagonalizing L. We highlight potential applications of
the transform through examples of wavelets on graphs corresponding
to a variety of different problem domains.},
doi = {10.1016/j.acha.2010.04.005},
file = {Hammond_2011_j-acha_wav_gsgt.pdf:Hammond_2011_j-acha_wav_gsgt.pdf:PDF},
keywords = {Graph theory; Wavelets; Spectral graph theory; Overcomplete wavelet
frames},
owner = {duvall},
timestamp = {2011.04.05}
}
@ARTICLE{Hampson_F_1998_j-ieee-tip_m_bnsdpr,
author = {F. J. Hampson and J.-C. Pesquet},
title = {$M$-band Nonlinear Subband Decompositions with Perfect Reconstruction},
journal = j-ieee-tip,
year = {1998},
volume = {7},
pages = {1547--1560},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {We investigate nonlinear multirate filterbanks with maximal decimation
and perfect reconstruction. Definitions of the desired properties
of such structures are given for general nonlinear filterbanks. We
then consider a triangular representation of linear filterbanks and
see that it may be easily extended to the nonlinear case. Furthermore,
general nonlinear filterbanks are presented, for which perfect reconstruction
is either inherently guaranteed or ensured subject to an easily verified
condition. Extensions to bidimensional filters are also discussed
and an application for nonlinear multiresolution schemes to feature
sieves is shown},
doi = {10.1109/83.725362},
file = {Hampson_F_1998_j-ieee-tip_m_bnsdpr.pdf:Hampson_F_1998_j-ieee-tip_m_bnsdpr.pdf:PDF},
keywords = {M-band nonlinear subband decompositions;bidimensional filters;decimation;images;linear
filterbanks;multirate filterbanks;nonlinear filterbanks;nonlinear
multiresolution schemes;perfect reconstruction;sieves;triangular
representation;image reconstruction;image resolution;nonlinear filters;two-dimensional
digital filters;},
owner = {duvall},
timestamp = {2011.04.08}
}
@ARTICLE{Healy_D_2003_j-four-anal-appl_fft_2siv,
author = {D. M. Healy and D. N. Rockmore and P. J. Kostelec and S. Moore},
title = {{FFT}s for the 2-Sphere --- Improvements and Variations},
journal = j-four-anal-appl,
year = {2003},
volume = {9},
pages = {341--385},
number = {4},
date-added = {2009-10-17 16:23:14 +0200},
date-modified = {2009-10-21 15:58:08 +0200},
owner = {duvall},
rating = {0},
timestamp = {2011.01.05},
uri = {papers://C319F6DA-DBA8-4257-A9FA-3BDE437CA713/Paper/p10}
}
@INPROCEEDINGS{Heeger_D_1995_p-acm-siggraph_pyr_btas,
author = {D. J. Heeger and J. R. Bergen},
title = {Pyramid-Based Texture Analysis/Synthesis},
booktitle = p-acm-siggraph,
year = {1995},
editor = {Robert Cook},
pages = {229--238},
month = {Aug.},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Heijmans_H_2000_j-ieee-tip_non_msds2mw,
author = {Heijmans, H. J. A. M. and Goutsias, J.},
title = {Nonlinear multiresolution signal decomposition schemes. II. {Morphological
wavelets}},
journal = j-ieee-tip,
year = {2000},
volume = {9},
pages = {1897--1913},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {For pt.I see ibid., vol.9, no.11, p.1862-76 (2000). In its original
form, the wavelet transform is a linear tool. However, it has been
increasingly recognized that nonlinear extensions are possible. A
major impulse to the development of nonlinear wavelet transforms
has been given by the introduction of the lifting scheme by Sweldens
(1995, 1996, 1998). The aim of this paper, which is a sequel to a
previous paper devoted exclusively to the pyramid transform, is to
present an axiomatic framework encompassing most existing linear
and nonlinear wavelet decompositions. Furthermore, it introduces
some, thus far unknown, wavelets based on mathematical morphology,
such as the morphological Haar wavelet, both in one and two dimensions.
A general and flexible approach for the construction of nonlinear
(morphological) wavelets is provided by the lifting scheme. This
paper briefly discusses one example, the max-lifting scheme, which
has the intriguing property that preserves local maxima in a signal
over a range of scales, depending on how local or global these maxima
are},
doi = {10.1109/83.877211},
file = {Heijmans_H_2000_j-ieee-tip_non_msds2mw.pdf:Heijmans_H_2000_j-ieee-tip_non_msds2mw.pdf:PDF},
keywords = {axiomatic framework;lifting scheme;mathematical morphology;max-lifting
scheme;morphological Haar wavelet;morphological wavelets;nonlinear
extension;nonlinear multiresolution signal decomposition schemes;wavelet
decompositions;wavelet transform;Haar transforms;channel bank filters;image
resolution;mathematical morphology;nonlinear filters;wavelet transforms;},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Heijmans_H_2005_j-acha_bui_nawul,
author = {Heijmans, H. J. A. M. and B. Pesquet-Popescu and G. Piella},
title = {Building nonredundant adaptive wavelets by update lifting},
journal = j-acha,
year = {2005},
volume = {18},
pages = {252--281},
number = {3},
month = {May},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Helbert_D_2006_tip_3d_dart,
author = {D. Helbert and P. Carr{\'e} and {\'E}. Andr{\`e}s},
title = {{3-D} Discrete Analytical Ridgelet Transform},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {3701--3714},
number = {12},
abstract = {In this paper, we propose an implementation of the 3-D Ridgelet transform:
the 3-D discrete analytical Ridgelet transform (3-D DART). This transform
uses the Fourier strategy for the computation of the associated 3-D
discrete Radon transform. The innovative step is the definition of
a discrete 3-D transform with the discrete analytical geometry theory
by the construction of 3-D discrete analytical lines in the Fourier
domain. We propose two types of 3-D discrete lines: 3-D discrete
radial lines going through the origin defined from their orthogonal
projections and 3-D planes covered with 2-D discrete line segments.
These discrete analytical lines have a parameter called arithmetical
thickness, allowing us to define a 3-D DART adapted to a specific
application. Indeed, the 3-D DART representation is not orthogonal,
It is associated with a flexible redundancy factor. The 3-D DART
has a very simple forward/inverse algorithm that provides an exact
reconstruction without any iterative method. In order to illustrate
the potentiality of this new discrete transform, we apply the 3-D
DART and its extension to the Local-DART (with smooth windowing)
to the denoising of 3-D image and color video. These experimental
results show that the simple thresholding of the 3-D DART coefficients
is efficient.},
file = {Helbert_D_2006_tip_3d_dart.pdf:Helbert_D_2006_tip_3d_dart.pdf:PDF},
owner = {duvall},
pdf = {Helbert_D_2006_tip_3d_dart.pdf},
timestamp = {2009.10.20}
}
@ARTICLE{Held_S_2010_j-ieee-tip_ste_wfrt,
author = {Held, S. and Storath, M. and Massopust, P. and Forster, B.},
title = {Steerable Wavelet Frames Based on the {Riesz} Transform},
journal = j-ieee-tip,
year = {2010},
volume = {19},
pages = {653--667},
number = {3},
month = {Mar. },
issn = {1057-7149},
abstract = { We consider an extension of the 1-D concept of analytical wavelet
to $n$-D which is by construction compatible with rotations. This
extension, called a monogenic wavelet, yields a decomposition of
the wavelet coefficients into amplitude, phase, and phase direction.
The monogenic wavelet is based on the hypercomplex monogenic signal
which is defined using Riesz transforms and perfectly isotropic wavelets
frames. Employing the new concept of Clifford frames, we can show
that the monogenic wavelet generates a wavelet frame. Furthermore,
this approach yields wavelet frames that are steerable with respect
to direction. Applications to descreening and contrast enhancement
illustrate the versatility of this approach to image analysis and
reconstruction. },
doi = {10.1109/TIP.2009.2036713},
file = {Held_S_2010_j-ieee-tip_ste_wfrt.pdf:Held_S_2010_j-ieee-tip_ste_wfrt.pdf:PDF},
owner = {duvall},
pdf = {Held_S_2010_j-ieee-tip_ste_wfrt.pdf},
timestamp = {2010.02.23}
}
@TECHREPORT{Hildreth_E_1980_tr_imp_ted,
author = {Hildreth, E. C.},
title = {Implementation of a Theory of Edge Detection},
institution = {MIT, Artificial Intelligence Lab},
year = {1980},
number = {AITR-579},
month = {Apr.},
abstract = {This report describes the implementation of a theory of edge detection,
proposed by Marr and Hildreth (1979). According to this theory, the
image is first processed independently through a set of different
size filters, whose shape is the Laplacian of a Gaussian, ***. Zero-crossings
in the output of these filters mark the positions of intensity changes
at different resolutions. Information about these zero-crossings
is then used for deriving a full symbolic description of changes
in intensity in the image, called the raw primal sketch. The theory
is closely tied with early processing in the human visual systems.
In this report, we first examine the critical properties of the initial
filters used in the edge detection process, both from a theoretical
and practical standpoint. The implementation is then used as a test
bed for exploring aspects of the human visual system; in particular,
acuity and hyperacuity. Finally, we present some preliminary results
concerning the relationship between zero-crossings detected at different
resolutions, and some observations relevant to the process by which
the human visual system integrates descriptions of intensity changes
obtained at different resolutions},
file = {Hildreth_E_1980_tr_imp_ted.pdf:Hildreth_E_1980_tr_imp_ted.pdf:PDF},
owner = {duvall},
pdf = {Hildreth_E_1980_tr_imp_ted.pdf},
timestamp = {2009.07.31}
}
@BOOK{Holscheider_M_1995_book_wav_at,
title = {Wavelets, an analysis tool},
publisher = {Oxford Science Publications},
year = {1995},
author = {Holschneider, M.},
owner = {duvall},
timestamp = {2009.07.14}
}
@ARTICLE{Jacques_L_2007_j-ijwmip_mul_pdiwaas,
author = {Jacques, L. and Antoine, J.-P.},
title = {Multiselective Pyramidal Decomposition of Images: wavelets with Adaptive
Angular Selectivity},
journal = j-ijwmip,
year = {2007},
volume = {5},
pages = {785--814},
number = {5},
abstract = {Many techniques have been devised these last ten years to add an appropriate
directionality concept in decompositions of images from the specific
transformations of a small set of atomic functions. Let us mention,
for instance, works on directional wavelets, steerable filters, dual-tree
wavelet transform, curvelets, wave atoms, ridgelet packets, etc.
In general, features that are best represented are straight lines
or smooth curves as those defining contours of objects (e.g. in curvelets
processing) or oriented textures (e.g. wave atoms, ridgelet packets).
However, real images present also a set of details less oriented
and more isotropic, like corners, spots, texture components, etc.
This paper develops an adaptive representation for all these image
elements, ranging from highly directional ones to fully isotropic
ones. This new tool can indeed be tuned relatively to these image
features by decomposing them into a Littlewood?Paley frame of directional
wavelets with variable angular selectivity. Within such a decomposition,
2D wavelets inherit some particularities of the biorthogonal circular
multiresolution framework in their angular behavior. Our method can
therefore be seen as an angular multiselectivity analysis of images.
Two applications of the proposed method are given at the end of the
paper, namely, in the fields of image denoising and N-term nonlinear
approximation.},
doi = {10.1142/S0219691307002051},
file = {Jacques_L_2007_j-ijwmip_mul_pdiwaas.pdf:Jacques_L_2007_j-ijwmip_mul_pdiwaas.pdf:PDF},
owner = {duvall},
pdf = {Jacques_L_2007_j-ijwmip_mul_pdiwaas.pdf},
timestamp = {2007.09.17}
}
@MISC{Jacques_L_2011_url_panorama_addendum,
author = {L. Jacques and L. Duval and C. Chaux and G. Peyr\'e},
title = {Addendum to ``{A} panorama on multiscale geometric representations,
intertwining spatial, directional and frequency selectivity''},
year = {2011},
note = {\url{http://www.laurent-duval.eu/siva-panorama-multiscale-geometric-representations.html}},
annote = {Addendum to \cite{Jacques_L_2011_j-sp_pan_mgrisdfs}},
owner = {duvall},
timestamp = {2010.02.28}
}
@ARTICLE{Jacques_L_2008_j-ieee-tip_geo_smpp,
author = {Jacques, L. and Vleeschouwer, C. D.},
title = {A Geometrical Study of Matching Pursuit Parametrization},
journal = j-ieee-tip,
year = {2008},
volume = {56},
pages = {2835--2848},
number = {7},
month = {Jul.},
owner = {duvall},
publisher = {New York, NY: Institute of Electrical and Electronics Engineers,
c1991-},
timestamp = {2011.01.05}
}
@INPROCEEDINGS{Jalobeanu_A_2001_p-icip_ima_deconv,
author = {Jalobeanu, A. and Kingsbury, N. and Zerubia, J.},
title = {Image deconvolution using hidden {Markov} tree modeling of complex
wavelet packets},
booktitle = p-icip,
year = {2001},
volume = {1},
pages = {201--204},
address = {Thessaloniki, Greece},
file = {Jalobeanu_A_2001_p-icip_ima_deconv.pdf:Jalobeanu_A_2001_p-icip_ima_deconv.pdf:PDF},
owner = {duvall},
pdf = {Jalobeanu_A_2001_p-icip_ima_deconv.pdf},
timestamp = {2010.08.27}
}
@ARTICLE{Jansen_M_2005_j-acha_mul_apstdfntm,
author = {M. Jansen and R. G. Baraniuk and S. Lavu},
title = {Multiscale Approximation of Piecewise Smooth Two-Dimensional Function
using Normal Triangulated Meshes},
journal = j-acha,
year = {2005},
volume = {19},
pages = {92--130},
number = {1},
month = {Jul.},
abstract = {Multiresolution triangulation meshes are widely used in computer graphics
for representing three-dimensional(3-d) shapes. We propose to use
these tools to represent 2-d piecewise smooth functions such as grayscale
images,because triangles have potential to more efficiently approximate
the discontinuities between the smooth pieces than other standard
tools like wavelets. We show that normal mesh subdivision is an efficient
triangulation, thanks to its local adaptivity to the discontinuities.
Indeed, we prove that, within a certain function class, the normal
mesh representation has an optimal asymptotic error decay rate as
the number of terms in the representation grows. This function class
is the so-called horizon class comprising constant regions separated
by smooth discontinuities,where the line of discontinuity is C2 continuous.
This optimal decay rate is possible because normal meshes automatically
generate a polyline (piecewise linear) approximation of each discontinuity,
unlike the blocky piecewise constant approximation of tensor product
wavelets. In this way, the proposed nonlinear multiscale normal mesh
decomposition is an anisotropic representation of the 2-d function.
The same idea of anisotropic representations lies at the basis of
decompositions such as wedgelet and curvelet transforms, but the
proposed normal mesh approach has a unique construction.},
file = {Jansen_M_2005_j-acha_mul_apstdfntm.pdf:Jansen_M_2005_j-acha_mul_apstdfntm.pdf:PDF},
owner = {duvall},
pdf = {Jansen_M_2005_j-acha_mul_apstdfntm.pdf},
timestamp = {2010.02.16}
}
@ARTICLE{Kaaniche_M_2011_PREPRINT_non_slsausssic,
author = {K\^aaniche, M. and Benazza-Benyahia, A. and Pesquet-Popescu, B. and
Pesquet, J.-C.},
title = {Non separable lifting scheme with adaptive update step for still
and stereo image coding},
journal = j-sp,
year = {2011},
note = {In press},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Kaaniche_M_2009_j-ieee-tip_vec_lssic,
author = {K\^aaniche, M. and Benazza-Benyahia, A. and Pesquet-Popescu, B. and
Pesquet, J.-C.},
title = {Vector Lifting Schemes for Stereo Image Coding},
journal = j-ieee-tip,
year = {2009},
volume = {18},
pages = {2463--2475},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {Many research efforts have been devoted to the improvement of stereo
image coding techniques for storage or transmission. In this paper,
we are mainly interested in lossy-to-lossless coding schemes for
stereo images allowing progressive reconstruction. The most commonly
used approaches for stereo compression are based on disparity compensation
techniques. The basic principle involved in this technique first
consists of estimating the disparity map. Then, one image is considered
as a reference and the other is predicted in order to generate a
residual image. In this paper, we propose a novel approach, based
on vector lifting schemes (VLS), which offers the advantage of generating
two compact multiresolution representations of the left and the right
views. We present two versions of this new scheme. A theoretical
analysis of the performance of the considered VLS is also conducted.
Experimental results indicate a significant improvement using the
proposed structures compared with conventional methods.},
doi = {10.1109/TIP.2009.2026672},
file = {Kaaniche_M_2009_j-ieee-tip_vec_lssic.pdf:Kaaniche_M_2009_j-ieee-tip_vec_lssic.pdf:PDF},
keywords = {disparity compensation;disparity map estimation;lossy-to-lossless
coding;progressive reconstruction;stereo compression;stereo image
coding;vector lifting scheme;image coding;image reconstruction;stereo
image processing;vectors;},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Kassim_A_2009_j-ieee-tip_hie_sbichqbt,
author = {Kassim, A. A. and W. S. Lee and Zonoobi, D.},
title = {Hierarchical Segmentation-Based Image Coding Using Hybrid Quad-Binary
Trees},
journal = j-ieee-tip,
year = {2009},
volume = {18},
pages = {1284--291},
number = {6},
month = {Jun. },
issn = {1057-7149},
abstract = {A novel segmentation-based image approximation and coding technique
is proposed. A hybrid quad-binary (QB) tree structure is utilized
to efficiently model and code geometrical information within images.
Compared to other tree-based representation such as wedgelets, the
proposed QB-tree based method is more efficient for a wide range
of contour features such as junctions, corners and ridges, especially
at low bit rates.},
doi = {10.1109/TIP.2009.2017339},
file = {Kassim_A_2009_j-ieee-tip_hie_sbichqbt.pdf:Kassim_A_2009_j-ieee-tip_hie_sbichqbt.pdf:PDF},
keywords = {code geometrical information;hierarchical image segmentation;hybrid
quad-binary trees;image approximation;image coding;approximation
theory;binary codes;image coding;image segmentation;quadtrees;},
owner = {duvall},
pdf = {Kassim_A_2009_j-ieee-tip_hie_sbichqbt.pdf},
timestamp = {2010.02.16}
}
@ARTICLE{Kerkyacharian_G_2007_j-elec-j-stat_nee_aeip,
author = {G. Kerkyacharian and P. Petrushev and D. Picard and T. Willer},
title = {Needlet algorithms for estimation in inverse problems},
journal = j-electron-j-stat,
year = {2007},
volume = {1},
pages = {30--76},
abstract = {We provide a new algorithm for the treatment of inverse problems which
combines the traditional SVD inversion with an appropriate thresholding
technique in a well chosen new basis. Our goal is to devise an inversion
procedure which has the advantages of localization and multiscale
analysis of wavelet representations without losing the stability
and computability of the SVD decompositions. To this end we utilize
the construction of localized frames (termed "needlets") built upon
the SVD bases. We consider two different situations: the "wavelet"
scenario, where the needlets are assumed to behave similarly to true
wavelets, and the "Jacobi-type" scenario, where we assume that the
properties of the frame truly depend on the SVD basis at hand (hence
on the operator). To illustrate each situation, we apply the estimation
algorithm respectively to the deconvolution problem and to the Wicksell
problem. In the latter case, where the SVD basis is a Jacobi polynomial
basis, we show that our scheme is capable of achieving rates of convergence
which are optimal in the $L_2$ case, we obtain interesting rates
of convergence for other $L_p$ norms which are new (to the best of
our knowledge) in the literature, and we also give a simulation study
showing that the NEED-D estimator outperforms other standard algorithms
in almost all situations.},
owner = {duvall},
timestamp = {2009.11.01},
url = {doi:10.1214/07-EJS014}
}
@BOOK{King_F_2009_book_hil_t,
title = {Hilbert Transforms},
publisher = {Cambridge University Press},
year = {2009},
author = {King, F. W.},
volume = {125},
series = {Encyclopedia Of Mathematics And Its Applications},
abstract = {The Hilbert transform has many uses, including solving problems in
aerodynamics, condensed matter physics, optics, fluids, and engineering.
Written in a style that will suit a wide audience (including the
physical sciences), this book will become the reference of choice
on the topic, whatever the subject background of the reader. It explains
all the common Hilbert transforms, mathematical techniques for evaluating
them, and has detailed discussions of their application. Especially
useful for researchers are the tabulation of analytically evaluated
Hilbert transforms, and an atlas that immediately illustrates how
the Hilbert transform alters a function. A collection of exercises
helps the reader to test their understanding of the material in each
chapter. The bibliography is a wide-ranging collection of references
both to the classical mathematical papers, and to a diverse array
of applications.},
file = {King_F_2009_book_hil_t-vol1.pdf:King_F_2009_book_hil_t-vol1.pdf:PDF;King_F_2009_book_hil_t-vol2.pdf:King_F_2009_book_hil_t-vol2.pdf:PDF},
owner = {duvall},
pdf = {King_F_2009_book_hil_t-vol1.pdf},
timestamp = {2009.07.24}
}
@ARTICLE{Kingsbury_N_1999_j-phil-trans-roy-soc-lond-a_ima_pcw,
author = {Kingsbury, N. G.},
title = {Image Processing with Complex Wavelets},
journal = j-phil-trans-roy-soc-lond-a,
year = {1999},
volume = {357},
pages = {2543--2560},
abstract = {We first review how wavelets may be used for multi-resolution image
processing, describing the filter-bank implementation of the discrete
wavelet transform (DWT) and how it may be extended via separable
filtering for processing images and other multi-dimensional signals.
We then show that the condition for inversion of the DWT (perfect
reconstruction) forces many commonly used wavelets to be similar
in shape, and that this shape produces severe shift dependence (variation
of DWTco efficient energy at any given scale with shift of the input
signal). It is also shown that separable filtering with the DWTprev
ents the transform from providing directionally selective filters
for diagonal image features. Complex wavelets can provide both shift
invariance and good directional selectivity, with only modest increases
in signal redundancy and computation load. However, development of
a complex wavelet transform (CWT) with perfect reconstruction and
good filter characteristics has proved difficult until recently.
We now propose the dual-tree CWTas a solution to this problem, yielding
a transform with attractive properties for a range of signal and
image processing applications, including motion estimation, denoising,
texture analysis and synthesis, and object segmentation.},
file = {Kingsbury_N_1999_j-phil-trans-roy-soc-lond-a_ima_pcw.pdf:Kingsbury_N_1999_j-phil-trans-roy-soc-lond-a_ima_pcw.pdf:PDF},
keywords = {image processing; wavelets; shift invariance; directional filters;
perfect reconstruction; complex filters},
owner = {duvall},
pdf = {Kingsbury_N_1999_j-phil-trans-roy-soc-lond-a_ima_pcw.pdf},
timestamp = {2008.04.11}
}
@INPROCEEDINGS{Kingsbury_N_1998_p-ieee-dspw_dua_tcwtntsidf,
author = {Kingsbury, N. G.},
title = {The dual-tree complex wavelet transform: a new technique for shift
invariance and directional filters},
booktitle = p-ieee-dspw,
year = {1998},
address = {Bryce Canyon, UT, USA},
month = {Aug. 9-12,},
annote = {number = {86},},
file = {Kingsbury_N_1998_p-ieee-dspw_dua_tcwtntsidf.ps:Kingsbury_N_1998_p-ieee-dspw_dua_tcwtntsidf.ps:PostScript},
owner = {duvall},
timestamp = {2007.06.07}
}
@ARTICLE{Kittipoom_P_2010_j-four-anal-appl_irr_sfgap,
author = {Kittipoom, P. and Kutyniok, G. and Lim, W.-Q.},
title = {Irregular Shearlet Frames: Geometry and Approximation Properties},
journal = j-four-anal-appl,
year = {2010},
pages = {1--36},
issn = {1069-5869},
abstract = {Recently, shearlet systems were introduced as a means to derive efficient
encoding methodologies for anisotropic features in 2-dimensional
data with a unified treatment of the continuum and digital setting.
