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Variational Bayesian approaches have been successfully applied to image segmentation. They usually rely on a Potts model for the hidden label variables and a Gaussian assumption on pixel intensities within a given class. Such models may however be limited, especially in the case of multicomponent images. We overcome this limitation with HOGMep, a Bayesian formulation based on a higher-order graphical model (HOGM) on labels and a Multivariate Exponential Power (MEP) prior for intensities in a class. Then, we develop an efficient statistical estimation method to solve the associated problem. Its flexibility accommodates to a broad range of applications, demonstrated on multicomponent image segmentation and restoration.
Discovering meaningful gene interactions is crucial for the identification of novel regulatory processes in cells. Building accurately the related graphs remains challenging due to the large number of possible solutions from available data. Nonetheless, enforcing a priori on the graph structure, such as modularity, may reduce network indeterminacy issues. BRANE Clust (Biologically-Related A priori Network Enhancement with Clustering) refines gene regulatory network (GRN) inference thanks to cluster information. It works as a post-processing tool for inference methods (i.e. CLR, GENIE3). In BRANE Clust, the clustering is based on the inversion of systems of linear equations involving a graph-Laplacian matrix promoting a modular structure. Our approach is validated on DREAM4 and DREAM5 datasets with objective measures, showing significant comparative improvements. We provide additional insights on the discovery of novel regulatory or co-expressed links in the inferred Escherichia coli network evaluated using the STRING database. The comparative pertinence of clustering is discussed computationally (SIMoNe, WGCNA, X-means) and biologically (RegulonDB). BRANE Clust software is available at: http://www-syscom.univ-mlv.fr/~pirayre/Codes-GRN-BRANE-clust.html.
The growing complexity of Cyber-Physical Systems (CPS), together with increasingly available parallelism provided by multi-core chips, fosters the parallelization of simulation. Simulation speed-ups are expected from co-simulation and parallelization based on model splitting into weak-coupled sub-models, as for instance in the framework of Functional Mockup Interface (FMI). However, slackened synchronization between sub-models and their associated solvers running in parallel introduces integration errors, which must be kept inside acceptable bounds. CHOPtrey denotes a forecasting framework enhancing the performance of complex system co-simulation, with a trivalent articulation. First, we consider the framework of a Computationally Hasty Online Prediction system (CHOPred). It allows to improve the trade-off between integration speed-ups, needing large communication steps, and simulation precision, needing frequent updates for model inputs. Second, smoothed adaptive forward prediction improves co-simulation accuracy. It is obtained by past-weighted extrapolation based on Causal Hopping Oblivious Polynomials (CHOPoly). And third, signal behavior is segmented to handle the discontinuities of the exchanged signals: the segmentation is performed in a Contextual and Hierarchical Ontology of Patterns (CHOPatt). Implementation strategies and simulation results demonstrate the framework ability to adaptively relax data communication constraints beyond synchronization points which sensibly accelerate simulation. The CHOPtrey framework extends the range of applications of standard Lagrange-type methods, often deemed unstable. The embedding of predictions in lag-dependent smoothing and discontinuity handling demonstrates its practical efficiency.
Comprehensive Two dimensional gas chromatography (GCxGC, or GC2D) plays a central role into the elucidation of complex samples. The automation of the identification of peak areas is of prime interest to obtain a fast and repeatable analysis of chromatograms. To determine the concentration of compounds or pseudo-compounds, templates of blobs are defined and superimposed on a reference chromatogram. The templates then need to be modified when different chromatograms are recorded. In this study, we present a chromatogram and template alignment method based on peak registration called BARCHAN. Peaks are identified using a robust mathematical morphology tool. The alignment is performed by a probabilistic estimation of a rigid transformation along the first dimension, and a non-rigid transformation in the second dimension, taking into account noise, outliers and missing peaks in a fully automated way. Resulting aligned chromatograms and masks are presented on two datasets. The proposed algorithm proves to be fast and reliable. It significantly reduces the time to results for GCxGC analysis.
