Sure-LET denoising toolbox: this toolbox performs denoising of images using the FB-SURE-LET-S and FB-SURE-LET-C methods, with two-dimensional oversampled, directional filter banks and Stein Unbiaised Risk Estimation for LInear Expansion of Threshold. Some functions require the FB_gen toolbox
COLT toolbox: Complex Oversampled Lapped Transform toolbox for time-frequency analysis/synthesis and spectrogram processing (coming in 2019?)
Matlab codes were created to illustrate the results presented in some of Jérôme Gauthier papers on optimization of multirate "oversampled filter banks" for denoising and image analysis purposes. You can use them freely for research purposes, as long as the
following paper is credited (successfully tested with Matlab 2007b for windows):
Matlab codes were created to illustrate the results presented in some of Caroline Chaux papers. You can use them freely for research purposes, as long as the
following papers are credited (successfully tested with Matlab 2007b for windows):
Bijection_Pairing_N_N2(index_In,flag_Pair) provides three different explicit bijections between [0,...,K] and some consistently growing (Cantor or triangle, Elegant or square, Power-Of-Two-Odd or POTO for 2-adic integer decomposition) subset of N2. It allows different strategies to wander across a set of two-dimensional integer coordinates.
The most famous pairing functions between N and N2 are Cantor polynomials:
= ((x+y)^2+x+3y)/2 or = ((x+y)^2+3x+y)/2).
Whether they are the only bijective polynomials (between N and N2) remains an open question. They parse the positive quadrant along parallel, anti-diagonal lines, starting from the (0,0) origin. The indices increase as growing triangles, following an l_1 norm, i.e. the sum of x and y is piece-wise constant and non-decreasing. It is given by: flag_Pair = 'Cantor' or 'c'.
A second pairing function grows in concentric squares. It elegantly mimics a max or l_infinity norm, with = x+(y+floor((x+1)/2))^2.
It is given by: flag_Pair = 'Elegant' or 'e'.
'Cantor' and 'Elegant' pairing are relatively symmetric around the main diagonal.
The third and last one (POTO pairing) is more asymmetric. It can be used when one index should grow quicker than the other (roughly hyperbolic). It is related to the 2-adic representation, or the decomposition of an integer into the product of a power of two and an odd number (Power-Of-Two-Odd). It corresponds to:
= 2^x*(2*y-1) - 1.
It is given by: flag_Pair = 'Elegant' or 'e'.
Without output argument, the code displays the competition between 'Cantor', 'Elegant' and 'POTO', up to the first integer both triangular and square: 36 (not 42, to my infinite sadness).
The bijection order is given by the dimension (1 or 2) of the input index.
A few references are provided for implementing pairing functions in higher dimensions.
BRANE Cut: Graph Inference for Gene Regulatory Networks
This paper jointly addresses the problems of chromatogram baseline correction and noise reduction. The proposed approach is based on modeling the series of chromatogram peaks as sparse with sparse derivatives, and on modeling the baseline as a low-pass signal. A convex optimization problem is formulated so as to encapsulate these non-parametric models. To account for the positivity of chromatogram peaks, an asymmetric penalty functions is utilized. A robust, computationally efficient, iterative algorithm is developed that is guaranteed to converge to the unique optimal solution. The approach, termed Baseline Estimation And Denoising with Sparsity (BEADS), is evaluated and compared with two state-of-the-art methods using both simulated and real chromatogram data. See paper page
SOOT: Sparse blind deconvolution with Smooth l_1/l_2 norm ratio
The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the l1/l2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact l1/l2 term, on an application to seismic data blind deconvolution.
For those looking for "matlab codes for ieee papers", we salute you