However, only very few construction strategies for discrete shearlet
systems are known so far. In this paper, we take a geometric approach
to this problem. Utilizing the close connection with group representations,
we first introduce and analyze an upper and lower weighted shearlet
density based on the shearlet group. We then apply this geometric
measure to provide necessary conditions on the geometry of the sets
of parameters for the associated shearlet systems to form a frame
for $L^2(\mathbb{R}^2)$, either when using all possible generators
or a large class exhibiting some decay conditions. While introducing
such a feasible class of shearlet generators, we analyze approximation
properties of the associated shearlet systems, which themselves lead
to interesting insights into homogeneous approximation abilities
of shearlet frames. We also present examples, such as oversampled
shearlet systems and co-shearlet systems, to illustrate the usefulness
of our geometric approach to the construction of shearlet frames.},
doi = {10.1007/s00041-010-9163-0},
file = {Kittipoom_P_2010_j-four-anal-appl_irr_sfgap.pdf:Kittipoom_P_2010_j-four-anal-appl_irr_sfgap.pdf:PDF},
keyword = {Mathematics and Statistics},
owner = {duvall},
publisher = {Birkhäuser Boston},
timestamp = {2011.03.04},
url = {http://dx.doi.org/10.1007/s00041-010-9163-0}
}
@ARTICLE{Knutsson_H_2005_j-spic_imp_iulsafs,
author = {Knutsson, H. and Andersson, M.},
title = {Implications of invariance and uncertainty for local structure analysis
filter sets},
journal = j-spic,
year = {2005},
volume = {20},
pages = {569--581},
abstract = {The paper discusses which properties of filter sets used in local
structure estimation that are the most important. Answers are provided
via the introduction of a number of fundamental invariances. Mathematical
formulations corresponding to the required invariances leads up to
the introduction of a new class of filter sets termed loglets. Loglets
are polar separable and have excellent uncertaintyproperties. The
directional part uses a spherical harmonics basis. Using loglets
it is shown how the concepts of quadrature and phase can be defined
in n-dimensions. It is also shown how a reliable measure of the certaintyof
the estimate can be obtained byfinding the deviation from the signal
model manifold. Local structure analysis algorithms are quite complex
and involve a lot more than the filters used. This makes comparisons
difficult to interpret from a filter point of view. To reduce the
number ?free? parameters and target the filter design aspects a number
of simple 2D experiments have been carried out. The evaluation supports
the claim that loglets are preferable to other designs. In particular
it is demonstrated that the loglet approach outperforms a Gaussian
derivative approach in resolution and robustness.},
file = {Knutsson_H_2005_j-spic_imp_iulsafs.pdf:Knutsson_H_2005_j-spic_imp_iulsafs.pdf:PDF},
owner = {duvall},
pdf = {Knutsson_H_2005_j-spic_imp_iulsafs.pdf},
timestamp = {2009.10.23}
}
@ARTICLE{Kovacevic_J_2007_ieee-spm_lif_bbaf1,
author = {Kova{\v{c}}evi{\'c}, J. and Chebira, A.},
title = {Life beyond bases: The advent of frames (Part {I})},
journal = j-ieee-spm,
year = {2007},
pages = {86--104},
month = {Jul.},
file = {Kovacevic_J_2007_ieee-spm_lif_bbaf1.pdf:Kovacevic_J_2007_ieee-spm_lif_bbaf1.pdf:PDF},
owner = {duvall},
pdf = {Kovacevic_J_2007_ieee-spm_lif_bbaf1.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Kovacevic_J_2007_ieee-spm_lif_bbaf2,
author = {Kova{\v{c}}evi{\'c}, J. and Chebira, A.},
title = {Life beyond bases: The advent of frames (Part {II})},
journal = j-ieee-spm,
year = {2007},
pages = {115--125},
month = {Sep.},
file = {Kovacevic_J_2007_ieee-spm_lif_bbaf2.pdf:Kovacevic_J_2007_ieee-spm_lif_bbaf2.pdf:PDF},
owner = {duvall},
pdf = {Kovacevic_J_2007_ieee-spm_lif_bbaf2.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Kovacevic_J_1995_tsp_non_ttdw,
author = {Kova{\v{c}}evi{\'c}, J. and Vetterli, M.},
title = {Nonseparable two- and three-dimensional wavelets},
journal = j-ieee-tsp,
year = {1995},
volume = {43},
pages = {1269--1273},
number = {5},
month = {May},
file = {Kovacevic_J_1995_tsp_non_ttdw.pdf:Kovacevic_J_1995_tsp_non_ttdw.pdf:PDF},
owner = {duvall},
pdf = {Kovacevic_J_1995_tsp_non_ttdw.pdf},
timestamp = {2007.12.13}
}
@ARTICLE{Kovacevic_J_1992_tit_non_mprfbwbrn,
author = {Kova{\v{c}}evi{\'c}, J. and Vetterli, M.},
title = {Nonseparable Multidimensional Perfect Reconstruction Filters Banks
and Wavelets Bases for {${\mathbb{R}}^n$}},
journal = j-ieee-tit,
year = {1992},
volume = {38},
pages = {533--555},
number = {2},
month = {Mar.},
file = {Kovacevic_J_1992_tit_non_mprfbwbrn.pdf:Kovacevic_J_1992_tit_non_mprfbwbrn.pdf:PDF},
owner = {duvall},
pdf = {Kovacevic_J_1992_tit_non_mprfbwbrn.pdf},
timestamp = {2009.07.14}
}
@ARTICLE{Krommweh_J_2009_j-acha_dir_hwft,
author = {J. Krommweh and G. Plonka},
title = {Directional {Haar} wavelet frames on triangles},
journal = j-acha,
year = {2009},
volume = {27},
pages = {215--234},
number = {2},
issn = {1063-5203},
abstract = {Traditional wavelets are not very effective in dealing with images
that contain orientated discontinuities (edges). To achieve a more
efficient representation one has to use basis elements with much
higher directional sensitivity. In recent years several approaches
like curvelets and shearlets have been studied providing essentially
optimal approximation properties for images that are piecewise smooth
and have discontinuities along C2-curves. While curvelets and shearlets
have compact support in frequency domain, we construct directional
wavelet frames generated by functions with compact support in time
domain. Our Haar wavelet constructions can be seen as special composite
dilation wavelets, being based on a generalized multiresolution analysis
(MRA) associated with a dilation matrix and a finite collection of
[`]shear' matrices. The complete system of constructed wavelet functions
forms a Parseval frame. Based on this MRA structure we provide an
efficient filter bank algorithm. The freedom obtained by the redundancy
of the applied Haar functions will be used for an efficient sparse
representation of piecewise constant images as well as for image
denoising.},
doi = {DOI: 10.1016/j.acha.2009.03.002},
file = {Krommweh_J_2009_j-acha_dir_hwft.pdf:Krommweh_J_2009_j-acha_dir_hwft.pdf:PDF},
keywords = {Haar wavelet frames; Non-separable wavelets; Composite dilation wavelets;
Dual frames; Sparse representation; Image denoising},
owner = {duvall},
pdf = {Krommweh_J_2009_j-acha_dir_hwft.pdf},
timestamp = {2009.12.08},
url = {http://www.sciencedirect.com/science/article/B6WB3-4VXMPVH-1/2/164801f99390b93b7838b6eabdce65ce}
}
@ARTICLE{Kutyniok_G_2007_j-wavelet-theory-appl_con_risf,
author = {G. Kutyniok and D. Labate},
title = {The construction of regular and irregular shearlet frames},
journal = {J. Wavelet Theory Appl.},
year = {2007},
volume = {1},
pages = {1--10},
file = {Kutyniok_G_2007_j-wavelet-theory-appl_con_risf.pdf:Kutyniok_G_2007_j-wavelet-theory-appl_con_risf.pdf:PDF},
owner = {duvall},
timestamp = {2011.03.24}
}
@ARTICLE{LePennec_E_2005_j-siam-mms_ban_ac,
author = {Le Pennec, E. and Mallat, S.},
title = {Bandelet image approximation and compression},
journal = j-siam-mms,
year = {2005},
volume = {4},
pages = {992--1039},
number = {3},
abstract = {Finding efficient geometric representations of images is a central
issue to improving image compression and noise removal algorithms.
We introduce bandelet orthogonal bases and frames that are adapted
to the geometric regularity of an image. Images are approximated
by finding a best bandelet basis or frame that produces a sparse
representation. For functions that are uniformly regular outside
a set of edge curves that are geometrically regular, the main theorem
proves that bandelet approximations satisfy an optimal asymptotic
error decay rate. A bandelet image compression scheme is derived.
For computational applications, a fast discrete bandelet transform
algorithm is introduced, with a fast best basis search which preserves
asymptotic approximation and coding error decay rates.},
doi = {http://dx.doi.org/10.1137/040619454},
file = {LePennec_E_2005_j-siam-mms_ban_ac.pdf:LePennec_E_2005_j-siam-mms_ban_ac.pdf:PDF},
keywords = {wavelets; bandelets; geometric representation; nonlinear approximation},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Lee_T_1996_j-ieee-tpami_ima_r2dgw,
author = {T. S. Lee},
title = {Image Representation Using {2D} {Gabor} Wavelets},
journal = j-ieee-tpami,
year = {1996},
volume = {18},
pages = {959--971},
number = {10},
month = {Oct.},
issn = {0162-8828},
abstract = {This paper extends to two dimensions the frame criterion developed
by Daubechies for one-dimensional wavelets, and it computes the frame
bounds for the particular case of 2D Gabor wavelets. Completeness
criteria for 2D Gabor image representations are important because
of their increasing role in many computer vision applications and
also in modeling biological vision, since recent neurophysiological
evidence from the visual cortex of mammalian brains suggests that
the filter response profiles of the main class of linearly-responding
cortical neurons (called simple cells) are best modeled as a family
of self-similar 2D Gabor wavelets. We therefore derive the conditions
under which a set of continuous 2D Gabor wavelets will provide a
complete representation of any image, and we also find self-similar
wavelet parametrization which allow stable reconstruction by summation
as though the wavelets formed an orthonormal basis. Approximating
a ldquo;tight frame rdquo; generates redundancy which allows low-resolution
neural responses to represent high-resolution images},
address = {Los Alamitos, CA, USA},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.541406},
file = {Lee_T_1996_j-ieee-tpami_ima_r2dgw.pdf:Lee_T_1996_j-ieee-tpami_ima_r2dgw.pdf:PDF},
keywords = {2D Gabor wavelets;coarse coding;computer vision;frame bounds;frame
criterion;image reconstruction;image representation;neurophysiology;self-similar
wavelet parametrization;visual cortex;computer vision;image coding;image
reconstruction;image representation;neurophysiology;wavelet transforms;},
owner = {duvall},
pdf = {Lee_T_1996_j-ieee-tpami_ima_r2dgw.pdf},
publisher = {IEEE Computer Society},
timestamp = {2010.02.26}
}
@ARTICLE{Lessig_C_2008_j-acm-tog_soh_oshws,
author = {Lessig, C. and Fiu E.},
title = {{SOHO}: Orthogonal and symmetric {Haar} wavelets on the sphere},
journal = j-acm-tog,
year = {2008},
volume = {27},
pages = {4:1--4:11},
number = {1},
month = {Mar.},
issn = {0730-0301},
abstract = {We propose the SOHO wavelet basis?the first spherical Haar wavelet
basis that is both orthogonal and symmetric, making it particularly
well suited for the approximation and processing of all-frequency
signals on the sphere. We obtain the basis with a novel spherical
subdivision scheme that defines a partition acting as the domain
of the basis functions. Our construction refutes earlier claims doubting
the existence of a basis that is both orthogonal and symmetric. Experimental
results for the representation of spherical signals verify that the
superior theoretical properties of the SOHO wavelet basis are also
relevant in practice.},
acmid = {1330515},
address = {New York, NY, USA},
articleno = {4},
doi = {10.1145/1330511.1330515},
file = {Lessig_C_2008_j-acm-tog_soh_oshws-preprint.pdf:Lessig_C_2008_j-acm-tog_soh_oshws-preprint.pdf:PDF},
issue = {1},
keywords = {Wavelet transform, spherical signals},
numpages = {11},
owner = {duvall},
publisher = {ACM},
timestamp = {2011.04.09},
url = {\url{http://doi.acm.org/10.1145/1330511.1330515}}
}
@ARTICLE{Lim_W_2010_j-ieee-tip_dis_stndtcssf,
author = {Lim, W.-Q.},
title = {The Discrete Shearlet Transform: A New Directional Transform and
Compactly Supported Shearlet Frames},
journal = j-ieee-tip,
year = {2010},
volume = {19},
pages = {1166--1180},
number = {5},
month = {May},
issn = {1057-7149},
abstract = {It is now widely acknowledged that analyzing the intrinsic geometrical
features of the underlying image is essential in many applications
including image processing. In order to achieve this, several directional
image representation schemes have been proposed. In this paper, we
develop the discrete shearlet transform (DST) which provides efficient
multiscale directional representation and show that the implementation
of the transform is built in the discrete framework based on a multiresolution
analysis (MRA). We assess the performance of the DST in image denoising
and approximation applications. In image approximations, our approximation
scheme using the DST outperforms the discrete wavelet transform (DWT)
while the computational cost of our scheme is comparable to the DWT.
Also, in image denoising, the DST compares favorably with other existing
transforms in the literature.},
doi = {10.1109/TIP.2010.2041410},
file = {Lim_W_2010_j-ieee-tip_dis_stndtcssf.pdf:Lim_W_2010_j-ieee-tip_dis_stndtcssf.pdf:PDF},
owner = {duvall},
pdf = {Lim_W_2010_j-ieee-tip_dis_stndtcssf.pdf},
timestamp = {2010.04.20}
}
@ARTICLE{Lindeberg_T_2011_j-math-imaging-vis_gen_gssaclssassstss,
author = {Lindeberg, T.},
title = {Generalized Gaussian scale-space axiomatics comprising linear scale-space,
affine scale-space and spatio-temporal scale-space},
journal = j-math-imaging-vis,
year = {2011},
volume = {40},
pages = {36--81},
month = {May},
doi = {10.1007/s10851-010-0242-2},
file = {Lindeberg_T_2011_j-math-imaging-vis_gen_gssaclssassstss-preprint.pdf:Lindeberg_T_2011_j-math-imaging-vis_gen_gssaclssassstss-preprint.pdf:PDF},
owner = {duvall},
timestamp = {2011.03.23},
url = {\url{http://www.csc.kth.se/~tony/earlyvision.html}}
}
@ARTICLE{Lindeberg_T_1993_j-math-imaging-vis_dis_dasspbllfe,
author = {Lindeberg, T.},
title = {Discrete Derivative Approximations with Scale-Space Properties: A
Basis for Low-Level Feature Extraction},
journal = j-math-imaging-vis,
year = {1993},
volume = {3},
pages = {349--379},
number = {4},
abstract = {It is developed how discrete derivative approximations can be dened
so that scale-space properties hold exactly also in the discrete
domain. Starting from a set of natural requirements on the rst processing
stages of a visual system, the visual front end, an axiomatic derivation
is given of how a multi-scale representation of derivative approximations
can be constructed from a discrete signal, so that it possesses an
algebraic structure similar to that possessed by the derivatives
of the traditional scale-space representation in the continuous domain.
A family of kernels is derived which constitute discrete analogues
to the continuous Gaussian derivatives. The representation has theoretical
advantages to other discretizations of the scalespace theory in the
sense that operators which commute before discretization commute
after discretization. Some computational implications of this are
that derivative approximations can be computed directly from smoothed
data, and that this will give exactly the same result as convolution
with the corresponding derivative approximation kernel. Moreover,
a number of normalization conditions are automatically satised.
The proposed methodology leads to a conceptually very simple scheme
of computations for multi-scale low-level feature extraction, consisting
of four basic steps; (i) large support convolution smoothing, (ii)
small support dierence computations, (iii) point operations for
computing dierential geometric entities, and (iv) nearest neighbour
op- erations for feature detection. Applications are given demonstrating
how the proposed scheme can be used for edge detection and junction
detection based on derivatives up to order three.},
file = {Lindeberg_T_1993_j-math-imaging-vis_dis_dasspbllfe.pdf:Lindeberg_T_1993_j-math-imaging-vis_dis_dasspbllfe.pdf:PDF},
keywords = {scale-space, visual front end, smoothing, Gaussian filtering, Gaussian
derivative, discrete approximation, edge detection, junction detection,
multi-scale representation, computer vision, digital signal processing},
owner = {duvall},
pdf = {Lindeberg_T_1993_j-math-imaging-vis_dis_dasspbllfe.pdf},
timestamp = {2009.05.26}
}
@PHDTHESIS{Lisowska_A_2005_phd_geo_wgdicp,
author = {Lisowska, A.},
title = {Geometrical wavelets and their generalizations in digital image coding
and processing},
school = {Univ. Silesia, Sosnowiec, Poland},
year = {2005},
abstract = {In recent years the problem of efficient image coding and processing
has gained popularity and is of great interest both for computer
scientists and mathematicians. Image coding which tends to obtain
efficient compression, especially progressive one, allows to save
time when sending images in a network and disc space during storage.
On the other hand image processing may be used for image quality
improvement as well as extraction of specific features. So, efficient
representation of an image plays a crucial role in computer graphics
because it forms the foundation for image coding and processing.
Recently, it has become evident that separable transforms, as for
example wavelet ones, are not the best ones in image representation
due to their disability of catching line discontinuities present
in images in the form of edges. What follows they are blind for image
geometry. To overcome that problem the competitive theory of geometrical
wavelets has arisen recently. As shown in literature, the use of
geometrical wavelets, thanks to better approximations, is superior
to nearly all of the classical wavelet based applications of image
coding (including compression) and processing. Investigations of
images may not be carried out without the relation to Human Visual
System. Recent researches in psychology of vision have proven that
the amount of information which is gathered by receptors of the retina
in the eye is far larger than dozens of bits per second which are
transmitted to the brain from the eye. Additionally, recent investigations
in neuropsychology give us information what kinds of signals are
perceived by brain in first order and which ones are less important.
Two main observations follow from the researches. The first one is
that, basing on better image approximations, it is possible to reduce
the amount of data used in representation. The second one makes us
realize that less important information, which does not reach the
brain, may be removed from an image without corruption of the visual
quality of an image. So two practical questions arise. How images
can be approximated better, which will lead to improving its coding
and processing properties? And how the most important information,
from the Human Visual System point of view, may be extracted from
an image in an automatic way? In this dissertation it has tried to
answer both these questions. Thus firstly, the generalization of
wedgelets (the class of geometrical wavelets) has been proposed and
it has been shown that thanks to better approximations of images
they improve the properties of image coding and processing in comparison
with classical wedgelets. Especially, the use of such generalized
wedgelets tends to produce more sparse representation of an image.
It has been additionally shown that generalized wedgelets give better
results in noisy image processing in comparison with other standard
methods. Secondly, the new application of geometrical wavelets in
extraction of different classes of signals with different importance
for perception by the human brain has been proposed. With the help
of such wavelets (especially beamlets) an operator has been defined,
which extracts such signals quite automatically. Thanks to the geometrical
approach, such solution is competitive in comparison with the other
ones described in literature. The results presented in the dissertation
appear to improve the results presented so far in literature, which
has been confirmed both theoretically and experimentally.},
file = {Lisowska_A_2005_phd_geo_wgdicp.pdf:Lisowska_A_2005_phd_geo_wgdicp.pdf:PDF},
owner = {duvall},
pdf = {Lisowska_A_2005_phd_geo_wgdicp.pdf},
timestamp = {2009.10.13}
}
@ARTICLE{Lounsbery_M_1997_j-acm-tog_mul_asatt,
author = {M. Lounsbery and T. D. DeRose and J. Warren},
title = {Multiresolution analysis for surfaces of arbitrary topological type},
journal = j-acm-tog,
year = {1997},
volume = {16},
pages = {34--73},
number = {1},
month = {Jan.},
abstract = {Multiresolution analysis and wavelets provide useful and efficient
tools for representing functions at multiple levels of detail. Wavelet
representations have been used in a broad range of applications,
including image compression, physical simulation, and numerical analysis.
In this article, we present a new class of wavelets, based on subdivision
surfaces, that radically extends the class of representable functions.
Whereas previous two-dimensional methods were restricted to functions
defined on $R^2$, the subdivision wavelets developed here may be
applied to functions defined on compact surfaces of arbitrary topological
type. We envision many applications of this work, including continuous
level-of-detail control for graphics rendering, compression of geometric
models, and acceleration of global illumination algorithms. Level-of-
detail control for spherical domains is illustrated using two examples:
shape approximation of a polyhedral model, and color approximation
of global terrain data.},
address = {New York, NY, USA},
file = {Lounsbery_M_1997_j-acm-tog_mul_asatt.pdf:Lounsbery_M_1997_j-acm-tog_mul_asatt.pdf:PDF},
keywords = {Compression, geometric modeling, level-of-detail control,splines,
subdivision surfaces, wavelets},
owner = {duvall},
publisher = {ACM},
timestamp = {2011.01.03}
}
@INPROCEEDINGS{Lu_Y_2003_p-spie-wasip_cri_ccsdmir,
author = {Lu, Y. and Do, M. N.},
title = {{CRISP} contourlets: a critically sampled directional multiresolution
image representation},
booktitle = p-spie-wasip,
year = {2003},
volume = {5207},
pages = {655--665},
abstract = {Directional multiresolution image representations have lately attracted
much attention. A number of new systems, such as the curvelet transform
and the more recent contourlet transform, have been proposed. A common
issue of these transforms is the redundancy in representation, an
undesirable feature for certain applications (e.g. compression).
Though some critically sampled transforms have also been proposed
in the past, they can only provide limited directionality or limited
flexibility in the frequency decomposition. In this paper, we propose
a filter bank structure achieving a nonredundant multiresolution
and multidirectional expansion of images. It can be seen as a critically
sampled version of the original contourlet transform (hence the name
CRISP-contourets) in the sense that the corresponding frequency decomposition
is similar to that of contourlets, which divides the whole spectrum
both angularly and radially. However, instead of performing the multiscale
and directional decomposition steps separately as is done in contourlets,
the key idea here is to use a combined iterated nonseparable filter
bank for both steps. Aside from critical sampling, the proposed transform
possesses other useful properties including perfect reconstruction,
flexible configuration of the number of directions at each scale,
and an efficient tree-structured implementation.},
file = {Lu_Y_2003_p-spie-wasip_cri_ccsdmir.pdf:Lu_Y_2003_p-spie-wasip_cri_ccsdmir.pdf:PDF},
owner = {duvall},
pdf = {Lu_Y_2003_p-spie-wasip_cri_ccsdmir.pdf},
timestamp = {2010.06.08}
}
@ARTICLE{Lu_Y_2007_tip_mul_dfbs,
author = {Lu, Y. M. and Do, M. N.},
title = {Multidimensional Directional Filter Banks and Surfacelets},
journal = j-ieee-tip,
year = {2007},
volume = {16},
pages = {918--931},
number = {4},
month = {Apr.},
issn = {1057-7149},
abstract = {In 1992, Bamberger and Smith proposed the directional filter bank
(DFB) for an efficient directional decomposition of 2-D signals.