Background Inferring gene networks from high-throughput data (RNA-Seq) constitutes an important step in the discovery of relevant regulatory relationships in organism cells. Despite the large number of available Gene Regulatory Network inference methods, the problem remains challenging: the underdetermination in the space of possible solutions requires additional constraints that incorporate a priori information on gene interactions.
Results Weighting all possible pairwise gene relationships by a probability of edge presence, we formulate the regulatory network inference as a discrete variational problem on graphs. We enforce biologically plausible coupling between groups and types of genes by minimizing an edge labeling functional coding for a priori structures. The optimization is carried out with Graph cuts, an approach popular in image processing and computer vision. We compare the inferred regulatory networks to results achieved by the mutual-information-based Context Likelihood of Relatedness (CLR) method and to the state-of-the-art GENIE3, winner of the DREAM4 multifactorial challenge.
Conclusions Our BRANE Cut approach infers more accurately the five DREAM4 in silico networks (with improvements from 6% to 11%). On a real Escherichia coli compendium, an improvement of 11.8% compared to CLR and 3% compared to GENIE3 is obtained in terms of Area Under Precision-Recall curve. Up to 48 additional verified interactions are obtained over GENIE3 for a given precision. On this dataset involving 4345 genes, our method achieves a performance similar to that of GENIE3, while being more than seven times faster. The BRANE Cut code is available at: http://www-syscom.univ-mlv.fr/~pirayre/Codes-GRN-BRANE-cut.html
Keywords: Gene network inference, high throughput data, optimization, network theory, maximum flow
AbstractThe 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 (Ricker wavelet).
Keywords: Smoothed l_1/l_2 regularization, norm ratio, sparsity, blind deconvolution, nonconvex optimization, preconditioned forward-backward algorithm, seismic data processing
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.
Keywords: baseline correction, baseline wander, baseline drift, sparse derivative, asymmetric penalty, low-pass filtering, convex optimization
Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data.
Keywords: Convex optimization; Parallel algorithms; Wavelet transforms; Adaptive filters; Geophysical signal processing; Signal restoration; Sparsity; Signal separation.
Valve trays column design for gas treatment still relies on empirical correlations developed on pilot units. The available correlations lead to large discrepancies and thus more experimental works are needed. The present hydrodynamic study was carried out on a Plexiglas 1.26 m per 0.1905 m absorption column containing four V-4 Glitsch valve trays. Water/air system was used at atmospheric pressure and ambient temperature. Liquid rate per weir unit length was varied between 3.2x10-3 m3.(m.s)-1 and 24.3x10-3 m3.(m.s)-1 and the kinetic gas factor between 0 and 3.5 Pa0.5. The following hydrodynamic parameters were determined: tray pressure drop, valves pressure drop, clear liquid height, mean emulsion height and liquid mean hold up on the tray. Correlations for clear liquid height, liquid mean hold up and emulsion height are proposed. Emulsion profiles characterisation was possible due to video records post-processing. Four different behaviours are identified for emulsion profiles according to liquid and gas velocities. Significant behaviour changes on the hydrodynamic parameters allowed the identification of three system limits: dumping, weeping and pre-flooding. Correlations are proposed for these limits and an operational diagram is presented.
Keywords: Absorption; Hydrodynamics; Multiphase flow; Scale up; Valve trays; Emulsion height profiles
Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the dataset after subtraction. The challenge consists in attenuating multiples without distorting primaries, despite the high cross-correlation between their waveform. For this purpose, this complicated wide-band problem is decomposed into a set of more tractable narrow-band problems using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via single-sample (unary) complex Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and rectifies more robustly small and large misalignment errors through phase and integer delay corrections . This approach greatly simplifies the matching filter estimation and, despite its simplicity, compares promisingly with standard adaptive 2D methods, on both synthetic and field data.
Keywords: multiples, processing, filtering, cross-correlation, wavelet, adaptive, model
The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.
Keywords: Review; Multiscale; Geometric representations; Oriented decompositions; Scale-space; Wavelets; Atoms; Sparsity; Redundancy; Bases; Frames; Edges; Textures; Image processing; Haar wavelet; Non-Euclidean wavelets
Highly boosted spark ignition engines must confront violent forms of pre-ignition limiting the maximal low-end torque. French research institute IFP presents here an innovative tool allowing a better understanding of this phe- nomenon and a structured reasoning considering all potential causes of this phenomenon. Advanced statistical analyses of the combustion process and direct visualisations inside the combustion chamber are successfully combined to accurately assess the development of pre-ignition. This coupled approach provides an efficient tool for analysis and development of new engines and new control concepts on IFP test beds.
Keywords: Combustion Analysis; Pre-ignition; Detection; Rumble; Knock
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.
Keywords: Filter design; frequency localization; inversion; lapped transforms; modulated filter banks; optimization; oversampled filter banks; time localization; inverse overlapped complex filter banks optimization; SURE denoising
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
Keywords: M-band wavelet transform; Block estimator; Stein's principle; denoising; dual-tree wavelet transform; frames; multichannel noise; multicomponent image; multivariate estimation; nonlinear estimation ; complex wavelet thresholding
Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is performed -- which occurs in particular when an additive noise is corrupting the signal to be analyzed -- it is useful to characterize the statistical properties of the dual-tree wavelet coefficients of this process. As dual-tree decompositions constitute overcomplete frame expansions, correlation structures are introduced among the coefficients, even when a white noise is analyzed. In this paper, we show that it is possible to provide an accurate description of the covariance properties of the dual-tree coefficients of a wide-sense stationary process. The expressions of the (cross-)covariance sequences of the coefficients are derived in the one and two-dimensional cases. Asymptotic results are also provided, allowing to predict the behaviour of the second-order moments for large lag values or at coarse resolution. In addition, the cross-correlations between the primal and dual wavelets, which play a primary role in our theoretical analysis, are calculated for a number of classical wavelet families. Simulation results are finally provided to validate these results.
Keywords: Covariance; Hilbert transform cross-correlation; dependence; dual-tree; filter banks; frames; noise; random processes; stationarity; statistics; wavelets
Comprehensive two-dimensional gas chromatography (GCxGC or GC2D) is a major advance for the detailed characterisation of petroleum products. This technique is based on two orthogonal dimensions of separation achieved by two chromatographic capillary columns of different chemistries and selectivities. High-frequency sampling between the two columns is achieved by a modulator, ensuring that the whole sample is transferred and analysed continuously in both separations. Thus, the peak capacity and the resoluting power dramatically increase. Besides, highly structured 2D chromatograms are obtained upon the volatility and the polarity of the solute to provide more accurate molecular identification of hydrocarbons. In this paper fundamental and practical considerations for implementation of GCxGC are reviewed. Selected applications obtained using a prototype of a GCxGC chromatograph developed in-house highlight the potential of the technique for molecular characterisation of middle distillates, sulphur speciation in diesel and analysis of effluents from petrochemical processes
We propose a two-dimensional generalization to the -band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.
Keywords: Direction selection; Hilbert transform; dual-tree; image denoising; wavelets
The detailed characterisation of middle distillates is essential for a better understanding of reactions involved in refining process. Owing to higher resolution power and enhanced sensitivity, comprehensive two-dimensional gas chromatography (GCxGC) is a powerful tool for improving characterisation of petroleum samples. The aim of this paper is to compare GCxGC and various ASTM methods - gas chromatography (GC), liquid chromatography (LC) and mass spectrometry (MS) - for group type separation and detailed hydrocarbon analysis. Best features of GCxGC are demonstrated and compared to these techniques in terms of cost, time consumption and accuracy. In particular, a new approach of simulated distillation (SimDis-GCxGC) is proposed: compared to the standard method ASTM D2887 it gives unequal information for better understanding of conversion process.