Due to the nonseparable nature of the system, extending the DFB to
higher dimensions while still retaining its attractive features is
a challenging and previously unsolved problem. We propose a new family
of filter banks, named NDFB, that can achieve the directional decomposition
of arbitrary N-dimensional (Nges2) signals with a simple and efficient
tree-structured construction. In 3-D, the ideal passbands of the
proposed NDFB are rectangular-based pyramids radiating out from the
origin at different orientations and tiling the entire frequency
space. The proposed NDFB achieves perfect reconstruction via an iterated
filter bank with a redundancy factor of N in N-D. The angular resolution
of the proposed NDFB can be iteratively refined by invoking more
levels of decomposition through a simple expansion rule. By combining
the NDFB with a new multiscale pyramid, we propose the surfacelet
transform, which can be used to efficiently capture and represent
surface-like singularities in multidimensional data},
doi = {10.1109/TIP.2007.891785},
file = {Lu_Y_2007_tip_mul_dfbs.pdf:Lu_Y_2007_tip_mul_dfbs.pdf:PDF},
owner = {duvall},
pdf = {Lu_Y_2007_tip_mul_dfbs.pdf},
timestamp = {2009.10.20}
}
@ARTICLE{Ma_J_2010_j-ieee-spm_cur_t,
author = {J. Ma and Plonka, G.},
title = {The Curvelet Transform --- a review of recent applications},
journal = j-ieee-spm,
year = {2010},
volume = {27},
pages = {118--133},
number = {2},
month = {Mar.},
issn = {1053-5888},
abstract = {Multiresolution methods are deeply related to image processing, biological
and computer vision, and scientific computing. The curvelet transform
is a multiscale directional transform that allows an almost optimal
nonadaptive sparse representation of objects with edges. It has generated
increasing interest in the community of applied mathematics and signal
processing over the years. In this article, we present a review on
the curvelet transform, including its history beginning from wavelets,
its logical relationship to other multiresolution multidirectional
methods like contourlets and shearlets, its basic theory and discrete
algorithm. Further, we consider recent applications in image/video
processing, seismic exploration, fluid mechanics, simulation of partial
different equations, and compressed sensing.},
doi = {10.1109/MSP.2009.935453},
file = {Ma_J_2010_j-ieee-spm_cur_t.pdf:Ma_J_2010_j-ieee-spm_cur_t.pdf:PDF},
keywords = {applied mathematics;compressed sensing;computer vision;curvelet transform;fluid
mechanics;image denoising;image processing;multiscale directional
transform;nonadaptive sparse representation;partial different equations;scientific
computing;seismic exploration;geophysical image processing;image
denoising;image representation;partial differential equations;wavelet
transforms;},
owner = {duvall},
pdf = {Ma_J_2010_j-ieee-spm_cur_t.pdf},
timestamp = {2010.08.30}
}
@ARTICLE{Mallat_S_2009_acha_geo_g,
author = {Mallat, S.},
title = {Geometrical grouplets},
journal = j-acha,
year = {2009},
volume = {26},
pages = {161--180},
number = {2},
month = {Mar.},
abstract = {Grouplet orthogonal bases and tight frames are constructed with association
fields that group points to take advantage of geometrical image regularities
in space or time. These association fields have a multiscale geometry
that can incorporate multiple junctions. A fast grouplet transform
is computed with orthogonal multiscale hierarchical groupings. A
grouplet transform applied to wavelet image coefficients defines
an orthogonal basis or a tight frame of grouping bandlets. Applications
to noise removal and image zooming are described.},
doi = {10.1016/j.acha.2008.03.004},
file = {Mallat_S_2009_acha_geo_g.pdf:Mallat_S_2009_acha_geo_g.pdf:PDF},
owner = {duvall},
pdf = {Mallat_S_2009_acha_geo_g.pdf},
timestamp = {2008.02.01}
}
@BOOK{Mallat_S_2009_book_wav_tspsw,
title = {A wavelet tour of signal processing: the sparse way},
publisher = {Academic Press},
year = {2009},
author = {Mallat, S.},
address = {San Diego, CA, USA},
edition = {3rd},
file = {Mallat_S_2009_book_wav_tspsw.pdf:Mallat_S_2009_book_wav_tspsw.pdf:PDF},
isbn = {978-0123743701},
owner = {duvall},
pdf = {Mallat_S_2008_book_wav_tspsw.pdf},
timestamp = {2009.05.19}
}
@ARTICLE{Mallat_S_1993_tsp_mat_ptfd,
author = {Mallat, S. and Zhang, Z.},
title = {Matching pursuits with time-frequency dictionaries},
journal = j-ieee-tsp,
year = {1993},
volume = {41},
pages = {3397--3415},
number = {12},
month = {Dec.},
abstract = {We introduce an algorithm, called matching pursuit, that decomposes
any signal into a linear expansion of waveforms that are selected
from a redundant dictionary of functions. These waveforms are chosen
in order to best match the signal structures. Matching pursuits are
general procedures to compute adaptive signal representations. With
a dictionary of Gabor functions a matching pursuit defines an adaptive
time-frequency transform. We derive a signal energy distribution
in the time-frequency plane, which does not include interference
terms, unlike Wigner and Cohen class distributions. A matching pursuit
isolates the signal structures that are coherent with respect to
a given dictionary. An application to pattern extraction from noisy
signals is described. We compare a matching pursuit decomposition
with a signal expansion over an optimized wavepacket orthonormal
basis, selected with the algorithm of Coifman and Wickerhauser.},
file = {Mallat_S_1993_tsp_mat_ptfd.pdf:Mallat_S_1993_tsp_mat_ptfd.pdf:PDF},
owner = {duvall},
pdf = {Mallat_S_1993_tsp_mat_ptfd.pdf},
timestamp = {2008.05.30}
}
@ARTICLE{Mallat_S_1989_tpami_the_msdwr,
author = {Mallat, S. G.},
title = {A theory for multiresolution signal decomposition: the wavelet representation},
journal = j-ieee-tpami,
year = {1989},
volume = {11},
pages = {674--693},
number = {7},
month = {Jul.},
issn = {0162-8828},
abstract = {Multiresolution representations are effective for analyzing the information
content of images. The properties of the operator which approximates
a signal at a given resolution were studied. It is shown that the
difference of information between the approximation of a signal at
the resolutions 2j+1 and 2j (where j is an integer) can be extracted
by decomposing this signal on a wavelet orthonormal basis of L2(Rn),
the vector space of measurable, square-integrable n-dimensional functions.
In L2(R), a wavelet orthonormal basis is a family of functions which
is built by dilating and translating a unique function \ψ(x).
This decomposition defines an orthogonal multiresolution representation
called a wavelet representation. It is computed with a pyramidal
algorithm based on convolutions with quadrature mirror filters. Wavelet
representation lies between the spatial and Fourier domains. For
images, the wavelet representation differentiates several spatial
orientations. The application of this representation to data compression
in image coding, texture discrimination and fractal analysis is discussed},
doi = {10.1109/34.192463},
file = {Mallat_S_1989_tpami_the_msdwr.pdf:Mallat_S_1989_tpami_the_msdwr.pdf:PDF},
keywords = {data compression, encoding, pattern recognition, picture processing},
owner = {duvall},
pdf = {Mallat_S_1989_tpami_the_msdwr.pdf},
timestamp = {2009.10.29}
}
@INPROCEEDINGS{Malvar_H_2000_p-dcc_fas_picww,
author = {Malvar, H. S.},
title = {Fast progressive image coding without wavelets},
booktitle = p-dcc,
year = {2000},
pages = {243--252},
address = {Snowbird, UT, USA},
month = {Mar. 28-30,},
abstract = {We introduce a new image compression algorithm that allows progressive
image
reconstruction ? both in resolution and in fidelity, with a fully
embedded bitstream.
The algorithm is based on bit-plane entropy coding of reordered transform
coefficients, similar to the progressive wavelet codec (PWC) previously
introduced.
Unlike PWC, however, our new progressive transform coder (PTC)
does not use wavelets; it performs the space-frequency decomposition
step via a
new lapped biorthogonal transform (LBT). PTC achieves a rate vs. distortion
performance that is comparable (within 2%) to that of the state-of-the-art
SPIHT
(set partitioning in hierarchical trees) codec. However, thanks to
the use of the
LBT, the space-frequency decomposition step in PTC reduces the number
of
multiplications per pixel by a factor of 2.7, and the number of additions
by about
15%, when compared to the fastest possible implementation of the ?9/7?
wavelet
transform via lifting. Furthermore, since most of the computation
in the LBT is
in fact performed by a DCT, our PTC codec can make full use of fast
software
and hardware modules for 1-D and 2-D DCTs.},
doi = {10.1109/DCC.2000.838164},
file = {Malvar_H_2000_p-dcc_fas_picww.pdf:Malvar_H_2000_p-dcc_fas_picww.pdf:PDF},
owner = {duvall},
pdf = {Malvar_H_2000_dcc_fas_picww.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Malvar_H_2003_j-ieee-tcsvt_low_ctqh264avc,
author = {Malvar, H. S. and Hallapuro, A. and Karczewicz, M. and Kerofsky,
L.},
title = {Low-complexity transform and quantization in {H.264/AVC}},
journal = j-ieee-tcsvt,
year = {2003},
volume = {13},
pages = {598--603},
number = {7},
month = {Jul.},
issn = {1051-8215},
abstract = {This paper presents an overview of the transform and quantization
designs in H.264. Unlike the popular 8 times;8 discrete cosine transform
used in previous standards, the 4 times;4 transforms in H.264 can
be computed exactly in integer arithmetic, thus avoiding inverse
transform mismatch problems. The new transforms can also be computed
without multiplications, just additions and shifts, in 16-bit arithmetic,
thus minimizing computational complexity, especially for low-end
processors. By using short tables, the new quantization formulas
use multiplications but avoid divisions.},
doi = {10.1109/TCSVT.2003.814964},
file = {Malvar_H_2003_j-ieee-tcsvt_low_ctqh264avc.pdf:Malvar_H_2003_j-ieee-tcsvt_low_ctqh264avc.pdf:PDF},
keywords = {16 bit; DCT; H.264 video coding standard; H.264/AVC; additions; arithmetic;
computational complexity minimization; discrete cosine transform;
integer arithmetic; low-complexity quantization; low-complexity transform;
low-end processors; multiplications; quantization formulas; shifts;
short tables; code standards; computational complexity; data compression;
digital arithmetic; quantisation (signal); telecommunication standards;
transform coding; transforms; video coding;},
owner = {duvall},
pdf = {Malvar_H_2003_j-ieee-tcsvt_low_ctqh264avc.pdf},
timestamp = {2010.02.15}
}
@ARTICLE{Manduchi_R_1998_tsp_eff_dfb,
author = {Manduchi, R. and Perona, P. and Shy, D.},
title = {Efficient deformable filter banks},
journal = j-ieee-tsp,
year = {1998},
volume = {46},
pages = {1168--1173},
number = {4},
month = {Apr.},
issn = {1053-587X},
abstract = {This article describes efficient schemes for the computation of a
large number of differently scaled/oriented filtered versions of
an image. We generalize the well-known steerable/scalable (?deformable?)
filter bank structure by imposing X-Y separability on the basis filters.
The resulting systems, designed by an iterative projections technique,
achieve substantial reduction of the computational cost. To reduce
the memory requirement, we adopt a multirate implementation. Due
to the inner sampling rate alteration, the resulting structure is
not shift invariant. We introduce a design criterion for multirate
deformable structures that jointly controls the approximation error
and the shift variance},
doi = {10.1109/78.668570},
file = {Manduchi_R_1998_tsp_eff_dfb.pdf:Manduchi_R_1998_tsp_eff_dfb.pdf:PDF},
keywords = {FIR filters, band-pass filters, filtering theory, image sampling,
iterative methods, least squares approximations},
owner = {duvall},
pdf = {Manduchi_R_1998_tsp_eff_dfb.pdf},
timestamp = {2009.11.01}
}
@BOOK{Marr_D_1982_book_vis_cihrpvi,
title = {Vision: A Computational Investigation into the Human Representation
and Processing of Visual Information},
publisher = {W. H. Freeman},
year = {1982},
author = {Marr, D.},
address = {San Francisco},
file = {:Marr_D_1982_book_vis_cihrpvi.zip:PDF},
isbn = {9780716712848},
owner = {duvall},
timestamp = {2009.10.01}
}
@ARTICLE{Marr_D_1980_j-proc-roy-soc-b_the_ed,
author = {Marr, D. and Hildreth, E.},
title = {Theory of Edge Detection},
journal = j-proc-roy-soc-b,
year = {1980},
volume = {207},
pages = {187--217},
number = {1167},
month = {Feb.},
abstract = {A theory of edge detection is presented. The analysis proceeds in
two parts. (1) Intensity changes, which occur in a natural image
over a wide range of scales, are detected separately at different
scales. An appropriate filter for this purpose at a given scale is
found to be the second derivative of a Gaussian, and it is shown
that, provided some simple conditions are satisfied, these primary
filters need not be orientation-dependent. Thus, intensity changes
at a given scale are best detected by finding the zero values of
$\nabla ^{2}$G(x, y)* I(x, y)$ for image I, where $G(x, y)$ is a
two-dimensional Gaussian distribution and $\nabla ^{2}$ is the Laplacian.
The intensity changes thus discovered in each of the channels are
then represented by oriented primitives called zero-crossing segments,
and evidence is given that this representation is complete. (2) Intensity
changes in images arise from surface discontinuities or from reflectance
or illumination boundaries, and these all have the property that
they are spatially localized. Because of this, the zero-crossing
segments from the different channels are not independent, and rules
are deduced for combining them into a description of the image. This
description is called the raw primal sketch. The theory explains
several basic psychophysical findings, and the operation of forming
oriented zero-crossing segments from the output of centre-surround
$\nabla ^{2}$G filters acting on the image forms the basis for a
physiological model of simple cells (see Marr & Ullman 1979).},
doi = {10.1098/rspb.1980.0020},
file = {Marr_D_1980_j-proc-roy-soc-b_the_ed.pdf:Marr_D_1980_j-proc-roy-soc-b_the_ed.pdf:PDF},
owner = {duvall},
timestamp = {2010.01.13}
}
@ARTICLE{Marr_D_1979_j-roy-stat-soc-b_com_thsv,
author = {D. Marr and T. Poggio},
title = {A Computational Theory of Human Stereo Vision},
journal = j-roy-stat-soc-b,
year = {1979},
volume = {204},
pages = {301--328},
number = {1156},
month = {May},
file = {Marr_D_1979_j-roy-stat-soc-b_com_thsv.pdf:Marr_D_1979_j-roy-stat-soc-b_com_thsv.pdf:PDF},
owner = {duvall},
pdf = {Marr_D_1979_j-roy-stat-soc-b_com_thsv.pdf},
timestamp = {2009.10.01}
}
@BOOK{Massopust_P_1994_book_fra_ffsw,
title = {Fractal Functions, Fractal Surfaces, and Wavelets},
publisher = {Academic Press},
year = {1994},
author = {Massopust, P.},
address = {Boston},
isbn = {9780124788404},
owner = {duvall},
timestamp = {2009.11.01}
}
@ARTICLE{Meyer_F_1997_j-acha_bru_tdiaic,
author = {F. G. Meyer and R. R. Coifman},
title = {Brushlets: A Tool for Directional Image Analysis and Image Compression},
journal = j-acha,
year = {1997},
volume = {4},
pages = {147--187},
number = {2},
issn = {1063-5203},
abstract = {We construct a new adaptive basis of functions which is reasonably
well localized with only one peak in frequency. We develop a compression
algorithm that exploits this basis to obtain the most economical
representation of the image in terms of textured patterns with different
orientations, frequencies, sizes, and positions. The technique directly
works in the Fourier domain and has potential applications for compression
of highly textured images, texture analysis, etc.},
doi = {DOI: 10.1006/acha.1997.0208},
file = {Meyer_F_1997_j-acha_bru_tdiaic.pdf:Meyer_F_1997_j-acha_bru_tdiaic.pdf:PDF},
owner = {duvall},
pdf = {Meyer_F_1997_j-acha_bru_tdiaic.pdf},
timestamp = {2009.10.20},
url = {http://www.sciencedirect.com/science/article/B6WB3-45MH2TF-8/2/26f109da3fd9f249aa4f21ceb5482349}
}
@INCOLLECTION{Meyer_Y_2001_incoll_osc_pipnee,
author = {Meyer, Y.},
title = {Oscillating Patterns in Image Processing and Nonlinear Evolution
Equations},
booktitle = {The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures},
publisher = {Amer. Math. Soc.},
year = {2001},
series = {Univ. Lect. Ser.},
owner = {duvall},
timestamp = {2010.02.16}
}
@ARTICLE{Monaci_G_2006_j-sp_ana_msgvr,
author = {Monaci, G. and Escoda, {\`O}. D. and Vandergheynst, P.},
title = {Analysis of multimodal sequences using geometric video representations},
journal = j-sp,
year = {2006},
volume = {86},
pages = {3534--3548},
number = {12},
month = {Dec.},
abstract = {This paper presents a novel method to correlate audio and visual data
generated by the same physical phenomenon, based on sparse geometric
representation of video sequences. The video signal is modeled as
a sum of geometric primitives evolving through time, that jointly
describe the geometric and motion content of the scene. The displacement
through time of relevant visual features, like the mouth of a speaker,
can thus be compared with the evolution of an audio feature to assess
the correspondence between acoustic and visual signals. Experiments
show that the proposed approach allows to localize and track the
speaker's mouth when several persons are present on the scene, in
presence of distracting motion, and without prior face or mouth detection.},
doi = {doi:10.1016/j.sigpro.2006.02.044},
file = {Monaci_G_2006_j-sp_ana_msgvr.pdf:Monaci_G_2006_j-sp_ana_msgvr.pdf:PDF},
keywords = {Multimodal data processing; Audiovisual association; Cross-modal localization;
Geometric video representation; Sparse redundant decomposition},
owner = {duvall},
publisher = {Elsevier},
timestamp = {2011.01.05}
}
@ARTICLE{Narcowich_F_2006_j-siam-math-anal_loc_tfs,
author = {F. J. Narcowich and P. Petrushev and J. D. Ward},
title = {Localized tight frames on spheres},
journal = j-siam-math-anal,
year = {2006},
volume = {38},
pages = {574--594},
number = {2},
owner = {duvall},
timestamp = {2011.01.05}
}
@INCOLLECTION{Nason_G_1995_incoll-was_sta_wtsa,
author = {Nason, G. P. and Silverman, B. W.},
title = {The stationary wavelet transform and some statistical applications},
booktitle = {Wavelets and Statistics},
publisher = {Springer Verlag},
year = {1995},
editor = {Antoniadis, A. and Oppenheim, G.},
volume = {103},
series = {Lecture Notes in Statistics},
pages = {281--300},
address = {New York, NY, USA},
file = {Nason_G_1995_incoll-was_sta_wtsa.pdf:Nason_G_1995_incoll-was_sta_wtsa.pdf:PDF},
owner = {duvall},
pdf = {Nason_G_1995_incoll-was_sta_wtsa.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Natarajan_B_1995_j-siam-comp_spa_asls,
author = {B. K. Natarajan},
title = {Sparse Approximate Solutions to Linear Systems},
journal = j-siam-comp,
year = {1995},
volume = {24},
pages = {227--234},
number = {2},
abstract = {The following problem is considered: given a matrix $A$ in ${\bf R}^{m\times
n}$, ($m$ rows and $n$ columns), a vector $b$ in ${\bf R}^m$, and
$\epsilon > 0$, compute a vector $x$ satisfying $\|Ax - b\|_{2} \leq
\epsilon $ if such exists, such that $x$ has the fewest number of
non-zero entries over all such vectors. It is shown that the problem
is NP-hard, but that the well-known greedy heuristic is good in that
it computes a solution with at most $\lceil 18 \operatorname{Opt}(\epsilon/2)\|{\bf
A}^{+}\|_{2}^{2} \ln ({\| b \|_{2}/\epsilon})\rceil$ non-zero entries,
where $\operatorname{Opt}(\epsilon/2)$ is the optimum number of nonzero
entries at error $\epsilon/2$, ${\textbf{A}}$ is the matrix obtained
by normalizing each column of $A$ with respect to the $L_{2}$ norm,
and $\textbf{A}^{+}$ is its pseudo-inverse.},
doi = {10.1137/S0097539792240406},
file = {Natarajan_B_1995_j-siam-comp_spa_asls.pdf:Natarajan_B_1995_j-siam-comp_spa_asls.pdf:PDF},
keywords = {sparse solutions; linear systems},
owner = {duvall},
pdf = {Natarajan_B_1995_j-siam-comp_spa_asls.pdf},
publisher = {SIAM},
timestamp = {2010.08.28},
url = {http://link.aip.org/link/?SMJ/24/227/1}
}
@ARTICLE{Neff_R_1997_j-ieee-tcsvt_ver_lbrvcbmp,
author = {Neff, R. and Zakhor, A.},
title = {Very-Low Bit-Rate Video Coding Based on Matching Pursuits},
journal = j-ieee-tcsvt,
year = {1997},
volume = {7},
pages = {158--171},
number = {1},
month = {Feb.},
file = {Neff_R_1997_j-ieee-tcsvt_ver_lbrvcbmp.pdf:Neff_R_1997_j-ieee-tcsvt_ver_lbrvcbmp.pdf:PDF},
owner = {duvall},
timestamp = {2010.08.30}
}
@ARTICLE{Nestares_O_1998_j-elec-im_eff_sdimirbgf,
author = {Nestares, O. and Navarro, R. and Portilla, J. and Tabernero, A.},
title = {Efficient Spatial Domain Implementation of a Multiscale Image Representation
Based on {Gabor} Functions},
journal = j-elec-im,
year = {1998},
volume = {7},
pages = {166--173},
number = {1},
file = {Nestares_O_1998_j-elec-im_eff_sdimirbgf.pdf:Nestares_O_1998_j-elec-im_eff_sdimirbgf.pdf:PDF},
owner = {duvall},
pdf = {Nestares_O_1998_j-elec-im_eff_sdimirbgf.pdf},
timestamp = {2009.11.19}
}
@ARTICLE{Nguyen_T_2007_j-ieee-tsp_cla_mdfb,
author = {T. T. Nguyen and S. Oraintara},
title = {A Class of Multiresolution Directional Filter Banks},
journal = j-ieee-tsp,
year = {2007},
volume = {55},
pages = {949--961},
number = {3},
month = {Mar. },
issn = {1053-587X},
abstract = {In this paper, we introduced a class of directional filter banks (DFBs)
having the previously proposed uniform DFB (uDFB) as a special case.
Except for the uDFB, each DFB in this class can be used to decompose
an image yielding up to 12 directions while maintaining perfect reconstruction
and maximal decimation. A multiresolution representation can be obtained
by repeating the same decomposition at the lowpass band. The permissible
property of the filter banks in cases of being implemented by a tree
structure and by direct implementation is discussed. The result shows
that only one DFB in the class, called the uniform quincunx DFB (uqDFB),
satisfies the permissible property when being implemented directly
without using the tree structure. The nonuniform quincunx DFB (nuqDFB)
is then constructed from the uqDFB by merging its two lowpass subbands.
An alternative structure for constructing the nuqDFB is presented.
The new structure, while yielding the same frequency partitioning,
allows the DFB to be realized with complexity comparable to that
of the separable wavelet filter bank. The connection between the
discrete filter bank and the continuous directional wavelet is also
established. Numerical experiments on directional feature extractions,
image denoising and nonlinear approximation are presented at the
end of the paper to demonstrate the potential of the nuqDFB},
doi = {10.1109/TSP.2006.887140},
file = {Nguyen_T_2007_j-ieee-tsp_cla_mdfb.pdf:Nguyen_T_2007_j-ieee-tsp_cla_mdfb.pdf:PDF},
keywords = {directional feature extractions;discrete filter bank;frequency partitioning;image
denoising;lowpass subbands;multiresolution directional filter banks;multiresolution
representation;nonlinear approximation;nonuniform quincunx DFB;separable
wavelet filter bank;tree structure;approximation theory;channel bank
filters;feature extraction;image denoising;image reconstruction;image
representation;image resolution;low-pass filters;trees (mathematics);wavelet
transforms;},
owner = {duvall},
pdf = {Nguyen_T_2007_j-ieee-tsp_cla_mdfb.pdf},
timestamp = {2010.02.24}
}
@ARTICLE{Ogden_J_1985_j-rca-eng_pyr_bcg,
author = {Ogden, J. M. and Adelson, E. H. and Bergen, J. R. and Burt, P. J.},
title = {Pyramid-Based Computer Graphics},
journal = j-rca-eng,
year = {1985},
volume = {30},
pages = {4--15},
number = {5},
abstract = {This paper describes pyramid solutions to graphics problems that have
proven difficult in other image representations. The "physics simulation"
approach grows more out of the physics and mathematical modelling
traditions. Greater realism can be achieved by using the ph},
file = {Ogden_J_1985_j-rca-eng_pyr_bcg.pdf:Ogden_J_1985_j-rca-eng_pyr_bcg.pdf:PDF},
owner = {duvall},
pdf = {Ogden_J_1985_j-rca-eng_pyr_bcg.pdf},
timestamp = {2009.12.22}
}
@ARTICLE{Olhede_S_2009_j-ieee-tsp_mon_wt,
author = {Olhede, S. C. and Metikas, G.},
title = {The Monogenic Wavelet Transform},
journal = j-ieee-tsp,
year = {2009},
volume = {57},
pages = {3426--3441},
number = {9},
month = {Sep.},
issn = {1053-587X},
abstract = {This paper extends the 1-D analytic wavelet transform to the 2-D monogenic
wavelet transform. The transformation requires care in its specification
to ensure suitable transform coefficients are calculated, and it
is constructed so that the wavelet transform may be considered as
both local and monogenic. This is consistent with defining the transform
as a real wavelet transform of a monogenic signal in analogy with
the analytic wavelet transform. Classes of monogenic wavelets are
proposed with suitable local properties. It is shown that the monogenic
wavelet annihilates anti-monogenic signals, that the monogenic wavelet
transform is phase-shift covariant and that the transform magnitude
is phase-shift invariant. A simple form for the magnitude and orientation
of the isotropic transform coefficients of a unidirectional signal
when observed in a rotated frame of reference is derived. The monogenic
wavelet ridges of local plane waves are given.},
doi = {10.1109/TSP.2009.2023397},
file = {Olhede_S_2009_j-ieee-tsp_mon_wt.pdf:Olhede_S_2009_j-ieee-tsp_mon_wt.pdf:PDF},
keywords = {1D analytic wavelet transform;2D monogenic wavelet transform;Hilbert
transform;Riesz transform;isotropic transform coefficient;local plane
wave;monogenic signal;phase-shift covariant;phase-shift invariant;unidirectional
signal;Hilbert transforms;signal processing;wavelet transforms;},
owner = {duvall},
pdf = {Olhede_S_2009_j-ieee-tsp_mon_wt.pdf},
timestamp = {2010.08.27}
}
@ARTICLE{Olshausen_B_1997_j-vis-res_spa_cobssev1,
author = {B. A. Olshausen and D. J. Field},
title = {Sparse coding with an overcomplete basis set: A strategy employed
by {V1}?},
journal = j-vis-res,
year = {1997},
volume = {37},
pages = {3311--3325},
number = {23},
issn = {0042-6989},
abstract = {The spatial receptive fields of simple cells in mammalian striate
cortex have been reasonably well described physiologically and can
be characterized as being localized, oriented, and bandpass, comparable
with the basis functions of wavelet transforms. Previously, we have
shown that these receptive field properties may be accounted for
in terms of a strategy for producing a sparse distribution of output
activity in response to natural images. Here, in addition to describing
this work in a more expansive fashion, we examine the neurobiological
implications of sparse coding. Of particular interest is the case
when the code is overcomplete--i.e., when the number of code elements
is greater than the effective dimensionality of the input space.
Because the basis functions are non-orthogonal and not linearly independent
of each other, sparsifying the code will recruit only those basis
functions necessary for representing a given input, and so the input-output
function will deviate from being purely linear. These deviations
from linearity provide a potential explanation for the weak forms
of non-linearity observed in the response properties of cortical
simple cells, and they further make predictions about the expected
interactions among units in response to naturalistic stimuli.},
doi = {DOI: 10.1016/S0042-6989(97)00169-7},
file = {Olshausen_B_1997_j-vis-res_spa_cobssev1.pdf:Olshausen_B_1997_j-vis-res_spa_cobssev1.pdf:PDF},
keywords = {Coding; V1; Gabor-wavelet; Natural images},
owner = {duvall},
pdf = {Olshausen_B_1997_j-vis-res_spa_cobssev1.pdf},
timestamp = {2009.11.01},
url = {http://www.sciencedirect.com/science/article/B6T0W-494SR70-19/2/b4c138506b06df6f332ced73e8501a3e}
}
@INPROCEEDINGS{Ouarti_N_2009_p-icip_bes_bsnswpd,
author = {N. Ouarti and G. Peyr\'e},
title = {Best Basis Search in a Non-stationary Wavelet Packets Dictionary},
booktitle = p-icip,
year = {2009},
address = {Cairo, Egypt},
month = {Nov. 7-11,},
owner = {duvall},
timestamp = {2011.01.03}
}
@INPROCEEDINGS{Pati_Y_1993_p-asilomar_ort_mprfaawd,
author = {Y. C. Pati and R. Rezaifar and P. S. Krishnaprasa},
title = {Orthogonal matching pursuit: recursive function approximation with
applications to wavelet decomposition},
booktitle = p-asilomar,
year = {1993},
month = {Nov.},
file = {Pati_Y_1993_p-asilomar_ort_mprfaawd.pdf:Pati_Y_1993_p-asilomar_ort_mprfaawd.pdf:PDF},
owner = {duvall},
pdf = {Pati_Y_1993_p-asilomar_ort_mprfaawd.pdf},
timestamp = {2010.02.16}
}
@ARTICLE{Pesquet_J_1996_tsp_tim_iowr,
author = {Pesquet, J.-C. and Krim, H. and Carfantan, H.},
title = {Time-invariant orthogonal wavelet representations},
journal = j-ieee-tsp,
year = {1996},
volume = {44},
pages = {1964--1970},
number = {8},
month = {Aug.},
abstract = {A simple construction of an orthonormal basis starting with a so-called
mother wavelet, together with an efficient implementation gained
the wavelet decomposition easy acceptance and generated a great research
interest in its applications. An orthonormal basis may not, however,
always be a suitable representation of a signal, particularly when
time (or space) invariance is a required property. The conventional
way around this problem is to use a redundant decomposition. We address
the time-invariance problem for orthonormal wavelet transforms and
propose an extension to wavelet packet decompositions. We show that
it,is possible to achieve time invariance and preserve the orthonormality.
We subsequently propose an efficient approach to obtain such a decomposition.
We demonstrate the importance of our method by considering some application
examples in signal reconstruction and time delay estimation},
file = {Pesquet_J_1996_tsp_tim_iowr.pdf:Pesquet_J_1996_tsp_tim_iowr.pdf:PDF},
owner = {duvall},
pdf = {Pesquet_J_1996_tsp_tim_iowr.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{PesquetPopescu_B_2001_p-icassp_thr_dlsmcvc,
author = {Pesquet-Popescu, B. and Bottreau, V.},
title = {Three-dimensional lifting schemes for motion compensated video compression},
booktitle = p-icassp,
year = {2001},
volume = {3},
pages = {1793--1796},
address = {Washington, DC, USA},
month = {May 7-11,},
abstract = {Three-dimensional wavelet decompositions are efficient tools for scalable
video coding. We show a lifting formulation for these decompositions.
The temporal wavelet transform is inherently nonlinear, due to the
motion estimation step, and the lifting formalism allows us to provide
several improvements to the scheme initially proposed by Choi and
Woods: a better processing of the uncovered areas is proposed and
an overlapped motion-compensated temporal filtering method is introduced
in the multiresolution decomposition. As shown by simulations, the
proposed method results in higher coding efficiency, while keeping
the scalability functionalities},
acmid = {1259331},
doi = {10.1109/ICASSP.2001.941289},
isbn = {0-7803-7041-4},
keywords = {coding efficiency;lifting formulation;motion estimation;multiresolution
decomposition;nonlinear transform;overlapped motion compensation;scalable
video coding;temporal filtering;temporal wavelet transform;three-dimensional
wavelet decompositions;video compression;data compression;filtering
theory;image resolution;motion compensation;motion estimation;transform
coding;video coding;wavelet transforms;},
numpages = {4},
owner = {duvall},
timestamp = {2011.04.08}
}
@ARTICLE{Peyre_G_2010_j-ieee-tsp_bes_bcs,
author = {G. Peyr\'e},
title = {Best Basis Compressed Sensing},
journal = j-ieee-tsp,
year = {2010},
volume = {58},
pages = {2613--2622},
number = {5},
month = {May},
issn = {1053-587X},
abstract = {This paper proposes a best basis extension of compressed sensing recovery.
Instead of regularizing the compressed sensing inverse problem with
a sparsity prior in a fixed basis, our framework makes use of sparsity
in a tree-structured dictionary of orthogonal bases. A new iterative
thresholding algorithm performs both the recovery of the signal and
the estimation of the best basis. The resulting reconstruction from
compressive measurements optimizes the basis to the structure of
the sensed signal. Adaptivity is crucial to capture the regularity
of complex natural signals. Numerical experiments on sounds and geometrical
images indeed show that this best basis search improves the recovery
with respect to fixed sparsity priors.},
doi = {10.1109/TSP.2010.2042490},
keywords = {best basis compressed sensing recovery;geometrical images;inverse
problem;iterative thresholding algorithm;signal estimation;signal
reconstruction;signal recovery;sparsity;tree structured dictionary;data
compression;iterative methods;signal reconstruction;trees (mathematics);},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Peyre_G_2009_j-ieee-tpami_tex_pg,
author = {G. Peyr\'e},
title = {Texture Processing with Grouplets},
journal = j-ieee-tpami,
year = {2009},
volume = {32},
pages = {733--746},
number = {4},
month = {Apr.},
issn = {0162-8828},
abstract = {This paper proposes a new method to synthesize and inpaint geometric
textures. The texture model is composed of a geometric layer that
drives the computation of a new grouplet transform. The geometry
is an orientation flow that follows the patterns of the texture to
analyze or synthesize. The grouplet transform extends the original
construction of Mallat and is adapted to the modeling of natural
textures. Each grouplet atoms is an elongated stroke located along
the geometric flow. These atoms exhibit a wide range of lengths and
widths, which is important to match the variety of structures present
in natural images. Statistical modeling and sparsity optimization
over these grouplet coefficients enable the synthesis of texture
patterns along the flow. This paper explores texture inpainting and
texture synthesis, which both require the joint optimization of the
geometric flow and the grouplet coefficients.},
doi = {10.1109/TPAMI.2009.54},
keywords = {geometric textures;grouplet atoms;grouplet transform;natural images;natural
textures modeling;sparsity optimization;statistical modeling;texture
synthesis;image texture;optimisation;transforms;Algorithms;Animals;Anisotropy;Biometry;Humans;Image
Processing, Computer-Assisted;Pattern Recognition, Automated;},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Peyre_G_2008_j-comm-pure-appl-math_ort_bbgia,
author = {G. Peyr{\'e} and S. Mallat},
title = {Orthogonal Bandlet Bases for Geometric Images Approximation},
journal = j-comm-pure-appl-math,
year = {2008},
volume = {61},
pages = {1173--1212},
number = {9},
month = {Sep.},
abstract = {This paper introduces orthogonal bandelet bases to approximate images
having some geometrical regularity. These bandelet bases are computed
by applying parametrized Alpert transform operators over an orthogonal
wavelet basis. These bandeletization operators depend upon a multiscale
geometric ?ow that is adapted to the image at each wavelet scale.
This bandelet construction has a hierarchical structure over wavelet
coef?cients taking advantage of existing regularity among these coef?cients.
It is proved that C? -images having singularities along Calpha-curves
are approximated in a best orthogonal bandelet basis with an optimal
asymptotic error decay. Fast algorithms and compression applications
are described.},
file = {Peyre_G_2008_j-comm-pure-appl-math_ort_bbgia.pdf:Peyre_G_2008_j-comm-pure-appl-math_ort_bbgia.pdf:PDF},
owner = {duvall},
pdf = {Peyre_G_2008_j-comm-pure-appl-math_ort_bbgia.pdf},
timestamp = {2009.10.20}
}
@ARTICLE{Plonka_G_2009_j-siam-mms_eas_pwt_nawtsrtdd,
author = {Plonka, G.},
title = {The easy path wavelet transform: A new adaptive wavelet transform
for sparse representation of two-dimensional data},
journal = j-siam-mms,
year = {2009},
volume = {7},
pages = {1474--1496},
number = {3},
file = {Plonka_G_2009_j-siam-mms_eas_pwt_nawtsrtdd.pdf:Plonka_G_2009_j-siam-mms_eas_pwt_nawtsrtdd.pdf:PDF},
owner = {duvall},
pdf = {Plonka_G_2009_j-siam-mms_eas_pwt_nawtsrtdd.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Portilla_J_2000_j-ijcv_par_tmbjscwc,
author = {Portilla, J. and Simoncelli, E. P.},
title = {A Parametric Texture Model based on Joint Statistics of Complex Wavelet
Coefficients},
journal = j-ijcv,
year = {2000},
volume = {40},
pages = {49--71},
month = {Oct.},
issn = {0920-5691},
file = {Portilla_J_2000_j-ijcv_par_tmbjscwc.pdf:Portilla_J_2000_j-ijcv_par_tmbjscwc.pdf:PDF},
owner = {duvall},
pdf = {Portilla_J_2000_ijcv_par_tmbjscwc.pdf},
timestamp = {2008.04.28}
}
@ARTICLE{Portilla_J_2003_tip_ima_dsmgwd,
author = {Portilla, J. and Strela, V. and Wainwright, M. J. and Simoncelli,
E. P.},
title = {Image denoising using scale mixtures of {Gaussians} in the wavelet
domain},
journal = j-ieee-tip,
year = {2003},
volume = {12},
pages = {1338--1351},
number = {11},
month = {Nov.},
owner = {duvall},
timestamp = {2007.06.07}
}
@ARTICLE{Quellec_G_2010_j-ieee-tip_ada_nwtlacbir,
author = {Quellec, G. and Lamard, M. and Cazuguel, G. and Cochener, B. and
Roux, C.},
title = {Adaptive Nonseparable Wavelet Transform via Lifting and its Application
to Content-Based Image Retrieval},
journal = j-ieee-tip,
year = {2010},
volume = {19},
pages = {25--35},
number = {1},
month = {Jan. },
issn = {1057-7149},
abstract = {We present in this paper a novel way to adapt a multidimensional wavelet
filter bank, based on the nonseparable lifting scheme framework,
to any specific problem. It allows the design of filter banks with
a desired number of degrees of freedom, while controlling the number
of vanishing moments of the primal wavelet (mathtilde NÂż moments)
and of the dual wavelet ( NÂż moments). The prediction and update
filters, in the lifting scheme based filter banks, are defined as
Neville filters of order mathtilde NÂż and NÂż , respectively. However,
in order to introduce some degrees of freedom in the design, these
filters are not defined as the simplest Neville filters. The proposed
method is convenient: the same algorithm is used whatever the dimensionality
of the signal, and whatever the lattice used. The method is applied
to content-based image retrieval (CBIR): an image signature is derived
from this new adaptive nonseparable wavelet transform. The method
is evaluated on four image databases and compared to a similar CBIR
system, based on an adaptive separable wavelet transform. The mean
precision at five of the nonseparable wavelet based system is notably
higher on three out of the four databases, and comparable on the
other one. The proposed method also compares favorably with the dual-tree
complex wavelet transform, an overcomplete nonseparable wavelet transform.},
doi = {10.1109/TIP.2009.2030479},
file = {Quellec_G_2010_j-ieee-tip_ada_nwtlacbir.pdf:Quellec_G_2010_j-ieee-tip_ada_nwtlacbir.pdf:PDF},
keywords = {Neville filters;adaptive nonseparable wavelet transform;adaptive separable
wavelet transform;content-based image retrieval;dual wavelet;dual-tree
complex wavelet transform;image databases;image signature;multidimensional
wavelet filter bank;nonseparable lifting scheme framework;primal
wavelet;channel bank filters;content-based retrieval;image processing;image
retrieval;visual databases;wavelet transforms;},
owner = {duvall},
pdf = {Quellec_G_2010_j-ieee-tip_ada_nwtlacbir.pdf},
timestamp = {2010.02.23}
}
@ARTICLE{Reissell_L_1996_j-graph-model-image-process_wav_mrcs,
author = {Reissell, L.-M.},
title = {Wavelet multiresolution representation of curves and surfaces},
journal = j-graph-model-image-process,
year = {1996},
volume = {58},
pages = {198--217},
number = {3},
month = {May},
abstract = {We develop wavelet methods for the multiresolution representation
of parametric curves and surfaces. To support the representation,
we construct a new family of compactly supported symmetric biorthogonal
wavelets with interpolating scaling functions. The wavelets in these
biorthogonal pairs have properties better suited for curves and surfaces
than many commonly used filters. We also give examples of the applications
of the wavelet approach: these include the derivation of compact
hierarchical curve and surface representations using modified wavelet
compression, the identification of smooth sections of surfaces, and
a subdivision-like intersection algorithm for discrete plane curves.},
file = {Reissell_L_1996_j-graph-model-image-process_wav_mrcs.pdf:Reissell_L_1996_j-graph-model-image-process_wav_mrcs.pdf:PDF},
owner = {duvall},
pdf = {Reissell_L_1996_j-graph-model-image-process_wav_mrcs.pdf},
timestamp = {2010.02.26}
}
@ARTICLE{Rioul_O_1992_tit_fas_adcwt,
author = {Rioul, O. and Duhamel, P.},
title = {Fast algorithms for discrete and continuous wavelet transforms},
journal = j-ieee-tit,
year = {1992},
volume = {38},
pages = {569--586},
number = {2},
month = {Mar.},
abstract = {Several algorithms are reviewed for computing various types of wavelet
transforms: the Mallat algorithm (1989), the `a trous' algorithm,
and their generalizations by Shensa. The goal of this work is to
develop guidelines for implementing discrete and continuous wavelet
transforms efficiently, and to compare the various algorithms obtained
and give an idea of possible gains by providing operation counts.
Most wavelet transform algorithms compute sampled coefficients of
the continuous wavelet transform using the filter bank structure
of the discrete wavelet transform. Although this general method is
already efficient, it is shown that noticeable computational savings
can be obtained by applying known fast convolution techniques, such
as the FFT (fast Fourier transform), in a suitable manner. The modified
algorithms are termed `fast' because of their ability to reduce the
computational complexity per computed coefficient from L to log L
(within a small constant factor) for large filter lengths L. For
short filters, smaller gains are obtained: `fast running FIR (finite
impulse response) filtering' techniques allow one to achieve typically
30% savings in computations},
file = {Rioul_O_1992_tit_fas_adcwt.pdf:Rioul_O_1992_tit_fas_adcwt.pdf:PDF},
owner = {duvall},
pdf = {Rioul_O_1992_tit_fas_adcwt.pdf},
timestamp = {2007.06.07}
}
@PHDTHESIS{Romberg_J_2003_phd_mul_gip,
author = {Romberg, J.},
title = {Multiscale geometric image processing},
school = {Rice university},
year = {2003},
month = {Jul.},
abstract = {Since their introduction a little more than 10 years ago, wavelets
have revolutionized image processing. Wavelet based algorithms define
the state-of-the-art for applications including image coding (JPEG-2000),
restoration, and segmentation. Despite their success, wavelets have
significant shortcomings in their treatment of edges. Wavelets do
not parsimoniously capture even the simplest geometrical structure
in images, and wavelet based processing algorithms often produce
images with ringing around the edges. As a first step towards accounting
for this structure, we will show how to explicitly capture the geometric
regularity of contours in cartoon images using the wedgelet representation
and a multiscale geometry model. The wedgelet representation builds
up an image out of simple piecewise constant functions with linear
discontinuities. We will show how the geometry model, by putting
a joint distribution on the orientations of the linear discontinuities,
allows us to weigh several factors when choosing the wedgelet representation:
the error between the representation and the original image, the
parsimony of the representation, and whether the wedgelets in the
representation form "natural" geometrical structures. We will analyze
a simple wedgelet coder based on these principles, and show that
it has optimal asymptotic performance for simple cartoon images.
Next, we turn our attention to piecewise smooth images; images that
are smooth away from a smooth contour. Using a representation composed
of wavelets and wedgeprints (wedgelets projected into the wavelet
domain), we develop a quadtree based prototype coder whose rate-distortion
performance is asymptotically near-optimal. We use these ideas to
implement a full-scale image coder that outperforms JPEG-2000 both
in peak signal to noise ratio (by 1--1.5dB at low bitrates) and visually.
Finally, we shift our focus to building a statistical image model
directly in the wavelet domain. For applications other than compression,
the approximate shift-invariance and directional selectivity of the
slightly redundant complex wavelet transform make it particularly
well-suited for modeling singularity structure. Around edges in images,
complex wavelet coefficients behave very predictably, exhibiting
dependencies that we will exploit using a hidden Markov tree model.
We demonstrate the effectiveness of the complex wavelet model with
several applications: image denoising, multiscale segmentation, and
feature extraction.},
file = {Romberg_J_2003_phd_mul_gip.pdf:Romberg_J_2003_phd_mul_gip.pdf:PDF},
owner = {duvall},
timestamp = {2010.12.20}
}
@ARTICLE{Rosenfeld_A_2001_j-entcs_dig_s,
author = {A. Rosenfeld and R. Klette},
title = {Digital Straightness},
journal = j-entcs,
year = {2001},
volume = {46},
pages = {1--32},
note = {8th Int. Workshop on Combinatorial Image Analysis (IWCIA)},
issn = {1571-0661},
abstract = {A digital arc is called [`]straight' if it is the digitization of
a straight line segment. Since the concept of digital straightness
was introduced in the mid-1970's, dozens of papers on the subject
have appeared; many characterizations of digital straight lines have
been formulated, and many algorithms for determining whether a digital
arc is straight have been defined. This paper reviews the literature
on digital straightness and discusses its relationship to other concepts
of geometry, the theory of words, and number theory.},
doi = {DOI: 10.1016/S1571-0661(04)80976-9},
file = {Rosenfeld_A_2001_j-entcs_dig_s.pdf:Rosenfeld_A_2001_j-entcs_dig_s.pdf:PDF},
owner = {duvall},
pdf = {Rosenfeld_A_2001_j-entcs_dig_s.pdf},
timestamp = {2009.11.19},
url = {http://www.sciencedirect.com/science/article/B75H1-4DDWJGP-7M/2/203cd8c8e11100fdc0fca32495f50dbe}
}
@INPROCEEDINGS{Rosiene_C_1999_p-iscas_ten_pwmdca,
author = {Rosiene, C. P. and Nguyen, T. Q.},
title = {Tensor-product wavelet vs. {Mallat} decomposition: a comparative
analysis},
booktitle = p-iscas,
year = {1999},
volume = {3},
pages = {431--434},
month = {Jul.},
abstract = {The two-dimensional tensor product wavelet transform is compared to
the Mallat representation for the purpose of data compression. It
is shown that the tensor product wavelet transform will always provide
a coding gain greater than or equal to that of the Mallat representation.
Further, the costs of obtaining the tensor product wavelet transform
are outlined},
doi = {10.1109/ISCAS.1999.778877},
file = {Rosiene_C_1999_p-iscas_ten_pwmdca.pdf:Rosiene_C_1999_p-iscas_ten_pwmdca.pdf:PDF},
keywords = {Mallat decomposition;coding gain;data compression;image compression;subband
coding;two-dimensional tensor product wavelet transform;data compression;image
coding;tensors;wavelet transforms;},
owner = {duvall},
pdf = {Rosiene_C_1999_p-iscas_ten_pwmdca.pdf},
timestamp = {2010.02.24}
}
@ARTICLE{Rosca_D_2007_j-four-anal-appl_wav_bsorp,
author = {Ro{\c{s}}ca, D.},
title = {Wavelet bases on the sphere obtained by radial projection},
journal = j-four-anal-appl,
year = {2007},
volume = {13},
pages = {421--434},
number = {4},
owner = {duvall},
publisher = {Springer},
timestamp = {2011.01.05}
}
@ARTICLE{Rubinstein_R_2010_j-proc-ieee_dic_srm,
author = {Rubinstein, R. and Bruckstein, A. M. and Elad, M.},
title = {Dictionaries for Sparse Representation Modeling},
journal = j-proc-ieee,
year = {2010},
volume = {98},
pages = {1045--1057},
number = {6},
month = {Jun.},
issn = {0018-9219},
abstract = {Sparse and redundant representation modeling of data assumes an ability
to describe signals as linear combinations of a few atoms from a
pre-specified dictionary. As such, the choice of the dictionary that
sparsifies the signals is crucial for the success of this model.