Keywords: Comprehensive two-dimensional gas chromatography; ASTM methods; Simulated distillation; Group type separation; Hydrocarbons
Seismic exploration provides information about the ground substructures. Seismic images are generally corrupted by several noise sources. Hence, efficient denoising procedures are required to improve the detection of essential geological information. Wavelet bases provide sparse representation for a wide class of signals and images. This property makes them good candidates for efficient filtering tools, allowing the separation of signal and noise coefficients. Recent works have improved their performance by modelling the intra- and inter-scale coefficient dependencies using hidden Markov models, since image features tend to cluster and persist in the wavelet domain. This work focuses on the use of lapped transforms associated with hidden Markov modelling. Lapped transforms are traditionally viewed as block-transforms, composed of M pass-band filters. Seismic data present oscillatory patterns and lapped transforms oscillatory bases have demonstrated good performances for seismic data compression. A dyadic like representation of lapped transform coefficient is possible, allowing a wavelet-like modelling of coefficients dependencies. We show that the proposed filtering algorithm often outperforms the wavelet performance both objectively (in terms of SNR) and subjectively: lapped transform better preserve the oscillatory features present in seismic data at low to moderate noise levels.
Keywords: seismic data filtering; lapped transforms; hidden Markov models
Comprehensive two-dimensional gas chromatography (GCxGC) has been investigated for the characterization of high valuable petrochemical samples from dehydrogenation of n-paraffins, Fischer-Tropsch and oligomerization processes. GCxGC separations, performed using a dual-jets CO2 modulator, were optimized using a test mixture representative of the hydrocarbons found in petrochemicals. For complex samples, a comparison of GCxGC qualitative and quantitative results with conventional gas chromatography (1D-GC) has demonstrated an improved resolution power of major importance for the processes: the group type separation has permitted the detection of aromatic compounds in the products from dehydrogenation of n-paraffins and from oligomerization, and the separation of alcohols from other hydrocarbons in Fischer-Tropsch products.
Keywords: Gas chromatography, comprehensive two-dimensional; Petrochemical samples; Hydrocarbons
An increasing attention is being paid to multispectral images for a great number of applications (medicine, agriculture, archeology, forestry, coastal management, remote sensing) because many features of the underlying scene have unique spectral characteristics that become apparent in imagery when viewing combinations of its different components. [...] Despite the dramatical technological advances in terms of spatial and spectral resolutions of the radiometers, data still suffer from several degradations. For instance, the sensor limited aperture, aberrations inherent to optical systems and mechanical vibrations create a blur effect in remote sensing images [JAI 89]. In optical remote sensing imagery, there are also many noise sources. Firstly, the number of photons received by each sensor during the obturation time may fluctuate around its average implying a photon noise. A thermal noise may be caused by the electronics of the recording and the communication channels during the data downlinking. Intermittent saturations of any detector in a radiometer may give rise to an impulsive noise whereas a structured periodic noise is generally caused by interferences between electronic components. Detector striping (resp. banding) are consequences of calibration differences among individual scanning detectors (resp. from scan-to-scan). Besides, component-to-component misregistration may occur : corresponding pixels in different components are not systematically associated with the same position on the ground. As a result, it is mandatory to apply deblurring, denoising and geometric corrections to the degraded observations in order to fully exploit the information they contain. In this respect, it is used to distinguish between on-board and on-ground processing. Indeed, on-board procedures should simultaneously fulfill real-time constraints and low mass memory requirements. The involved acquisition bit-rates are high (especially for very high resolution missions) and hence, they complicate the software implementation of enhancement processing. [...]
This introductory paper aims at summarizing some problems and state-of-the-art techniques encountered in image processing for material analysis and design. Developing generic methods for this purpose is a complex task given the variability of the different image acquisition modalities (optical, scanning or transmission electron microscopy; surface analysis instrumentation, electron tomography, micro-tomography...), and material composition (porous, fibrous, granular, hard materials, membranes, surfaces and interfaces...). This paper presents an overview of techniques that have been and are currently developed to address this diversity of problems, such as segmentation, texture analysis, multiscale and directional features extraction, stochastic models and rendering, among others. Finally, it provides references to enter the issues, challenges and opportunities in materials characterization.