In general, the choice of a proper dictionary can be done using one
of two ways: i) building a sparsifying dictionary based on a mathematical
model of the data, or ii) learning a dictionary to perform best on
a training set. In this paper we describe the evolution of these
two paradigms. As manifestations of the first approach, we cover
topics such as wavelets, wavelet packets, contourlets, and curvelets,
all aiming to exploit 1-D and 2-D mathematical models for constructing
effective dictionaries for signals and images. Dictionary learning
takes a different route, attaching the dictionary to a set of examples
it is supposed to serve. From the seminal work of Field and Olshausen,
through the MOD, the K-SVD, the Generalized PCA and others, this
paper surveys the various options such training has to offer, up
to the most recent contributions and structures.},
doi = {10.1109/JPROC.2010.2040551},
keywords = {dictionary learning;mathematical data model;redundant signal representation
modeling;signal sampling;sparse signal representation modeling;training
set;signal representation;signal sampling;wavelet transforms;},
owner = {duvall},
timestamp = {2010.08.30}
}
@ARTICLE{Rudin_L_1992_j-phys-d_non_tvbnra,
author = {Rudin, L. I. and Osher, S. and Fatemi, E.},
title = {Nonlinear total variation based noise removal algorithms},
journal = j-phys-d,
year = {1992},
volume = {60},
pages = {259--268},
number = {1-4},
month = {Nov.},
abstract = {A constrained optimization type of numerical algorithm for removing
noise from images is presented. The total variation of the image
is minimized subject to constraints involving the statistics of the
noise. The constraints are imposed using Lagrange multipliers. The
solution is obtained using the gradient-projection method. This amounts
to solving a time dependent partial differential equation on a manifold
determined by the constraints. As t --> \infty the solution converges
to a steady state which is the denoised image. The numerical algorithm
is simple and relatively fast. The results appear to be state-of-the-art
for very noisy images. The method is noninvasive, yielding sharp
edges in the image. The technique could be interpreted as a first
step of moving each level set of the image normal to itself with
velocity equal to the curvature of the level set divided by the magnitude
of the gradient of the image, and a second step which projects the
image back onto the constraint set.},
doi = {10.1016/0167-2789(92)90242-F},
file = {Rudin_L_1992_j-phys-d_non_tvbnra.pdf:Rudin_L_1992_j-phys-d_non_tvbnra.pdf:PDF},
owner = {duvall},
page = {259--268},
timestamp = {2008.11.23}
}
@INPROCEEDINGS{Said_M_2009_p-dgci_mul_dg,
author = {Said, M. and Lachaud, J.-O. and Feschet, F.},
title = {Multiscale discrete geometry},
booktitle = p-dgci,
year = {2009},
series = ser-lncs,
pages = {118--131},
address = {{M}ontr{\'e}al, {Q}u{\'e}bec {C}anada },
publisher = {{S}pringer },
abstract = {{T}his paper presents a first step in analyzing how digital shapes
behave with respect to multiresolution. {W}e first present an analysis
of the covering of a standard digital straight line by a multi-resolution
grid. {W}e then study the multi-resolution of {D}igital {S}traight
{S}egments ({DSS}): we provide a sublinear algorithm computing the
exact characteristics of a {DSS} whenever it is a subset of a known
standard line. {W}e finally deduce an algorithm for computing a multiscale
representation of a digital shape, based only on a {DSS} decomposition
of its boundary.},
affiliation = {{L}aboratoire de {M}ath{\'e}matiques - {LAMA} - {CNRS} : {UMR}5127
- {U}niversit{\'e} de {S}avoie - {L}aboratoire de {L}ogique, {A}lgorithmique
et {I}nformatique - {LLAIC}1 - {U}niversit{\'e} d'{A}uvergne - {C}lermont-{F}errand
{I} },
audience = {internationale },
collaboration = {{G}eo{DIB} ({ANR}-06-{BLAN}-0225) },
file = {Said_M_2009_p-dgci_mul_dg.pdf:Said_M_2009_p-dgci_mul_dg.pdf:PDF},
keywords = {multiscale geometry - digital contours - standard lines - digital
straight segment recognition - Stern-Brocot tree - multi-resolution},
language = {{A}nglais},
owner = {duvall},
pdf = {Said_M_2009_p-dgci_mul_dg.pdf},
timestamp = {2010.02.26},
url = {http://hal.archives-ouvertes.fr/hal-00413681/en/}
}
@ARTICLE{Llonch_S_2010_j-patt-rec_3d_frssr,
author = {Sala Llonch, R. and Kokiopoulou, E. and To\v{s}i{\'c}, I. and Frossard,
P.},
title = {{3D} face recognition with sparse spherical representations},
journal = j-patt-rec,
year = {2010},
volume = {43},
pages = {824--834},
number = {3},
month = {Mar.},
issn = {0031-3203},
abstract = {This paper addresses the problem of 3D face recognition using simultaneous
sparse approximations on the sphere. The 3D face point clouds are
first aligned with a fully automated registration process. They are
then represented as signals on the 2-sphere in order to preserve
depth and geometry information. Next, we implement a dimensionality
reduction process with simultaneous sparse approximations and subspace
projection. It permits to represent each 3D face by only a few spherical
functions that are able to capture the salient facial characteristics,
and hence to preserve the discriminant facial information. We eventually
perform recognition by effective matching in the reduced space, where
linear discriminant analysis can be further activated for improved
recognition performance. The 3D face recognition algorithm is evaluated
on the FRGC v.1.0 data set, where it is shown to outperform classical
state-of-the-art solutions that work with depth images.},
doi = {DOI: 10.1016/j.patcog.2009.07.005},
file = {Llonch_S_2010_j-patt-rec_3d_frssr.pdf:Llonch_S_2010_j-patt-rec_3d_frssr.pdf:PDF},
keywords = {Sparse representations; Dimensionality reduction; Spherical representations;
3D face recognition},
owner = {duvall},
timestamp = {2011.01.05},
url = {http://www.sciencedirect.com/science/article/B6V14-4WT3WG7-1/2/90b71f122fe206e818fc9f2a8633dad9}
}
@ARTICLE{Sampat_M_2009_tip_com_wssnisi,
author = {Sampat, M. P. and Wang, Z. and Gupta, S. and Bovik, A. C. and Markey,
M. K.},
title = {Complex Wavelet Structural Similarity: A New Image Similarity Index},
journal = j-ieee-tip,
year = {2009},
volume = {18},
pages = {2402--2418},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {The monogenic signal is the natural 2-D counterpart of the 1-D analytic
signal. We propose to transpose the concept to the wavelet domain
by considering a complexified version of the Riesz transform which
has the remarkable property of mapping a real-valued (primary) wavelet
basis of $L_2({BBR}^2)$ into a complex one. The Riesz operator is
also steerable in the sense that it give access to the Hilbert transform
of the signal along any orientation. Having set those foundations,
we specify a primary polyharmonic spline wavelet basis of $L_2({BBR}^2)$
that involves a single Mexican-hat-like mother wavelet (Laplacian
of a B-spline). The important point is that our primary wavelets
are quasi-isotropic: they behave like multiscale versions of the
fractional Laplace operator from which they are derived, which ensures
steerability. We propose to pair these real-valued basis functions
with their complex Riesz counterparts to specify a multiresolution
monogenic signal analysis. This yields a representation where each
wavelet index is associated with a local orientation, an amplitude
and a phase. We give a corresponding wavelet-domain method for estimating
the underlying instantaneous frequency. We also provide a mechanism
for improving the shift and rotation-invariance of the wavelet decomposition
and show how to implement the transform efficiently using perfect-
reconstruction filterbanks. We illustrate the specific feature- extraction
capabilities of the representation and present novel examples of
wavelet-domain processing; in particular, a robust, tensor-based
analysis of directional image patterns, the demodulation of interferograms,
and the reconstruction of digital holograms.},
doi = {10.1109/TIP.2009.2027628},
file = {Sampat_M_2009_tip_com_wssnisi.pdf:Sampat_M_2009_tip_com_wssnisi.pdf:PDF},
keywords = {Not Available Non-controlled Indexing Not Available Author Keywords
Complex wavelet structural similarity index (CW-SSIM), image similarity,
structural similarity (SSIM) index Medical Subject Heading (MeSH
Terms) Not Available PACS Codes Not Available DOE Thesaurus Terms
Not Available References No references available on IEEE Xplore.
Citing Documents No citing documents available on IEEE Xplore. Access
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Email/Printer Friendly Format Multiresolution Monogenic Signal Analysis
Using the Riesz?Laplace Wavelet Transform Unser, M., Sage, D., Van
De Ville, D. This paper appears in: Image Processing, IEEE Transactions
on Publication Date: Nov. 2009 Volume: 18,, Issue: 11 On page(s):
2402-2418 ISSN: 1057- 7149 Digital Object Identifier: 10.1109/TIP.2009.2027628
First Published: 2009-07-14 Current Version Published: 2009-10-13
Abstract The monogenic signal is the natural 2-D counterpart of the
1-D analytic signal. We propose to transpose the concept to the wavelet
domain by considering a complexified version of the Riesz transform
which has the remarkable property of mapping a real-valued (primary)
wavelet basis of $L_2({BBR}^2)$ into a complex one. The Riesz operator
is also steerable in the sense that it give access to the Hilbert
transform of the signal along any orientation. Having set those foundations,
we specify a primary polyharmonic spline wavelet basis of $L_2({BBR}^2)$
that involves a single Mexican-hat-like mother wavelet (Laplacian
of a B-spline). The important point is that our primary wavelets
are quasi-isotropic: they behave like multiscale versions of the
fractional Laplace operator from which they are derived, which ensures
steerability. We propose to pair these real-valued basis functions
with their complex Riesz counterparts to specify a multiresolution
monogenic signal analysis. This yields a representation where each
wavelet index is associated with a local orientation, an amplitude
and a phase. We give a corresponding wavelet-domain method for estimating
the underlying instantaneous frequency. We also provide a mechanism
for improving the shift and rotation-invariance of the wavelet decomposition
and show how to implement the transform efficiently using perfect-
reconstruction filterbanks. We illustrate the specific feature- extraction
capabilities of the representation and present novel examples of
wavelet-domain processing; in particular, a robust, tensor-based
analysis of directional image patterns, the demodulation of interferograms,
and the reconstruction of digital holograms. Index Terms Inspec Controlled
Indexing Not Available},
owner = {duvall},
timestamp = {2009.10.15}
}
@INPROCEEDINGS{Schroder_P_1995_p-acm-siggraph_sph_werfs,
author = {P. Schr{\"{o}}der and W. Sweldens},
title = {Spherical wavelets: efficiently representing functions on the sphere},
booktitle = p-acm-siggraph,
year = {1995},
pages = {161--172},
abstract = {Wavelets have proven to be powerful bases for use in numerical
analysis and signal processing. Their power lies in the fact that
they only require a small number of coefficients to represent general
functions and large data sets accurately. This allows compression
and efficient computations. Classical constructions have been
limited to simple domains such as intervals and rectangles. In this
paper we present a wavelet construction for scalar functions defined
on the sphere. We show how biorthogonal wavelets with custom
properties can be constructed with the lifting scheme. The bases
are extremely easy to implement and allow fully adaptive subdivisions.
We give examples of functions defined on the sphere, such
as topographic data, bidirectional reflection distribution functions,
and illumination, and show how they can be efficiently represented
with spherical wavelets.},
doi = {10.1145/218380.218439},
file = {Schroder_P_1995_p-acm-siggraph_sph_werfs.pdf:Schroder_P_1995_p-acm-siggraph_sph_werfs.pdf:PDF},
keywords = {wavelets, sphere},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Secker_A_2003_j-ieee-tip_lif_bimatlimatfhsvc,
author = {A. Secker and D. Taubman},
title = {Lifting-based invertible motion adaptive transform ({LIMAT}) framework
for highly scalable video compression},
journal = j-ieee-tip,
year = {2003},
volume = {12},
pages = {1530--1542},
number = {12},
month = {Dec.},
owner = {duvall},
timestamp = {2011.01.03}
}
@INPROCEEDINGS{Selesnick_I_2001_p-ciss_cha_dhtpwb,
author = {Selesnick, I. W.},
title = {The Characterization and Design of {Hilbert} Transform Pairs of Wavelet
Bases},
booktitle = p-ciss,
year = {2001},
address = {Baltimore, USA},
month = {Mar.},
owner = {duvall},
timestamp = {2009.07.20}
}
@ARTICLE{Selesnick_I_2001_spl_hil_tpwb,
author = {Selesnick, I. W. },
title = {{Hilbert} transform pairs of wavelet bases},
journal = spl,
year = {2001},
volume = {8},
pages = {170--173},
number = {6},
month = {Jun.},
abstract = {This paper considers the design of pairs of wavelet bases where the
wavelets form a Hilbert transform pair. The derivation is based on
the limit functions defined by the infinite product formula. It is
found that the scaling filters should be offset from one another
by a half sample. This gives an alternative derivation and explanation
for the result by Kingsbury (1999), that the dual-tree DWT is (nearly)
shift-invariant when the scaling filters satisfy the same offset},
booktitle = {IEEE Trans. on Signal Processing},
doi = {10.1109/97.923042},
file = {Selesnick_I_2001_spl_hil_tpwb.pdf:Selesnick_I_2001_spl_hil_tpwb.pdf:PDF},
owner = {duvall},
pdf = {Selesnick_I_2001_spl_hil_tpwb.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Selesnick_I_2005_spm_dua_tcwt,
author = {Selesnick, I. W. and Baraniuk, R. G. and Kingsbury, N. G.},
title = {The dual-tree complex wavelet transform},
journal = j-ieee-spm,
year = {2005},
volume = {22},
pages = {123--151},
number = {6},
month = {Nov.},
file = {Selesnick_I_2005_spm_dua_tcwt.pdf:Selesnick_I_2005_spm_dua_tcwt.pdf:PDF},
owner = {duvall},
pdf = {Selesnick_I_2005_spm_dua_tcwt.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Shapiro_J_1993_j-ieee-tsp_emb_iczwc,
author = {Shapiro, J. M.},
title = {Embedded image coding using zerotrees of wavelet coefficients},
journal = j-ieee-tsp,
year = {1993},
volume = {41},
pages = {3445--3462},
month = {Dec.},
issn = {1053-587X},
abstract = {The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably
effective, image compression algorithm, having the property that
the bits in the bit stream are generated in order of importance,
yielding a fully embedded code. The embedded code represents a sequence
of binary decisions that distinguish an image from the "null" image.
Using an embedded coding algorithm, an encoder can terminate the
encoding at any point thereby allowing a target rate or target distortion
metric to be met exactly. Also, given a bit stream, the decoder can
cease decoding at any point in the bit stream and still produce exactly
the same image that would have been encoded at the bit rate corresponding
to the truncated bit stream. In addition to producing a fully embedded
bit stream, the EZW consistently produces compression results that
are competitive with virtually all known compression algorithms on
standard test images. Yet this performance is achieved with a technique
that requires absolutely no training, no pre-stored tables or codebooks,
and requires no prior knowledge of the image source. The EZW algorithm
is based on four key concepts: (1) a discrete wavelet transform or
hierarchical subband decomposition, (2) prediction of the absence
of significant information across scales by exploiting the self-similarity
inherent in images, (3) entropy-coded successive-approximation quantization,
and (4) universal lossless data compression which is achieved via
adaptive arithmetic coding},
doi = {10.1109/78.258085},
file = {Shapiro_J_1993_j-ieee-tsp_emb_iczwc.pdf:Shapiro_J_1993_j-ieee-tsp_emb_iczwc.pdf:PDF},
owner = {duvall},
pdf = {Shapiro_J_1993_j-ieee-tsp_emb_iczwc.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Shen_L_2006_tsp_ima_dtf,
author = {Shen, L. and Papadakis, M. and Kakadiaris, I. A. and Konstantinidis,
I. and Kouri, D. and Hoffman, D.},
title = {Image denoising using a tight frame},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {1254--1263},
number = {5},
month = may,
issn = {1057-7149},
abstract = {We present a general mathematical theory for lifting frames that allows
us to modify existing filters to construct new ones that form Parseval
frames. We apply our theory to design nonseparable Parseval frames
from separable (tensor) products of a piecewise linear spline tight
frame. These new frame systems incorporate the weighted average operator,
the Sobel operator, and the Laplacian operator in directions that
are integer multiples of 45°. A new image denoising algorithm is
then proposed, tailored to the specific properties of these new frame
filters. We demonstrate the performance of our algorithm on a diverse
set of images with very encouraging results.},
doi = {10.1109/TIP.2005.864240},
file = {Shen_L_2006_tsp_ima_dtf.pdf:Shen_L_2006_tsp_ima_dtf.pdf:PDF},
owner = {duvall},
pdf = {Shen_L_2006_tsp_ima_dtf.pdf},
timestamp = {2009.05.20}
}
@ARTICLE{Shensa_M_1992_j-ieee-tsp_dis_wtwatma,
author = {Shensa, M. J.},
title = {The discrete wavelet transform: wedding the \`a trous and {Mallat}
algorithms},
journal = j-ieee-tsp,
year = {1992},
volume = {40},
pages = {2464--2482},
number = {10},
month = {Oct.},
abstract = {In a general sense this paper represents an effort
to clarify the relationship of discrete and continuous wavelet
transforms. More narrowly, it focuses on bringing together two
separately motivated implementations of the wavelet transform,
the algorithme U trous and Mallat?s multiresolution decomposition.
It is observed that these algorithms are both special
cases of a single filter bank structure, the discrete wavelet
transform, the behavior of which is governed by one?s choice
of filters. In fact, the h trow algorithm, originally devised as a
computationally efficient implementation, is more properly
viewed as a nonorthonormal multiresolution algorithm for
which the discrete wavelet transform is exact. Moreover, it is
shown that the commonly used Lagrange i~ trous filters are in
one-to-one correspondence with the convolutional squares of
the Daubechies filters for orthonormal wavelets of compact
support.
A systematic framework for the discrete wavelet transform
is provided, and conditions are derived under which it computes
the continuous wavelet transform exactly. Suitable filter
constraints for finite energy and boundedness of the discrete
transform are also derived. Finally, relevant signal processing
parameters are examined, and it is remarked that orthonormality
is balanced by restrictions on resolution.},
doi = {10.1109/78.157290},
file = {Shensa_M_1992_j-ieee-tsp_dis_wtwatma.pdf:Shensa_M_1992_j-ieee-tsp_dis_wtwatma.pdf:PDF},
owner = {duvall},
timestamp = {2007.06.15}
}
@ARTICLE{Shi_X_2006_spl_rot_iosfb,
author = {X. Shi and A. L. Ribeiro Castro and R. Manduchi and R. Montgomery},
title = {Rotational Invariant Operators based on Steerable Filter Banks},
journal = spl,
year = {2006},
volume = {13},
number = {11},
month = {Nov.},
file = {Shi_X_2006_spl_rot_iosfb.pdf:Shi_X_2006_spl_rot_iosfb.pdf:PDF},
owner = {duvall},
pdf = {Shi_X_2006_spl_rot_iosfb.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Shukla_R_2005_tip_rat_dotscappi,
author = {Shukla, R. and Dragotti, P. L. and Do, M. N. and Vetterli, M.},
title = {Rate-Distorsion optimized tree-structured compression algorithms
for piecewise polynomial images},
journal = j-ieee-tip,
year = {2005},
volume = {14},
pages = {343--359},
number = {3},
month = {Mar.},
file = {Shukla_R_2005_tip_rat_dotscappi.pdf:Shukla_R_2005_tip_rat_dotscappi.pdf:PDF},
owner = {duvall},
pdf = {Shukla_R_2005_tip_rat_dotscappi.pdf},
timestamp = {2008.02.04}
}
@ARTICLE{Simoncelli_E_1996_tip_ste_wfloa,
author = {E. P. Simoncelli and H. Farid},
title = {Steerable wedge filters for local orientation analysis},
journal = j-ieee-tip,
year = {1996},
volume = {5},
pages = {1377--1382},
number = {9},
month = {Sep.},
issn = {1057-7149},
abstract = {Steerable filters have been used to analyze local orientation patterns
in imagery. Such filters are typically based on directional derivatives,
whose symmetry produces orientation responses that are periodic with
period \π, independent of image structure. We present a more
general set of steerable filters that alleviate this problem},
doi = {10.1109/83.535851},
file = {Simoncelli_E_1996_tip_ste_wfloa.pdf:Simoncelli_E_1996_tip_ste_wfloa.pdf:PDF},
keywords = {edge detection, filtering theory, image processing, interpolation},
optyear = {1996},
owner = {duvall},
pdf = {Simoncelli_E_1996_tip_ste_wfloa.pdf},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Simoncelli_E_1995_icip_ste_pfamdc,
author = {Simoncelli, E. P. and Freeman, W. T.},
title = {The steerable pyramid: a flexible architecture for multiscale derivative
computation},
booktitle = p-icip,
year = {1995},
pages = {444--447},
file = {Simoncelli_E_1995_icip_ste_pfamdc.pdf:Simoncelli_E_1995_icip_ste_pfamdc.pdf:PDF},
optmonth = {Oct.},
optvolume = {III},
owner = {duvall},
pdf = {Simoncelli_E_1995_icip_ste_pfamdc.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Simoncelli_E_1992_tit_shi_mst,
author = {Simoncelli, E. P. and Freeman, W. T. and Adelson, E. H. and Heeger,
D. J.},
title = {Shiftable Multi-scale Transforms},
journal = j-ieee-tit,
year = {1992},
volume = {38},
pages = {587--607},
number = {2},
month = {Mar.},
note = {Special Issue on Wavelets},
abstract = {Orthogonal wavelet transforms have recently become a popular representation
for multi-scale signal and image analysis. One of the major drawbacks
of these representations is their lack of translation invariance:
the content of wavelet subbands is unstable under translations of
the input signal. Wavelet transforms are also unstable with respect
to dilations of the input signal, and in two dimensions, rotations
of the input signal. We formalize these problems by defining a type
of translation invariance that we call "shiftability". In the spatial
domain, shiftability corresponds to a lack of aliasing; thus, the
conditions under which the property holds are specified by the sampling
theorem. Shiftability may also be considered in the context of other
domains, particularly orientation and scale. We explore ``jointly
shiftable'' transforms that are simultaneously shiftable in more
than one domain. Two examples of jointly shiftable transforms are
designed and implemented: a one-dimensional transform that is jointly
shiftable in position and scale, and a two-dimensional transform
that is jointly shiftable in position and orientation. We demonstrate
the usefulness of these image representations for scale-space analysis,
stereo disparity measurement, and image enhancement.},
abstract-url = {http://www.cis.upenn.edu/~eero/ABSTRACTS/simoncelli91-abstract.html},
file = {Simoncelli_E_1992_tit_shi_mst.pdf:Simoncelli_E_1992_tit_shi_mst.pdf:PDF},
owner = {duvall},
pdf = {Simoncelli_E_1992_tit_shi_mst.pdf},
pdf-url = {http://www.cns.nyu.edu/pub/eero/simoncelli91-reprint.pdf},
ps-url = {ftp://ftp.cis.upenn.edu/pub/eero/simoncelli91.ps.Z},
timestamp = {2007.06.07}
}
@INPROCEEDINGS{Smith_M_1984_p-icassp_pro_derfbtssc,
author = {Smith, M. J. T. and Barnwell, T. P.},
title = {A procedure for designing exact reconstruction filter banks for tree
structured subband coders},
booktitle = p-icassp,
year = {1984},
volume = {9},
pages = {421--424},
address = {San Diego, CA, USA},
month = {Mar. 19-21},
abstract = {In recent years, tree-structured analysis/reconstruction systems have
been extensively studied for use in subband coders for speech. In
such systems, it is important that the individual channel signals
be decimated in such a way that the number of samples coded and transmitted
does not exceed the number of samples in the original speech signal.
Under this constraint, the systems presented in the past have sought
to remove the aliasing distortion while minimizing the overall analysis/reconstruction
distortion. In this paper, it is shown that it is possible to design
tree-structured analysis/reconstruction systems which meet the sampling
rate condition and which also result in exact reconstruction of the
input signal. This paper develops the conditions for exact reconstruction
and presents a general method for designing the corresponding high
quality analysis and reconstruction filters.},
owner = {duvall},
timestamp = {2008.11.23}
}
@ARTICLE{Smith_M_1995_j-ieee-tip_rec_tvfbsic,
author = {Smith, M. J. T. and Chung, W. C.-L.},
title = {Recursive time-varying filter banks for subband image coding},
journal = j-ieee-tip,
year = {1995},
volume = {4},
pages = {885--895},
number = {7},
month = jul,
issn = {1057-7149},
abstract = {Filter banks, subband/wavelets, and multiresolution decompositions
that employ recursive filters have been considered previously and
are recognized for their efficiency in partitioning the frequency
spectrum. This paper presents an analysis of a new infinite impulse
response (IIR) filter bank in which these computationally efficient
filters may be changed adaptively in response to the input. The new
filter bank framework is presented and discussed in the context of
subband image coding. In the absence of quantization errors, exact
reconstruction can be achieved. By the proper choice of an adaptation
scheme, it is shown that recursive linear time-varying (LTV) filter
banks can yield improvement over conventional ones},
doi = {10.1109/83.392331},
file = {Smith_M_1995_j-ieee-tip_rec_tvfbsic.pdf:Smith_M_1995_j-ieee-tip_rec_tvfbsic.pdf:PDF},
keywords = {IIR filter bank;adaptation scheme;computationally efficient filters;exact
image reconstruction;frequency spectrum partitioning;infinite impulse
response filter bank;multiresolution decompositions;quantization
errors;recursive linear time-varying filter banks;subband image coding;subband/wavelets;IIR
filters;band-pass filters;delay circuits;filtering theory;image coding;image
reconstruction;image resolution;recursive filters;time-varying filters;},
owner = {duvall},
timestamp = {2011.04.08}
}
@INPROCEEDINGS{VanSpaendonck_R_2000_p-icip_non_rdscw,
author = {van Spaendonck, R. and Fernandes, F. and Coates, M. and Burrus, C.},
title = {Non-redundant, Directionally selective, complex wavelets},
booktitle = p-icip,
year = {2000},
volume = {2},
pages = {379--382},
address = {Istanbul, Turkey},
month = {Sep.},
abstract = {Poor directional selectivity, a major disadvantage of the 2D separable
discrete wavelet transform (DWT), has heretofore been circumvented
either by using highly redundant, nonseparable wavelet transforms
or by using restrictive designs to obtain a pair of wavelet trees.
In this paper, we demonstrate that superior directional selectivity
may be obtained with no redundancy in any separable wavelet transform.
We achieve this by projecting the wavelet transform coefficients
onto the Softy space of signals and decimating before processing.
A novel reconstruction step guarantees perfect reconstruction within
this critically-sampled framework.},
doi = {10.1109/ICIP.2000.899399},
issn = {1522-4880},
keywords = {2D separable discrete wavelet transform;DWT;Softy space projection;directional
selectivity;filter bank;image processing;nonredundant directionally
selective complex wavelets;perfect reconstruction;separable wavelet
transform;channel bank filters;discrete wavelet transforms;filtering
theory;image processing;image reconstruction;},
owner = {duvall},
timestamp = {2009.07.20}
}
@ARTICLE{Starck_J_2002_tip_cur_tid,
author = {Starck, J.-L. and Cand{\`e}s, E. J. and Donoho, D. L.},
title = {The curvelet transform for image denoising},
journal = j-ieee-tip,
year = {2002},
volume = {11},
pages = {670--685},
number = {6},
month = {Jun.},
issn = {1057-7149},
abstract = {We describe approximate digital implementations of two new mathematical
transforms, namely, the ridgelet transform and the curvelet transform.
Our implementations offer exact reconstruction, stability against
perturbations, ease of implementation, and low computational complexity.
A central tool is Fourier-domain computation of an approximate digital
Radon transform. We introduce a very simple interpolation in the
Fourier space which takes Cartesian samples and yields samples on
a rectopolar grid, which is a pseudo-polar sampling set based on
a concentric squares geometry. Despite the crudeness of our interpolation,
the visual performance is surprisingly good. Our ridgelet transform
applies to the Radon transform a special overcomplete wavelet pyramid
whose wavelets have compact support in the frequency domain. Our
curvelet transform uses our ridgelet transform as a component step,
and implements curvelet subbands using a filter bank of a`
trous wavelet filters. Our philosophy throughout is that transforms
should be overcomplete, rather than critically sampled. We apply
these digital transforms to the denoising of some standard images
embedded in white noise. In the tests reported here, simple thresholding
of the curvelet coefficients is very competitive with "state of the
art" techniques based on wavelets, including thresholding of decimated
or undecimated wavelet transforms and also including tree-based Bayesian
posterior mean methods. Moreover, the curvelet reconstructions exhibit
higher perceptual quality than wavelet-based reconstructions, offering
visually sharper images and, in particular, higher quality recovery
of edges and of faint linear and curvilinear features. Existing theory
for curvelet and ridgelet transforms suggests that these new approaches
can outperform wavelet methods in certain image reconstruction problems.
The empirical results reported here are in encouraging agreement},
doi = {10.1109/TIP.2002.1014998},
file = {Starck_J_2002_tip_cur_tid.pdf:Starck_J_2002_tip_cur_tid.pdf:PDF},
keywords = {Fourier transforms Radon transforms channel bank filters filtering
theory image reconstruction interpolation wavelet transforms white
noise ; Cartesian samples Fourier space Fourier-domain approximate
digital Radon transform approximate digital implementations concentric
squares geometry curvelet coefficients curvelet transform decimated
wavelet transforms exact reconstruction filter bank frequency domain
image denoising interpolation low computational complexity overcomplete
wavelet pyramid pseudo-polar sampling set rectopolar grid ridgelet
transform stability tree-based Bayesian posterior mean methods trous
wavelet filters undecimated wavelet transforms visual performance
wavelet-based image reconstruction white noise},
owner = {duvall},
pdf = {Starck_J_2002_tip_cur_tid.pdf},
timestamp = {2009.07.14}
}
@ARTICLE{Starck_J_2004_j-adv-imag-electron-phys_red_tamca,
author = {J.-L. Starck and M. Elad and D. L. Donoho},
title = {Redundant Multiscale Transforms and their Application for Morphological
Component Analysis},
journal = j-adv-imag-electron-phys,
year = {2004},
volume = {132},
pages = {287--348},
file = {Starck_J_2004_j-adv-imag-electron-phys_red_tamca-preprint.pdf:Starck_J_2004_j-adv-imag-electron-phys_red_tamca-preprint.pdf:PDF},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Starck_J_2006_j-astron-astrophys_wav_rcs,
author = {Starck, J.-L. and Moudden, Y. and Abrial, P. and Nguyen, M.},
title = {Wavelets, ridgelets and curvelets on the sphere},
journal = j-astron-astrophys,
year = {2006},
volume = {446},
pages = {1191--1204},
month = {Feb.},
abstract = {We present in this paper new multiscale transforms on the sphere,
namely the isotropic undecimated wavelet transform, the pyramidal
wavelet transform, the ridgelet transform and the curvelet transform.
All of these transforms can be inverted i.e. we can exactly reconstruct
the original data from its coefficients in either representation.
Several applications are described. We show how these transforms
can be used in denoising and especially in a Combined Filtering Method,
which uses both the wavelet and the curvelet transforms, thus benefiting
from the advantages of both transforms. An application to component
separation from multichannel data mapped to the sphere is also described
in which we take advantage of moving to a wavelet representation.},
file = {Starck_J_2006_j-astron-astrophys_wav_rcs.pdf:Starck_J_2006_j-astron-astrophys_wav_rcs.pdf:PDF},
keywords = {cosmic microwave background; methods: data analysis; methods: statistical},
owner = {duvall},
pdf = {Starck_J_2006_j-astron-astrophys_wav_rcs.pdf},
timestamp = {2010.02.15}
}
@BOOK{Starck_J_2010_book_spa_ispwcmd,
title = {Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological
Diversity},
publisher = {Cambridge University Press},
year = {2010},
author = {Starck, J.-L. and Murtagh, F. and Fadili, J. M.},
abstract = {This book presents the state of the art in sparse and multiscale image
and signal processing, covering linear multiscale transforms, such
as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale
transforms based on the median and mathematical morphology operators.
Recent concepts of sparsity and morphological diversity are described
and exploited for various problems such as denoising, inverse problem
regularization, sparse signal decomposition, blind source separation,
and compressed sensing. This book weds theory and practice in examining
applications in areas such as astronomy, biology, physics, digital
media, and forensics. A final chapter explores a paradigm shift in
signal processing, showing that previous limits to information sampling
and extraction can be overcome in very significant ways. Matlab and
IDL code accompany these methods and applications to reproduce the
experiments and illustrate the reasoning and methodology of the research
available for download at the associated Web site.},
file = {Starck_J_2010_book_spa_ispwcmd.pdf:Starck_J_2010_book_spa_ispwcmd.pdf:PDF},
isbn = {0521119138},
owner = {duvall},
timestamp = {2010.11.24}
}
@ARTICLE{Steffen_P_1993_tsp_the_rmbwb,
author = {Steffen, P. and Heller, P. N. and Gopinath, R. A. and Burrus, C.
S.},
title = {Theory of regular {$M$}-band wavelet bases},
journal = j-ieee-tsp,
year = {1993},
volume = {41},
pages = {3497--3511},
number = {12},
month = {Dec.},
file = {Steffen_P_1993_tsp_the_rmbwb.pdf:Steffen_P_1993_tsp_the_rmbwb.pdf:PDF},
owner = {duvall},
pdf = {Steffen_P_1993_tsp_the_rmbwb.pdf},
timestamp = {2007.06.07}
}
@ARTICLE{Storath_M_2011_j-siam-j-imaging-sci_dir_mapdmct,
author = {Storath, M.},
title = {Directional Multiscale Amplitude and Phase Decomposition by the Monogenic
Curvelet Transform},
journal = j-siam-j-imaging-sci,
year = {2011},
volume = {4},
pages = {57--78},
number = {1},
abstract = {We reconsider the continuous curvelet transform from a signal processing
point of view. We show that the analyzing elements of the curvelet
transform, the curvelets, can be understood as analytic signals in
the sense of the partial Hilbert transform. We then generalize the
usual curvelets by the monogenic curvelets, which are analytic signals
in the sense of the Riesz transform. They yield a new transform,
called the monogenic curvelet transform. This transform has the useful
property that it behaves at the fine scales like the usual curvelet
transform and at the coarse scales like the monogenic wavelet transform.
In particular, the new transform is highly anisotropic at the fine
scales and yields a well-interpretable amplitude/phase decomposition
of the transform coefficients over all scales. We illustrate the
advantage of this new directional multiscale amplitude/phase decomposition
for the estimation of directional regularity.},
doi = {http://dx.doi.org/10.1137/100803924},
file = {Storath_M_2011_j-siam-j-imaging-sci_dir_mapdmct.pdf:Storath_M_2011_j-siam-j-imaging-sci_dir_mapdmct.pdf:PDF;Storath_M_2011_j-siam-j-imaging-sci_dir_mapdmct-prepriint.pdf:Storath_M_2011_j-siam-j-imaging-sci_dir_mapdmct-prepriint.pdf:PDF},
keywords = {curvelet transform, analytic signal, monogenic signal, Hilbert transform,
Riesz transform, directional wavelet transform},
owner = {duvall},
timestamp = {2011.04.12}
}
@ARTICLE{Sweldens_W_1997_j-siam-math-anal_lif_scsgw,
author = {W. Sweldens},
title = {The lifting scheme: a construction of second generation wavelets},
journal = j-siam-math-anal,
year = {1997},
volume = {29},
pages = {511--546},
number = {2},
owner = {duvall},
timestamp = {2010.02.24}
}
@ARTICLE{Sweldens_W_1996_j-acha_lif_scdcbw,
author = {W. Sweldens},
title = {The lifting scheme: a custom-design construction of biorthogonal
wavelets},
journal = j-acha,
year = {1996},
volume = {3},
pages = {186--200},
number = {2},
month = {Apr.},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Szatmary_K_1992_j-mon-not-roy-astron-soc_per_lcsvsyl,
author = {Szatm{\'a}ry, K. and Vink{\'o}, J.},
title = {Periodicities of the light curve of the semiregular variable star
{Y Lyncis}},
journal = j-mon-not-roy-astron-soc,
year = {1992},
volume = {256},
pages = {321--328},
owner = {duvall},
timestamp = {2010.02.13}
}
@ARTICLE{Tanaka_T_2006_tsp_dir_doprfirfbfof,
author = {Tanaka, T.},
title = {A direct design of oversampled perfect reconstruction {FIR} filter
banks of 50\%-overlapping filters},
journal = j-ieee-tsp,
year = {2006},
volume = {54},
pages = {3011--3022},
number = {8},
month = {Aug.},
doi = {10.1109/TSP.2006.875384},
file = {Tanaka_T_2006_tsp_dir_doprfirfbfof.pdf:Tanaka_T_2006_tsp_dir_doprfirfbfof.pdf:PDF},
owner = {duvall},
pdf = {Tanaka_T_2006_tsp_dir_doprfirfbfof.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Tanaka_T_2004_tsp_gen_lpbtolpprfbls,
author = {Tanaka, T. and Yamashita, Y.},
title = {The generalized lapped pseudo-biorthogonal transform: Oversampled
linear-phase perfect reconstruction filter banks with lattice structures},
journal = j-ieee-tsp,
year = {2004},
volume = {52},
pages = {434--446},
number = {2},
month = {Feb.},
file = {Tanaka_T_2004_tsp_gen_lpbtolpprfbls.pdf:Tanaka_T_2004_tsp_gen_lpbtolpprfbls.pdf:PDF},
owner = {duvall},
pdf = {Tanaka_T_2004_tsp_gen_lpbtolpprfbls.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Tanaka_Y_2010_j-ieee-tip_ada_dwtbdp,
author = {Tanaka, Y. and Hasegawa, M. and Kato, S. and Ikehara, M. and Nguyen,
T. Q.},
title = {Adaptive Directional Wavelet Transform Based on Directional Prefiltering},
journal = j-ieee-tip,
year = {2010},
volume = {19},
pages = {934--945},
number = {4},
month = {Apr.},
issn = {1057-7149},
abstract = {This paper proposes an efficient approach for adaptive directional
wavelet transform (WT) based on directional prefiltering. Although
the adaptive directional WT is able to transform an image along diagonal
orientations as well as traditional horizontal and vertical directions,
it sacrifices computation speed for good image coding performance.
We present two efficient methods to find the best transform directions
by prefiltering using 2-D filter bank or 1-D directional WT along
two fixed directions. The proposed direction calculation methods
achieve comparable image coding performance comparing to the conventional
one with less complexity. Furthermore, transform direction data of
the proposed method can be used for content-based image retrieval
to increase retrieval ratio.},
doi = {10.1109/TIP.2009.2038820},
file = {Tanaka_Y_2010_j-ieee-tip_ada_dwtbdp.pdf:Tanaka_Y_2010_j-ieee-tip_ada_dwtbdp.pdf:PDF},
keywords = {2-D filter bank;adaptive directional wavelet transform;complexity;content-based
image retrieval;directional prefiltering;image coding;channel bank
filters;image coding;image retrieval;wavelet transforms;},
owner = {duvall},
pdf = {Tanaka_Y_2010_j-ieee-tip_ada_dwtbdp.pdf},
timestamp = {2010.05.15}
}
@ARTICLE{Tanaka_Y_2009_tip_mul_irc2d1ddfb,
author = {Tanaka, Y. and Ikehara, M. and Nguyen, T. Q.},
title = {Multiresolution Image Representation Using Combined {2-D} and {1-D}
Directional Filter Banks},
journal = j-ieee-tip,
year = {2009},
volume = {18},
pages = {269--280},
number = {2},
month = {Feb.},
issn = {1057-7149},
abstract = {In this paper, effective multiresolution image representations using
a combination of 2-D filter bank (FB) and directional wavelet transform
(WT) are presented. The proposed methods yield simple implementation
and low computation costs compared to previous 1-D and 2-D FB combinations
or adaptive directional WT methods. Furthermore, they are nonredundant
transforms and realize quad- tree like multiresolution representations.
In applications on nonlinear approximation, image coding, and denoising,
the proposed filter banks show visual quality improvements and have
higher PSNR than the conventional separable WT or the contourlet.},
doi = {10.1109/TIP.2008.2008078},
file = {Tanaka_Y_2009_tip_mul_irc2d1ddfb.pdf:Tanaka_Y_2009_tip_mul_irc2d1ddfb.pdf:PDF},
owner = {duvall},
pdf = {Tanaka_Y_2009_tip_mul_irc2d1ddfb.pdf},
timestamp = {2009.10.27}
}
@INPROCEEDINGS{Taubman_D_1999_p-icip_ada_nsltic,
author = {Taubman, D.},
title = {Adaptive, non-separable lifting transforms for image compression},
booktitle = p-icip,
year = {1999},
volume = {3},
pages = {772--776},
address = {Kobe, Japan},
month = {Oct. 24-28},
abstract = {In the context of high performance image compression algorithms, such
as that emerging as the JPEG 2000 standard, the wavelet transform
has demonstrated excellent compression performance with natural images.
Like all waveform coding techniques, however, performance suffers
in the neighbourhood of oriented edges clad with artificial imagery
such as text and graphics. In this paper, we explore some of the
opportunities offered by the framework of lifting for developing
adaptive wavelet transforms to improve performance under these conditions},
doi = {10.1109/ICIP.1999.817221},
file = {Taubman_D_1999_p-icip_ada_nsltic.pdf:Taubman_D_1999_p-icip_ada_nsltic.pdf:PDF},
keywords = {JPEG 2000 standard;adaptive wavelet transforms;image compression;non-separable
lifting transforms;performance;waveform coding;wavelet transform;data
compression;image coding;wavelet transforms;},
owner = {duvall},
timestamp = {2010.11.12}
}
@ARTICLE{Taubman_D_1994_j-ieee-tip_ori_asci,
author = {Taubman, D. and Zakhor, A.},
title = {Orientation adaptive subband coding of images},
journal = j-ieee-tip,
year = {1994},
volume = {3},
pages = {421--437},
number = {4},
month = {Jul.},
issn = {1057-7149},
abstract = {In the subband coding of images, directionality of image features
has thus far been exploited very little. The proposed subband coding
scheme utilizes orientation of local image features to avoid the
highly objectionable Gibbs-like phenomena observed at reconstructed
image edges with conventional subband schemes at low bit rates, At
comparable bit rates, the subjective image quality obtained by our
orientation adaptive scheme is considerably enhanced over a conventional
separable subband coding scheme, as well as other separable approaches
such as the JPEG compression standard},
doi = {10.1109/83.298396},
file = {Taubman_D_1994_j-ieee-tip_ori_asci.pdf:Taubman_D_1994_j-ieee-tip_ori_asci.pdf:PDF},
keywords = {image coding;image features;low bit rates;orientation adaptive subband
coding;subjective image quality;data compression;image coding;},
owner = {duvall},
pdf = {Taubman_D_1994_j-ieee-tip_ori_asci.pdf},
timestamp = {2010.02.27}
}
@BOOK{Taubman_D_2002_book_jpe_2000icfsp,
title = {{JPEG2000}: Image Compression Fundamentals, Standards and Practice},
publisher = {Kluwer Academic},
year = {2002},
author = {Taubman, D. S. and Marcellin, M. W.},
isbn = {9780792375197},
owner = {duvall},
timestamp = {2010.01.12}
}
@ARTICLE{Treitel_S_1971_j-ieee-tge_des_mspf,
author = {Treitel, S. and Shanks, J. L.},
title = {The Design of Multistage Separable Planar Filters},
journal = j-ieee-tge,
year = {1971},
volume = {9},
pages = {106-27},
number = {1},
month = {Jan.},
issn = {0018-9413},
abstract = {A two-dimensional, or planar, digital filter can be described in terms
of its planar response function, which is in the form of a matrix
of weighting coefficients, or filter array. In many instances the
dimensions of these matrices are so large that their implementation
as ordinary planar convolutional filters becomes computationally
inefficient. It is possible to expand the given coefficient matrix
into a finite and convergent sum of matrix-valued stages. Each stage
can be separated with no error into the product of an m-length column
vector multiplied into an n-length row vector, where m is the number
of rows and n is the number of columns of the original filter array.
Substantial savings in computer storage and speed result if the given
filter array can be represented with a tolerably small error by the
first few stages of the expansion. Since each constituent stage consists
of two vector-valued factors, further computational economies accrue
if the one-dimensional sequences described by these vectors are in
turn approximated by one-dimensional recursive filters. Two geophysical
examples have been selected to illustrate how the present design
techniques may be reduced to practice.},
doi = {10.1109/TGE.1971.271457},
file = {Treitel_S_1971_j-ieee-tge_des_mspf.pdf:Treitel_S_1971_j-ieee-tge_des_mspf.pdf:PDF},
owner = {duvall},
pdf = {Treitel_S_1971_j-ieee-tge_des_mspf.pdf},
timestamp = {2010.02.26}
}
@ARTICLE{Tropp_J_2006_tit_jus_rcpmissn,
author = {Tropp, J. A.},
title = {Just relax: convex programming methods for identifying sparse signals
in noise},
journal = j-ieee-tit,
year = {2006},
volume = {52},
pages = {1030--1051},
number = {3},
month = {Mar.},
issn = {0018-9448},
abstract = {This paper studies a difficult and fundamental problem that arises
throughout electrical engineering, applied mathematics, and statistics.
Suppose that one forms a short linear combination of elementary signals
drawn from a large, fixed collection. Given an observation of the
linear combination that has been contaminated with additive noise,
the goal is to identify which elementary signals participated and
to approximate their coefficients. Although many algorithms have
been proposed, there is little theory which guarantees that these
algorithms can accurately and efficiently solve the problem. This
paper studies a method called convex relaxation, which attempts to
recover the ideal sparse signal by solving a convex program. This
approach is powerful because the optimization can be completed in
polynomial time with standard scientific software. The paper provides
general conditions which ensure that convex relaxation succeeds.
As evidence of the broad impact of these results, the paper describes
how convex relaxation can be used for several concrete signal recovery
problems. It also describes applications to channel coding, linear
regression, and numerical analysis},
doi = {10.1109/TIT.2005.864420},
file = {Tropp_J_2006_tit_jus_rcpmissn.pdf:Tropp_J_2006_tit_jus_rcpmissn.pdf:PDF},
owner = {duvall},
pdf = {Tropp_J_2006_tit_jus_rcpmissn.pdf},
timestamp = {2008.11.23}
}
@ARTICLE{Tropp_J_2005_j-ieee-tit_gre_garsa,
author = {Tropp, J. A.},
title = {Greed is good: algorithmic results for sparse approximation},
journal = j-ieee-tit,
year = {2004},
volume = {50},
pages = {2231--2242},
number = {10},
month = {Oct.},
issn = {0018-9448},
abstract = {This article presents new results on using a greedy algorithm, orthogonal
matching pursuit (OMP), to solve the sparse approximation problem
over redundant dictionaries. It provides a sufficient condition under
which both OMP and Donoho's basis pursuit (BP) paradigm can recover
the optimal representation of an exactly sparse signal. It leverages
this theory to show that both OMP and BP succeed for every sparse
input signal from a wide class of dictionaries. These quasi-incoherent
dictionaries offer a natural generalization of incoherent dictionaries,
and the cumulative coherence function is introduced to quantify the
level of incoherence. This analysis unifies all the recent results
on BP and extends them to OMP. Furthermore, the paper develops a
sufficient condition under which OMP can identify atoms from an optimal
approximation of a nonsparse signal. From there, it argues that OMP
is an approximation algorithm for the sparse problem over a quasi-incoherent
dictionary. That is, for every input signal, OMP calculates a sparse
approximant whose error is only a small factor worse than the minimal
error that can be attained with the same number of terms.},
doi = {10.1109/TIT.2004.834793},
file = {Tropp_J_2005_j-ieee-tit_gre_garsa.pdf:Tropp_J_2005_j-ieee-tit_gre_garsa.pdf:PDF},
keywords = { BP paradigm; Donoho's basis pursuit; OMP; atoms identification; cumulative
coherence function; greedy algorithm; iterative method; linear programming;
nonsparse signal; optimal approximation; orthogonal matching pursuit;
quasiincoherent dictionary; redundant dictionary; sparse approximation
problem; algorithm theory; approximation theory; dictionaries; linear
programming; redundant number systems; signal processing; sparse
matrices;},
owner = {duvall},
pdf = {Tropp_J_2005_j-ieee-tit_gre_garsa.pdf},
timestamp = {2010.02.16}
}
@ARTICLE{Unser_M_2011_j-ieee-tip_ste_ptwfl2rd,
author = {M. Unser and N. Chenouard and D. Van De Ville},
title = {Steerable Pyramids and Tight Wavelet Frames in ${L}_2(\mathbb{R}^d)$},
journal = j-ieee-tip,
year = {2011},
note = {Preprint, in press},
abstract = {We present a functional framework for the design of tight steerable
wavelet frames in any number of dimensions. The 2D version of the
method can be viewed as a generalization of Simoncelli's steerable
pyramid that gives access to a larger palette of steerable wavelets
via a suitable parametrization. The backbone of our construction
is a primal isotropic wavelet frame that provides the multiresolution
decomposition of the signal. The steerable wavelets are obtained
by applying a one-to-many mapping (Nth-order generalized Riesz transform)
to the primal ones. The shaping of the steerable wavelets is controlled
by an M × M unitary matrix (where M is the number of wavelet channels)
that can be selected arbitrarily; this allows for a much wider range
of solutions than the traditional equiangular configuration (steerable
pyramid). We give a complete functional description of these generalized
wavelet transforms and derive their steering equations. We describe
some concrete examples of transforms, including some built around
a Mallat-type multiresolution analysis of $L_2(R^d)$, and provide
a fast FFT-based decomposition algorithm. We also propose a principal-component-based
method for signal-adapted wavelet design. Finally, we present some
illustrative examples together with a comparison of the denoising
performance of various brands of steerable transforms. The results
are in favor of an optimized wavelet design (equalized PCA) which
consistently performs best.},
file = {Unser_M_2011_j-ieee-tip_ste_ptwfl2rd.pdf:Unser_M_2011_j-ieee-tip_ste_ptwfl2rd.pdf:PDF},
owner = {duvall},
timestamp = {2011.04.10}
}
@ARTICLE{Unser_M_2009_tip_mul_msarlwt,
author = {Unser, M. and Sage, D. and Van De Ville, D.},
title = {Multiresolution Monogenic Signal Analysis Using the {R}iesz-{Laplace}
Wavelet Transform},
journal = j-ieee-tip,
year = {2009},
volume = {18},
pages = {2402--2418},
number = {11},
month = {Nov.},
issn = {1057-7149},
abstract = {The monogenic signal is the natural 2-D counterpart of the 1-D analytic
signal. We propose to transpose the concept to the wavelet domain
by considering a complexified version of the Riesz transform which
has the remarkable property of mapping a real-valued (primary) wavelet
basis of $L_2({BBR}^2)$ into a complex one. The Riesz operator is
also steerable in the sense that it give access to the Hilbert transform
of the signal along any orientation. Having set those foundations,
we specify a primary polyharmonic spline wavelet basis of $L_2({BBR}^2)$
that involves a single Mexican-hat-like mother wavelet (Laplacian
of a B-spline). The important point is that our primary wavelets
are quasi-isotropic: they behave like multiscale versions of the
fractional Laplace operator from which they are derived, which ensures
steerability. We propose to pair these real-valued basis functions
with their complex Riesz counterparts to specify a multiresolution
monogenic signal analysis. This yields a representation where each
wavelet index is associated with a local orientation, an amplitude
and a phase. We give a corresponding wavelet-domain method for estimating
the underlying instantaneous frequency. We also provide a mechanism
for improving the shift and rotation-invariance of the wavelet decomposition
and show how to implement the transform efficiently using perfect-
reconstruction filterbanks. We illustrate the specific feature- extraction
capabilities of the representation and present novel examples of
wavelet-domain processing; in particular, a robust, tensor-based
analysis of directional image patterns, the demodulation of interferograms,
and the reconstruction of digital holograms.},
doi = {10.1109/TIP.2009.2027628},
file = {Unser_M_2009_tip_mul_msarlwt.pdf:Unser_M_2009_tip_mul_msarlwt.pdf:PDF},
owner = {duvall},
pdf = {Unser_M_2009_tip_mul_msarlwt.pdf},
timestamp = {2009.10.15}
}
@INPROCEEDINGS{Unser_M_2009_p-icip_hig_ortswf,
author = {M. Unser and Van De Ville, D.},
title = {Higher-Order {Riesz} Transforms and Steerable Wavelet Frames},
booktitle = p-icip,
year = {2009},
pages = {3757--3760},
address = {Cairo, Egypt},
month = {Nov. 7-10},
abstract = {We introduce an Nth-order extension of the Riesz transform in d dimensions.
We prove that this generalized transform has the following remarkable
properties: shift-invariance, scale-invariance, innerproduct preservation,
and steerability. The pleasing consequence is that the transform
maps any primary wavelet frame (or basis) of L2(?d) into another
"steerable" wavelet frame, while preserving the frame bounds. The
concept provides a rigorous functional counterpart to Simoncelli's
steerable pyramid whose construction was entirely based on digital
filter design. The proposed mechanism allows for the specification
of wavelets with any order of steerability in any number of dimensions;
it also yields a perfect reconstruction filterbank algorithm. We
illustrate the method using a Mexican-hat-like polyharmonic spline
wavelet transform as our primary frame.},
file = {Unser_M_2009_p-icip_hig_ortswf.pdf:Unser_M_2009_p-icip_hig_ortswf.pdf:PDF},
keywords = {wavelet transform, steerable filters, frames, multiresolution analysis},
owner = {duvall},
pdf = {Unser_M_2009_p-icip_hig_ortswf.pdf},
timestamp = {2009.11.01}
}
@ARTICLE{Unser_M_2008_tip_pai_wbmrasr,
author = {Unser, M. and Van De Ville, D.},
title = {The Pairing of a Wavelet Basis with a Mildly Redundant Analysis via
Subband Regression},
journal = j-ieee-tip,
year = {2008},
volume = {17},
pages = {2040--2052},
number = {11},
month = {Nov.},
abstract = {A distinction is usually made between wavelet bases and wavelet frames.
The former are associated with a one-to-one representation of signals,
which is somewhat constrained but most efficient computationally.
The latter are over-complete, but they offer advantages in terms
of flexibility (shape of the basis functions) and shift-invariance.
In this paper, we propose a framework for improved wavelet analysis
based on an appropriate pairing of a wavelet basis with a mildly
redundant version of itself (frame). The processing is accomplished
in four steps: 1) redundant wavelet analysis, 2) wavelet-domain processing,
3) projection of the results onto the wavelet basis, and 4) reconstruction
of the signal from its nonredundant wavelet expansion. The wavelet
analysis is pyramid-like and is obtained by simple modification of
Mallat's filterbank algorithm (e.g., suppression of the down-sampling
in the wavelet channels only). The key component of the method is
the subband regression filter (Step 3) which computes a wavelet expansion
that is maximally consistent in the least squares sense with the
redundant wavelet analysis. We demonstrate that this approach significantly
improves the performance of soft-threshold wavelet denoising with
a moderate increase in computational cost. We also show that the
analysis filters in the proposed framework can be adjusted for improved
feature detection; in particular, a new quincunx Mexican-hat-like
wavelet transform that is fully reversible and essentially behaves
the (??2)th Laplacian of a Gaussian.},
file = {Unser_M_2008_tip_pai_wbmrasr.pdf:Unser_M_2008_tip_pai_wbmrasr.pdf:PDF},
pdf = {Unser_M_2008_tip_pai_wbmrasr.pdf},
timestamp = {2009.11.15}
}
@BOOK{Vaidyanathan_P_1993_book_mul_sfb,
title = {Multirate systems and filter banks},
publisher = {Prentice Hall},
year = {1993},
author = {Vaidyanathan, P. P.},
address = {Englewoods Cliffs, NJ, USA},
owner = {duvall},
timestamp = {2008.11.26}
}
@ARTICLE{DeValois_R_1982_j-vis-res_spa_fscmvc,
author = {R. L. De Valois and D. G. Albrecht and L. G. Thorell},
title = {Spatial frequency selectivity of cells in macaque visual cortex},
journal = j-vis-res,
year = {1982},
volume = {22},
pages = {545--559},
number = {5},
abstract = {We measured the spatial frequency contrast sensitivity of cells in
the primate striate cortex at two different eccentricities to provide
quantitative statistics from a large population of cells. Distributions
of the peak frequencies and bandwidths are presented and examined
in relationship to (a) each other, (b) absolute contrast sensitivity,
(c) orientation tuning, (d)retinal eccentricity, and (e) cell type.
Simple and complex cells are examined in relationship to linear/nonlinear
(that is, X/Y) properties; a procedure is described which provides
a simple, reliable and quantitative method for classifying and describing
striate cells. Among other things, it is shown that (a) many stirate
cells have quite narrow spatial bandwidths and (b) at a given retinal
eccentricity, the distribution of peak frequency covers a wide range
of frequencies; these findings support the basic multiple channel
notion. The orientation tuning and spatial frequency tuning which
occurs at the level of striate cortex (in a positively correlated
fashion) suggests that the cells might best be considered as two-dimensional
spatial filters.},
file = {DeValois_R_1982_j-vis-res_spa_fscmvc.PDF:DeValois_R_1982_j-vis-res_spa_fscmvc.PDF:PDF},
owner = {duvall},
timestamp = {2009.11.01}
}
@ARTICLE{VanDeVille_D_2008_tip_com_wbsmlp,
author = {Van De Ville, D. and Unser, M.},
title = {Complex Wavelet Bases, Steerability, and the {Marr}-Like Pyramid},
journal = j-ieee-tip,
year = {2008},
volume = {17},
pages = {2063--2080},
number = {11},
month = {Nov.},
abstract = {Our aim in this paper is to tighten the link between wavelets, some
classical image-processing operators, and David Marr's theory of
early vision. The cornerstone of our approach is a new complex wavelet
basis that behaves like a smoothed version of the Gradient-Laplace
operator. Starting from first principles, we show that a single-generator
wavelet can be defined analytically and that it yields a semi-orthogonal
complex basis of L2(?2), irrespective of the dilation matrix used.
We also provide an efficient FFT-based filterbank implementation.
We then propose a slightly redundant version of the transform that
is nearly translation-invariant and that is optimized for better
steerability (Gaussian-like smoothing kernel). We call it the Marr-like
wavelet pyramid because it essentially replicates the processing
steps in Marr's theory of early vision.We use it to derive a primal
wavelet sketch which is a compact description of the image by a multiscale,
subsampled edge map. Finally, we provide an efficient iterative algorithm
for the reconstruction of an image from its primal wavelet sketch.},
file = {VanDeVille_D_2008_tip_com_wbsmlp.pdf:VanDeVille_D_2008_tip_com_wbsmlp.pdf:PDF},
pdf = {VanDeVille_D_2008_tip_com_wbsmlp.pdf},
timestamp = {2009.11.15}
}
@INCOLLECTION{Vandergheynst_P_2006_incoll_ima_crd,
author = {Vandergheynst, P. and Frossard, P.},
title = {Image Coding Using Redundant Dictionaries},
booktitle = {Document and image compression},
publisher = {CRC Press},
year = {2006},
editor = {M. Barni},
isbn = {0849335566},
owner = {duvall},
timestamp = {2011.01.05}
}
@ARTICLE{Vandergheynst_P_2002_j-ieee-tip_dir_dwtda,
author = {Vandergheynst, P. and Gobbers, J.-F.},
title = {Directional dyadic wavelet transforms: design and algorithms},
journal = j-ieee-tip,
year = {2002},
volume = {11},
pages = {363--372},
number = {4},
month = {Apr.},
issn = {1057-7149},
abstract = {We propose a simple and efficient technique for designing translation
invariant dyadic wavelet transforms (DWTs) in two dimensions. Our
technique relies on an extension of the work of Duval-Destin et al.
(1993) where dyadic decompositions are constructed starting from
the continuous wavelet transform. The main advantage of this framework
is that it allows for a lot of freedom in designing two-dimensional
(2-D) dyadic wavelets. We use this property to construct directional
wavelets, whose orientation filtering capabilities are very important
in image processing. We address the efficient implementation of these
decompositions by constructing approximate QMFs through an L 2 optimization.
We also propose and study an efficient implementation in the Fourier
domain for dealing with large filters},
doi = {10.1109/TIP.2002.999670},
keywords = {2D dyadic wavelets;Fourier domain;approximate QMF;continuous wavelet
transform;directional dyadic wavelet transforms;dyadic decompositions;image
analysis;image processing;optimization;orientation filtering;translation
invariant dyadic wavelet transforms;wavelet transforms design;filtering
theory;image processing;quadrature mirror filters;wavelet transforms;},
owner = {duvall},
timestamp = {2011.01.03}
}
@INCOLLECTION{Vandergheynst_P_2010_incoll_wav_s,
author = {P. Vandergheynst and Y. Wiaux},
title = {Wavelets on the sphere},
booktitle = {Four short courses in harmonic analysis: wavelets, frames, time-frequency
methods, and applications to signal and image analysis},
publisher = {Birkh{\"a}user},
year = {2010},
editor = {P. Massoput and B. Forster-Heinlein},
address = {Boston},
owner = {duvall},
timestamp = {2010.03.04}
}
@ARTICLE{Velisavljevic_V_2006_tip_dir_amdrsf,
author = {Velisavljevi{\'c}, V. and Beferull-Lozano, B. and Vetterli, M. and
Dragotti, P. L.},
title = {Directionlets: Anisotropic multi-directional representation with
separable filtering},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {1916--1933},
number = {7},
month = {July},
abstract = {In spite of the success of the standard wavelet transform (WT) in
image processing in recent years, the efficiency of its representation
is limited by the spatial isotropy of its basis functions built in
the horizontal and vertical directions. One-dimensional (1-D) discontinuities
in images (edges and contours) that are very important elements in
visual perception, intersect too many wavelet basis functions and
lead to a nonsparse representation. To efficiently capture these
anisotropic geometrical structures characterized by many more than
the horizontal and vertical directions, a more complex multidirectional
(M-DIR) and anisotropic transform is required. We present a new lattice-based
perfect reconstruction and critically sampled anisotropic M-DIR WT.
The transform retains the separable filtering and subsampling and
the simplicity of computations and filter design from the standard
two-dimensional WT, unlike in the case of some other directional
transform constructions (e.g., curvelets, contourlets, or edgelets).
The corresponding anisotropic basis functions (directionlets) have
directional vanishing moments along any two directions with rational
slopes. Furthermore, we show that this novel transform provides an
efficient tool for nonlinear approximation of images, achieving the
approximation power O(N-1.55), which, while slower than the optimal
rate O(N-2), is much better than O(N-1) achieved with wavelets, but
at similar complexity.},
doi = {10.1109/TIP.2006.877076},
file = {Velisavljevic_V_2006_tip_dir_amdrsf.pdf:Velisavljevic_V_2006_tip_dir_amdrsf.pdf:PDF},
keywords = {Directional vanishing moments, directionlets, filter banks, geometry,
multidirection, multiresolution, separable filtering, sparse image
representation, wavelets.},
owner = {duvall},
pdf = {Velisavljevic_V_2006_tip_dir_amdrsf.pdf},
timestamp = {2007.07.18}
}
@BOOK{Vetterli_M_1995_book_wav_sc,
title = {Wavelets and Subband Coding},
publisher = {Prentice-Hall},
year = {1995},
author = {M. Vetterli and J. Kova\v{c}evi\'{c}},
address = {Englewood Cliffs},
file = {Vetterli_M_1995_book_wav_sc.pdf:Vetterli_M_1995_book_wav_sc.pdf:PDF;Slides:Vetterli_M_1995_book_wav_sc-slides.zip:PDF},
key = {wlet},
owner = {duvall},
pdf = {Vetterli_M_1995_book_wav_sc.pdf},
timestamp = {2007.07.13}
}
@ARTICLE{Wakin_M_2006_j-ieee-tip_wav_dacpsi,
author = {M. Wakin and J. Romberg and H. Choi and R. Baraniuk},
title = {Wavelet-domain Approximation and Compression of Piecewise Smooth
Images},
journal = j-ieee-tip,
year = {2006},
volume = {15},
pages = {1071--1087},
number = {5},
month = {May},
owner = {duvall},
timestamp = {2011.01.03}
}
@INPROCEEDINGS{Wang_Z_2005_p-icassp_tra_iiscwd,
author = {Wang, Z. and Simoncelli, E. P.},
title = {Translation Insensitive Image Similarity in Complex Wavelet Domain},
booktitle = p-icassp,
year = {2005},
volume = {2},
pages = {573--576},
address = {Philadelphia, PA, USA},
month = {Mar. 19-23,},
abstract = {We propose a complex wavelet domain image similarity measure, which
is simultaneously insensitive to luminance change, contrast change
and spatial translation. The key idea is to make use of the fact
that these image distortions lead to consistent magnitude and/or
phase changes of local wavelet coefficients. Since small scaling
and rotation of images can be locally approximated by translation,
the proposed measure also shows robustness to spatial scaling and
rotation when these geometric distortions are small relative to the
size of the wavelet filters. Compared with previous methods, the
proposed measure is computationally efficient, and can evaluate the
similarity of two images without a precise registration process at
the front end.},
doi = {10.1109/ICASSP.2005.1415469},
file = {Wang_Z_2005_p-icassp_tra_iiscwd-poster.pdf:Wang_Z_2005_p-icassp_tra_iiscwd-poster.pdf:PDF;Wang_Z_2005_p-icassp_tra_iiscwd.pdf:Wang_Z_2005_p-icassp_tra_iiscwd.pdf:PDF},
issn = {1520-6149},
keywords = {complex wavelet domain; contrast change; image registration; luminance
change; magnitude changes; phase changes; spatial rotation; spatial
scaling; translation insensitive image similarity measure; wavelet
filters; approximation theory; image processing; wavelet transforms;},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Watson_A_1987_j-comput-vision-graph-image-process_cor_trcsni,
author = {Watson, A. B.},
title = {The cortex transform: rapid computation of simulated neural images},
journal = j-comput-vision-graph-image-process,
year = {1987},
volume = {39},
pages = {311--327},
number = {3},
issn = {0734-189X},
address = {San Diego, CA, USA},
doi = {http://dx.doi.org/10.1016/S0734-189X(87)80184-6},
owner = {duvall},
publisher = {Academic Press Professional, Inc.},
timestamp = {2010.02.26}
}
@INPROCEEDINGS{Wedekind_J_2007_p-icspc_ste_fghdtwt,
author = {Wedekind, J. and Amavasai, B. P. and Dutton, K.},
title = {Steerable filters generated with the hypercomplex dual-tree wavelet
transform},
booktitle = p-icspc,
year = {2007},
pages = {1291--1294},
address = {Dubai, United Arab Emirates},
month = {Nov. 24-27,},
abstract = {The use of wavelets in the image processing domain is still in its
infancy, and largely associated with image compression. With the
advent of the dual-tree hypercomplex wavelet transform (DHWT) and
its improved shift invariance and directional selectivity, applications
in other areas of image processing are more conceivable. This paper
discusses the problems and solutions in developing the DHWT and its
inverse. It also offers a practical implementation of the algorithms
involved. The aim of this work is to apply the DHWT in machine vision.
Tentative work on a possible new way of feature extraction is presented.
The paper shows that 2-D hypercomplex basis wavelets can be used
to generate steerable filters which allow rotation as well as translation.},
file = {Wedekind_J_2007_p-icspc_ste_fghdtwt.pdf:Wedekind_J_2007_p-icspc_ste_fghdtwt.pdf:PDF},
owner = {duvall},
pdf = {Wedekind_J_2007_icspc_ste_fghdtwt.pdf},
timestamp = {2008.04.08}
}
@TECHREPORT{Weickert_J_1997_tr_sca_sdj,
author = {Weickert, J. and Ishikawa, S. and Imiya, A.},
title = {Scale-space has been discovered in {Japan}},
institution = {University of Copenhagen},
year = {1997},
number = {DIKU-TR-97/18},
file = {Weickert_J_1997_tr_sca_sdj.ps:Weickert_J_1997_tr_sca_sdj.ps:PostScript},
owner = {duvall},
timestamp = {2009.11.01}
}
@TECHREPORT{Weiss_J_1995_tr_hil_tww,
author = {Weiss, J.},
title = {The {Hilbert} transform of wavelets are wavelets},
institution = {Applied Mathematics Group},
year = {1995},
file = {:Weiss_J_1995_tr_hil_tww.pdf:PDF},
owner = {duvall},
pdf = {Weiss_J_1995_tr_hil_tww.pdf},
timestamp = {2007.06.27}
}
@ARTICLE{Wiaux_Y_2005_j-astrophys-j_cor_pbsew,
author = {Wiaux, Y. and Jacques, L. and Vandergheynst, P.},
title = {Correspondence principle between spherical and {Euclidean} wavelets},
journal = j-astrophys-j,
year = {2005},
volume = {632},
pages = {15--28},
number = {1},
month = {Oct.},
owner = {duvall},
publisher = {UChicago Press},
timestamp = {2011.01.05}
}
@ARTICLE{Wiaux_Y_2006_j-astrophys-j_fas_dcssf,
author = {Wiaux, Y. and Jacques, L. and Vielva, P. and Vandergheynst, P.},
title = {Fast directional correlation on the sphere with steerable filters},
journal = j-astrophys-j,
year = {2006},
volume = {652},
pages = {820--832},
number = {1},
month = {Nov.},
owner = {duvall},
publisher = {UChicago Press},
timestamp = {2011.01.05}
}
@ARTICLE{Wiaux_Y_2008_j-mon-not-roy-astron-soc_exa_rdws,
author = {Wiaux, Y. and McEwen, J. D. and Vandergheynst, P. and Blanc, O.},
title = {Exact reconstruction with directional wavelets on the sphere},
journal = j-mon-not-roy-astron-soc,
year = {2008},
volume = {388},
pages = {770--788},
number = {2},
month = {Aug.},
owner = {duvall},
publisher = {London: Priestley and Weale, 1833-},
timestamp = {2011.01.05}
}
@ARTICLE{Wiaux_Y_2008_j-mon-not-roy-astron-soc_non_galmmwmapd,
author = {Wiaux, Y. and Vielva, P. and Barreiro, R. B. and Mart{\'\i}nez-Gonz{\'a}lez,
E. and Vandergheynst, P.},
title = {Non-{Gaussianity} analysis on local morphological measures of {WMAP}
data},
journal = j-mon-not-roy-astron-soc,
year = {2008},
volume = {385},
pages = {939--947},
number = {2},
month = {Apr.},
abstract = {The decomposition of a signal on the sphere with the steerable wavelet
constructed from the second Gaussian derivative gives access to the
orientation, signed-intensity, and elongation of the signal's local
features. In the present work, the non-Gaussianity of the WMAP temperature
data of the cosmic microwave background (CMB) is analyzed in terms
of the first four moments of the statistically isotropic random fields
associated with these local morphological measures, at wavelet scales
corresponding to angular sizes between 27.5 arcminutes and 30 degrees
on the celestial sphere. While no detection is made neither in the
orientation analysis nor in the elongation analysis, a strong detection
is made in the excess kurtosis of the signed-intensity of the WMAP
data. The non-Gaussianity is observed with a significance level below
0.5% at a wavelet scale corresponding to an angular size around 10
degrees, and confirmed at neighbour scales. This supports a previous
detection of an excess of kurtosis in the wavelet coefficient of
the WMAP data with the axisymmetric Mexican hat wavelet (Vielva et
al. 2004). Instrumental noise and foreground emissions are not likely
to be at the origin of the excess of kurtosis. Large-scale modulations
of the CMB related to some unknown systematics are rejected as possible
origins of the detection. The observed non-Gaussianity may therefore
probably be imputed to the CMB itself, thereby questioning the basic
inflationary scenario upon which the present concordance cosmological
model relies. Taking the CMB temperature angular power spectrum of
the concordance cosmological model at face value, further analysis
also suggests that this non-Gaussianity is not confined to the directions
on the celestial sphere with an anomalous signed-intensity.},
file = {Wiaux_Y_2008_j-mon-not-roy-astron-soc_non_galmmwmapd-preprint.pdf:Wiaux_Y_2008_j-mon-not-roy-astron-soc_non_galmmwmapd-preprint.pdf:PDF},
owner = {duvall},
publisher = {London: Priestley and Weale, 1833-},
timestamp = {2011.01.05}
}
@MISC{Wickerhauser_M_1991_misc_lec_nwp,
author = {Wickerhauser, M. V.},
title = {{INRIA} Lectures on Wavelet Packet Algorithms},
howpublished = {Lecture notes, INRIA},
year = {1991},
abstract = {We begin by defining continuous wavelet packets on R. These are square-integrable
functions with prescribed smoothness and other properties, which
we shall develop to establish the main notions. Our construction
will be directed toward numerical applications, so we will restrict
ourselves to the quadrature mirror filter algorithm. Next we will
define several discrete algorithms and explore their advantages and
disadvantages. We will show the correspondence between wavelet packets
and coefficients computed from sampled signals, and relate the convergence
of this approximation to the smoothness of the signal. We will define
information cost functions and the "best-basis"
method. We will count operations and consider practical matters like
the memory requirements of the algorithms, periodizing, the spreading
of the support of aperiodic wavelet packets, and the combinatorics
of constructing wavelet packet bases of increasing generality. In
parallel, we will develop smooth orthogonal local trigonometric transforms.
These are properly considered transposes of wavelet packet methods,
or alternatively conjugates of wavelet packet methods by the Fourier
transform. We will describe both continuous and},
file = {Wickerhauser_M_1991_misc_lec_nwp.pdf:Wickerhauser_M_1991_misc_lec_nwp.pdf:PDF},
owner = {duvall},
pages = {31--99},
pdf = {Wickerhauser_M_1991_misc_lec_nwp.pdf},
timestamp = {2010.01.11}
}
@ARTICLE{Willett_R_2003_tmi_pla_maresplmi,
author = {Willett, R. M. and Nowak, R. D.},
title = {Platelets: a multiscale approach for recovering edges and surfaces
in photon-limited medical imaging},
journal = j-ieee-tmi,
year = {2003},
volume = {22},
pages = {332--350},
number = {3},
month = {Mar.},
issn = {0278-0062},
abstract = {The nonparametric multiscale platelet algorithms presented in this
paper, unlike traditional wavelet-based methods, are both well suited
to photon-limited medical imaging applications involving Poisson
data and capable of better approximating edge contours. This paper
introduces platelets, localized functions at various scales, locations,
and orientations that produce piecewise linear image approximations,
and a new multiscale image decomposition based on these functions.
Platelets are well suited for approximating images consisting of
smooth regions separated by smooth boundaries. For smoothness measured
in certain Holder classes, it is shown that the error of m-term platelet
approximations can decay significantly faster than that of m-term
approximations in terms of sinusoids, wavelets, or wedgelets. This
suggests that platelets may outperform existing techniques for image
denoising and reconstruction. Fast, platelet-based, maximum penalized
likelihood methods for photon-limited image denoising, deblurring
and tomographic reconstruction problems are developed. Because platelet
decompositions of Poisson distributed images are tractable and computationally
efficient, existing image reconstruction methods based on expectation-maximization
type algorithms can be easily enhanced with platelet techniques.
Experimental results suggest that platelet-based methods can outperform
standard reconstruction methods currently in use in confocal microscopy,
image restoration, and emission tomography.},
doi = {10.1109/TMI.2003.809622},
file = {Willett_R_2003_tmi_pla_maresplmi.pdf:Willett_R_2003_tmi_pla_maresplmi.pdf:PDF},
keywords = {Poisson distribution, biomedical imaging, biomedical optical imaging,
image denoising, image reconstruction, medical image processing,
positron emission tomography, single photon emission computed tomography,
smoothing methods},
owner = {duvall},
pdf = {Willett_R_2003_tmi_pla_maresplmi.pdf},
timestamp = {2009.11.02}
}
@ARTICLE{Wilson_R_1992_j-ieee-tit_gen_wtfamftaiasa,
author = {Wilson, R. and Calway, A. D. and Pearson, E. R. S.},
title = {A generalized wavelet transform for {F}ourier analysis: the multiresolution
{F}ourier transform and its application to image and audio signal
analysis},
journal = j-ieee-tit,
year = {1992},
volume = {38},
pages = {674--690},
number = {2},
month = {mar.},
issn = {0018-9448},
abstract = {A wavelet transform specifically designed for Fourier analysis at
multiple scales is described and shown to be capable of providing
a local representation which is particularly well suited to segmentation
problems. It is shown that, by an appropriate choice of analysis
window and sampling intervals, it is possible to obtain a Fourier
representation which can be computed efficiently and overcomes the
limitations of using a fixed scale of window, yet by virtue of its
symmetry properties allows simple estimation of such fundamental
signal parameters as instantaneous frequency and onset time/position.
The transform is applied to the segmentation of both image and audio
signals, demonstrating its power to deal with signal events which
are localized in either time/space or frequency. Feature extraction
and segmentation are performed through the introduction of a class
of multiresolution Markov models, whose parameters represent the
signal events underlying the segmentation},
doi = {10.1109/18.119730},
file = {Wilson_R_1992_j-ieee-tit_gen_wtfamftaiasa.pdf:Wilson_R_1992_j-ieee-tit_gen_wtfamftaiasa.pdf:PDF},
keywords = {Fourier analysis;audio signal analysis;feature extraction;image segmentation;instantaneous
frequency;multiple scales;multiresolution Fourier transform;multiresolution
Markov models;onset time/position;parameter estimation;symmetry properties;wavelet
transform;Fourier analysis;Fourier transforms;Markov processes;audio
signals;parameter estimation;picture processing;signal processing;transforms;},
owner = {duvall},
pdf = {Wilson_R_1992_j-ieee-tit_gen_wtfamftaiasa.pdf},
timestamp = {2010.09.27}
}
@INPROCEEDINGS{Witkin_A_1984_p-icassp_sca_sfnamsd,
author = {Witkin, A. P.},
title = {Scale-space filtering: A new approach to multi-scale description},
booktitle = p-icassp,
year = {1984},
volume = {9},
pages = {150--153},
month = {Mar.},
abstract = {The extrema in a signal and its first few derivatives provide a useful
general purpose qualitative description for many kinds of signals.
A fundamental problem in computing such descriptions is scale: a
derivative must be taken over some neighborhood, but there is seldom
a principled basis for choosing its size. Scale-space filtering is
a method that describes signals qualitatively, managing the ambiguity
of scale in an organized and natural way. The signal is first expanded
by convolution with gaussian masks over a continuum of sizes. This
"scale- space" image is then collapsed, using its qualitative structure,
into a tree providing a concise but complete qualitative description
covering all scales of observation. The description is further refined
by applying a stability criterion, to identify events that persist
of large changes in scale.},
file = {Witkin_A_1984_p-icassp_sca_sfnamsd.pdf:Witkin_A_1984_p-icassp_sca_sfnamsd.pdf:PDF},
owner = {duvall},
pdf = {Witkin_A_1984_p-icassp_sca_sfnamsd.pdf},
timestamp = {2009.10.20}
}
@BOOK{Wornell_G_1995_book_sig_pfwba,
title = {Signal Processing with Fractals: A Wavelet Based Approach},
publisher = {Prentice Hall},
year = {1995},
author = {Wornell, G.},
isbn = {978-0131209992},
owner = {duvall},
timestamp = {2009.10.20}
}
@ARTICLE{Xia_X_1995_acha_f_tdnmw,
author = {Xia, X. G. and Suter, B. W.},
title = {A familly of two-dimensional nonseparable {Malvar} wavelets},
journal = j-acha,
year = {1995},
volume = {2},
pages = {243--256},
file = {Xia_X_1995_acha_f_tdnmw.pdf:Xia_X_1995_acha_f_tdnmw.pdf:PDF},
owner = {duvall},
pdf = {Xia_X_1995_acha_f_tdnmw.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Xiong_Z_1996_j-ieee-spl_dct_beic,
author = {Z. Xiong and Guleryuz, O. G. and Orchard, M. T.},
title = {A {DCT}-based embedded image coder},
journal = j-ieee-spl,
year = {1996},
volume = {3},
pages = {289--290},
number = {11},
month = {Nov.},
issn = {1070-9908},
abstract = {Since Shapiro (see ibid., vol.41, no.12, p. 445, 1993) published his
work on embedded zerotree wavelet (EZW) image coding, there have
been increased research activities in image coding centered around
wavelets. We first point out that the wavelet transform is just one
member in a family of linear transformations, and the discrete cosine
transform (DCT) can also be coupled with an embedded zerotree quantizer.
We then present such an image coder that outperforms any other DCT-based
coder published in the literature, including that of the Joint Photographers
Expert Group (JPEG). Moreover, our DCT-based embedded image coder
gives higher peak signal-to-noise ratios (PSNR) than the quoted results
of Shapiro's EZW coder},
doi = {10.1109/97.542157},
file = {Xiong_Z_1996_j-ieee-spl_dct_beic.pdf:Xiong_Z_1996_j-ieee-spl_dct_beic.pdf:PDF},
keywords = {DCT based embedded image coder;JPEG coder;Joint Photographers Expert
Group;PSNR;Shapiro EZW coder;discrete cosine transform;embedded zerotree
quantizer;embedded zerotree wavelet image coding;image coder;linear
transformations;peak signal-to-noise ratios;wavelet transform;discrete
cosine transforms;image coding;transform coding;wavelet transforms;},
owner = {duvall},
pdf = {Xiong_Z_1996_j-ieee-spl_dct_beic.pdf},
timestamp = {2010.02.26}
}
@INPROCEEDINGS{Xu_D_2003_p-spie-wasip_ani_2dwprtta,
author = {Xu, D. and Do, M. N.},
title = {Anisotropic {2D} wavelet packets and rectangular tiling: theory and
algorithms},
booktitle = p-spie-wasip,
year = {2003},
pages = {619--630},
abstract = {We propose a new subspace decomposition scheme called anisotropic
wavelet packets which broadens the existing definition of 2-D wavelet
packets. By allowing arbitrary order of row and column decompositions,
this scheme fully considers the adaptivity, which helps find the
best bases to represent an image. We also show that the number of
candidate tree structures in the anisotropic case is much larger
than isotropic case. The greedy algorithm and double-tree algorithm
are then presented and experimental results are shown.},
doi = {10.1117/12.506601},
file = {Xu_D_2003_p-spie-wasip_ani_2dwprtta.pdf:Xu_D_2003_p-spie-wasip_ani_2dwprtta.pdf:PDF},
owner = {duvall},
pdf = {Xu_D_2003_p-spie-wasip_ani_2dwprtta.pdf},
timestamp = {2010.02.15}
}
@ARTICLE{Xu_J_2010_j-vcir_rip_ntip,
author = {J. Xu and L. Yang and D. Wu},
title = {Ripplet: A new transform for image processing},
journal = j-vcir,
year = {2010},
volume = {21},
pages = {627--639},
number = {7},
month = {Oct.},
issn = {1047-3203},
abstract = {Efficient representation of images usually leads to improvements in
storage efficiency, computational complexity and performance of image
processing algorithms. Efficient representation of images can be
achieved by transforms. However, conventional transforms such as
Fourier transform and wavelet transform suffer from discontinuities
such as edges in images. To address this problem, we propose a new
transform called ripplet transform. The ripplet transform is a higher
dimensional generalization of the curvelet transform, designed to
represent images or two-dimensional signals at different scales and
different directions. Specifically, the ripplet transform allows
arbitrary support c and degree d while the curvelet transform is
just a special case of the ripplet transform (Type I) with c = 1
and d = 2. Our experimental results demonstrate that the ripplet
transform can provide efficient representation of edges in images.
The ripplet transform holds great potential for image processing
such as image restoration, image denoising and image compression.},
doi = {DOI: 10.1016/j.jvcir.2010.04.002},
file = {Xu_J_2010_j-vcir_rip_ntip.pdf:Xu_J_2010_j-vcir_rip_ntip.pdf:PDF},
keywords = {Harmonic analysis; Fourier transform; Wavelet transform; Curvelet
transform; Image representation; Image compression; Transform coding;
Image denoising},
owner = {duvall},
timestamp = {2010.12.06},
url = {http://www.sciencedirect.com/science/article/B6WMK-4YWXSG0-1/2/1aadc76f25ac3b6920def08e0a78b0e8}
}
@ARTICLE{Yeo_B_2008_j-ieee-tip_con_ifb2s,
author = {Yeo, B. T. T. and Wanmei Ou and Golland, P.},
title = {On the Construction of Invertible Filter Banks on the 2-Sphere},
journal = j-ieee-tip,
year = {2008},
volume = {17},
pages = {283--300},
number = {3},
month = {Mar.},
issn = {1057-7149},
abstract = {The theories of signal sampling, filter banks, wavelets, and ldquoovercomplete
waveletsrdquo are well established for the Euclidean spaces and are
widely used in the processing and analysis of images. While recent
advances have extended some filtering methods to spherical images,
many key challenges remain. In this paper, we develop theoretical
conditions for the invertibility of filter banks under continuous
spherical convolution. Furthermore, we present an analogue of the
Papoulis generalized sampling theorem on the 2-Sphere. We use the
theoretical results to establish a general framework for the design
of invertible filter banks on the sphere and demonstrate the approach
with examples of self-invertible spherical wavelets and steerable
pyramids. We conclude by examining the use of a self-invertible spherical
steerable pyramid in a denoising experiment and discussing the computational
complexity of the filtering framework},
doi = {10.1109/TIP.2007.915550},
file = {Yeo_B_2008_j-ieee-tip_con_ifb2s.pdf:Yeo_B_2008_j-ieee-tip_con_ifb2s.pdf:PDF},
owner = {duvall},
timestamp = {2009.10.31}
}
@ARTICLE{Yin_B_2008_j-spic_dir_lbwtmdic,
author = {Yin, B. C. and Li, X. and Shi, Y. H. and Zhang, F .Z. and Zhang,
N.},
title = {Directional lifting-based wavelet transform for multiple description
image coding},
journal = j-spic,
year = {2008},
volume = {23},
pages = { 42--57},
number = {1},
month = {Jan.},
owner = {duvall},
timestamp = {2011.01.03}
}
@ARTICLE{Zhang_X_1999_tsp_ort_cfbwpd,
author = {Zhang, X.-P. and Desai, M. D. and Peng, Y.-N.},
title = {Orthogonal complex filter banks and wavelets: some properties and
design},
journal = j-ieee-tsp,
year = {1999},
volume = {47},
pages = {1039--1048},
number = {4},
month = {Apr.},
abstract = {Previous wavelet research has primarily focused on real-valued wavelet
bases. However, complex wavelet bases offer a number of potential
advantageous properties. For example, it has been suggested that
the complex Daubechies wavelet can be made symmetric. However, these
papers always imply that if the complex basis has a symmetry property,
then it must exhibit linear phase as well. In this paper, we prove
that a linear-phase complex orthogonal wavelet does not exist. We
study the implications of symmetry and linear phase for both complex
and real-valued orthogonal wavelet bases. As a byproduct, we propose
a method to obtain a complex orthogonal wavelet basis having the
symmetry property and approximately linear phase. The numerical analysis
of the phase response of various complex and real Daubechies wavelets
is given. Both real and complex-symmetric orthogonal wavelet can
only have symmetric amplitude spectra. It is often desired to have
asymmetric amplitude spectra for processing general complex signals.
Therefore, we propose a method to design general complex orthogonal
perfect reconstruct filter banks (PRFBs) by a parameterization scheme.
Design examples are given. It is shown that the amplitude spectra
of the general complex conjugate quadrature filters (CQFs) can be
asymmetric with respect the zero frequency. This method can be used
to choose optimal complex orthogonal wavelet basis for processing
complex signals such as in radar and sonar},
doi = {10.1109/78.752601},
file = {Zhang_X_1999_tsp_ort_cfbwpd.pdf:Zhang_X_1999_tsp_ort_cfbwpd.pdf:PDF},
owner = {duvall},
pdf = {Zhang_X_1999_tsp_ort_cfbwpd.pdf},
timestamp = {2007.06.16}
}
@ARTICLE{Zhang_Z_2009_j-comput-math-appl_edg_dabdwt,
author = {Zhang, Z. and Ma, S. and Liu, H. and Gong, Y.},
title = {An edge detection approach based on directional wavelet transform},
journal = j-comput-math-appl,
year = {2009},
volume = {57},
pages = {1265--1271},
number = {8},
issn = {0898-1221},
abstract = {The standard 2D wavelet transform (WT) has been an effective tool
in image processing. In recent years, many new transforms have been
proposed successively, such as curvelets, bandlets, directional wavelet
transform etc, which inherit the merits of the standard WT, and are
more adequate at the 2D image processing tasks. Intuitively, it seemed
that applying these novel tools to edge detection should acquire
finer performance. In this paper, we propose an edge detection approach
based on directional wavelet transform which retains the separable
filtering and the simplicity of computations and filter design from
the standard 2D WT. In addition, the corresponding gradient magnitude
is redefined and a new algorithm for non-maximum suppression is described.
The experimental results of edge detection for several test images
are provided to demonstrate our approach.},
address = {Tarrytown, NY, USA},
doi = {http://dx.doi.org/10.1016/j.camwa.2008.11.013},
file = {Zhang_Z_2009_j-comput-math-appl_edg_dabdwt.pdf:Zhang_Z_2009_j-comput-math-appl_edg_dabdwt.pdf:PDF},
keywords = {Edge detection; Directional wavelet transform; Feature extraction;
Non-maximum suppression; Image processing},
owner = {duvall},
pdf = {Zhang_Z_2009_j-comput-math-appl_edg_dabdwt.pdf},
publisher = {Pergamon Press, Inc.},
timestamp = {2009.10.20}
}
@INPROCEEDINGS{Zhou_J_2005_spie-wav_mul_ofb,
author = {Zhou, J. and Do, M. N.},
title = {Multidimensional Oversampled Filter Banks},
booktitle = p-spie-wasip,
year = {2005},
editor = {M. Papadakis and A. F. Laine and M. A. Unser},
volume = {5914},
pages = {591424.1--591424.12},
address = {San Diego, CA, USA},
month = {Jul. 31-Aug. 3,},
abstract = {We present the characterization and design of multidimensional oversampled
FIR filter banks. In the polyphase domain, the perfect reconstruction
condition for an oversampled filter bank amounts to the invertibility
of the analysis polyphase matrix, which is a rectangular FIR matrix.
For a nonsubsampled FIR filter bank, its analysis polyphase matrix
is the FIR vector of analysis filters. A major challenge is how to
extend algebraic geometry techniques, which only deal with polynomials
(that is, causal filters), to handle general FIR filters. We propose
a novel method to map the FIR representation of the nonsubsampled
filter bank into a polynomial one by simply introducing a new variable.
Using algebraic geometry and Groebner bases, we propose the existence,
computation, and characterization of FIR synthesis filters given
FIR analysis filters. We explore the design problem of MD nonsubsampled
FIR filter banks by a mapping approach. Finally, we extend these
results to general oversampled FIR filter banks.},
file = {Zhou_J_2005_spie-wav_mul_ofb.pdf:Zhou_J_2005_spie-wav_mul_ofb.pdf:PDF},
location = {San Diego, USA},
owner = {duvall},
pdf = {Zhou_J_2005_spie-wav_mul_ofb.pdf},
timestamp = {2008.11.26}
}
@ARTICLE{Zuidwijk_R_2000_j-siam-math-anal_dir_tswa,
author = {Rob A. Zuidwijk},
title = {Directional and Time-Scale Wavelet Analysis},
journal = j-siam-math-anal,
year = {2000},
volume = {31},
pages = {416--430},
number = {2},
abstract = {Combined use of the X-ray (Radon) transform and the wavelet transform
has proved to be useful in application areas such as diagnostic medicine
and seismology. The wavelet X-ray transform performs one-dimensional
wavelet transforms along lines in $\RR^n$ which are parameterized
in the same fashion as for the X-ray transform. The reconstruction
formula for this transform gives rise to a continuous family of elementary
projections. These projections provide the building blocks of a directional
wavelet analysis of functions in several variables. Discrete wavelet
X-ray transforms are described which make use of wavelet orthonormal
bases and, more generally, of biorthogonal systems of wavelet Riesz
bases. Some attention is given to approximation results which involve
wavelet X-ray analysis in several directions.},
doi = {10.1137/S0036141098333359},
file = {Zuidwijk_R_2000_j-siam-math-anal_dir_tswa.pdf:Zuidwijk_R_2000_j-siam-math-anal_dir_tswa.pdf:PDF},
keywords = {wavelet X-ray transform; wavelet frame; wavelet transform; X-ray transform;
Radon transform; windowed Radon transform; local Radon transform;
reconstruction formula; wavelet orthonormal basis; biorthogonal wavelet
expansion},
owner = {duvall},
publisher = {SIAM},
timestamp = {2010.12.13},
url = {http://link.aip.org/link/?SJM/31/416/1}
}
@BOOK{Muller_P_1999_book_bay_iwbm,
title = {Bayesian Inference in Wavelet Based Models},
publisher = {Springer Verlag},
year = {1999},
editor = {M\"uller, P. and Vidakovic, B.},
volume = {141},
series = ser-lncs,
edition = {1st},
owner = {duvall},
timestamp = {2011.04.08}
}
@BOOK{Topiwala_P_1998_book_wav_ivc,
title = {Wavelet image and video compression},
publisher = {Kluwer Academic},
year = {1998},
editor = {Topiwala, P. N.},
file = {Topiwala_P_1998_book_wav_ivc.pdf:Topiwala_P_1998_book_wav_ivc.pdf:PDF},
owner = {duvall},
timestamp = {2007.06.05}
}
@BOOK{Welland_G_2003_book_bey_w,
title = {Beyond wavelets},
publisher = {Academic Press},
year = {2003},
editor = {G. Welland},
number = {10},
series = {Studies in Computational Mathematics},
month = {Sep.},
abstract = {Description "Beyond Wavelets" presents state-of-the-art theories,
methods, algorithms, and applications of mathematical extensions
for classical wavelet analysis. Wavelets, introduced 20 years ago
by Morlet and Grossmann and developed very rapidly during the 1980's
and 1990's, has created a common link between computational mathematics
and other disciplines of science and engineering. Classical wavelets
have provided effective and efficient mathematical tools for time-frequency
analysis which enhances and replaces the Fourier approach. However,
with the current advances in science and technology, there is an
immediate need to extend wavelet mathematical tools as well. "Beyond
Wavelets" presents a list of ideas and mathematical foundations for
such extensions, including: continuous and digital ridgelets, brushlets,
steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet
frames, and quasi-affine wavelets. Wavelet subband algorithms are
extended to pyramidal directional and nonuniform filter banks. In
addition, this volume includes a method for tomographic reconstruction
using a mechanical image model and a statistical study for independent
adaptive signal representation. Investigators already familiar with
wavelet methods from areas such as engineering, statistics, and mathematics
will benefit by owning this volume. Audience anyone interested in
wavelet technology, including mathematicians, physical scientists,
engineers, etc. Contents Preface Digital Ridgelet Transform based
Trude Ridge Functions, D.L. Donoho and A.G. Flesia. Digital Implementation
of Ridgelet Packets, A.G. Flesia, H. Hel-Or, A. Averbuch, E.J. Cand
s, R.R. Coifman andD.L. Donoho. Brushlets: Steerable Wavelet Packets,
F.G. Meyer and R.R. Coifman. Countourlets, M.N. Do and M. Vetterli.
ENO-wavelet Tranforms and Some Applications, T.F. Chan and Hao-Min
Zhou. A Mechanical Image Model for Bayesian Tomographic Reconstruction,
S. Zhao and H.Cai. Sparsity vs. Statistical Independence in Adaptive
Signal Representations: A Case Study of the Spike Process, B. B nichou
and N. Saito. Nonuniform Filter Banks: New Results and Open Problems,
S. Akkarakaran and P.P. Vaidyanathan. Recent Development of Spline
Wavelet Frames with Compact Support, C.K> Chui and J. St ckler. Affine,
Quasi-Affine and Co-Affine Wavelets, P. Gressman, D. Labate, G. Weiss
and E.N. Wilson. Index.},
isbn = {978-0-12-743273-1},
owner = {duvall},
timestamp = {2010.02.27}
}
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