Keywords: Image Processing, Image-based Analysis, Materials science, Stochastic modeling, Surface Science, Texture Analysis, Work-flow
Both random and structured perturbations affect seismic data. Their removal, to unveil meaningful geophysical information, requires additional priors. Seismic multiples are one form of structured perturbations related to wave-field bouncing. In this paper, we model these undesired signals through a time-varying filtering process accounting for inaccuracies in amplitude, time-shift and average frequency of available templates. We recast the problem of jointly estimating the filters and the signal of interest (primary) in a new convex variational formulation, allowing the incorporation of knowledge about the noise statistics. By making some physically plausible assumptions about the slow time variations of the filters, and by adopting a potential promoting the sparsity of the primary in a wavelet frame, we design a primal-dual algorithm which yields good performance in the provided simulation examples.
This tutorial paper aims at summarizing some problems, ranging from analytical chemistry to novel chemical sensors, that can be addressed with classical or advanced methods of signal and image processing. We gather them under the denomination of "chemical sensing". It is meant to introduce the special session "Signal Processing for Chemical Sensing" with a large overview of issues which have been and remain to be addressed in this application domain, including chemical analysis leading to PARAFAC/tensor methods, hyper spectral imaging, ion-sensitive sensors, artificial nose, chromatography, mass spectrometry, etc. For enlarging and illustrating the points of view of this tutorial, the invited papers of the session consider other applications (NMR, Raman spectroscopy, recognition of explosive compounds, etc.) addressed by various methods, e.g. source separation, Bayesian, and exploiting typical chemical signal priors like positivity, linearity, unit-concentration or sparsity.
Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high cross-correlation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple model-based adaptive subtraction, using single-sample unary filters' estimation in a complex wavelet transformed domain. The method offers more robustness to incoherent noise through redundant decomposition. It is first tested on synthetic data, then applied on real-field data, with a single-model adaptation and a combination of several multiple models.
Due to complex subsurface structure properties, seismic records often suffer from coherent noises such as multiples. These undesired signals may hide the signal of interest, thus raising difficulties in interpretation. We propose a new variational framework based on Maximum A Posteriori (MAP) estimation. More precisely, the problem of multiple removal is formulated as a minimization problem involving time-varying filters, assuming that a disturbance signal template is available and the target signal is sparse in some orthonormal basis. We show that estimating multiples is equivalent to identifying filters and we propose to employ recently proposed convex optimization procedures based on proximity operators to solve the problem. The performance of the proposed approach as well as its robustness to noise is demonstrated on realistically simulated data. [Keywords: convex optimization, wavelets, time-varying filters, regularization]
Directional filters are commonly used tools in modern seismic data processing to address coherent signals, depending on their apparent slowness or slope. This operation enhances the characterization of the great variety of signals present in a seismic dataset that enables a better characterization of the subsurface structure. This paper compares two complementary local adaptive multiscale directional filters: a directional filter bank based on dual-tree M-band wavelets and a novel local slant stack transform (LSST) based filter in the timescale domain. Their differences reside in redundancy levels and slope (directional) resolution. A structural similarity index measure has been employed to objectively compare both approaches on a real seismic dataset example.
Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between multiples and their prediction, and thus to minimize the multiples in the input dataset after the subtraction. In this paper we focus on the subtraction element. The proposed complex wavelet transform based approach simplifies the matching filter estimation.
Redundancy in wavelets and filter banks has the potential to greatly improve signal and image denoising. Having de- veloped a framework for optimized oversampled complex lapped transforms, we propose their association with the sta- tistically efficient Stein’s principle in the context of mean square error estimation. Under Gaussian noise assumptions, expectations involving the (unknown) original data are ex- pressed using the observation only. Two forms of Stein’s Un- biased Risk Estimators, derived in the coefficient and the spa- tial domain respectively, are proposed, the latter being more computationally expensive. These estimators are then em- ployed for denoising with linear combinations of elementary threshold functions. Their performances are compared to the oracle, and addressed with respect to the redundancy. They are finally tested against other denoising algorithms. They prove competitive, yielding especially good results for tex- ture preservation.
Seismic data and their complexity still challenge signal processing algorithms in several applications. The advent of wavelet transforms has allowed improvements in tackling denoising problems. We propose here coherent noise filtering in seismic data with the dual-tree M-band wavelet transform. They offer the possibility to decompose data locally with improved multiscale directions and frequency bands. Denoising is performed in a deterministic fashion in the directional subbands, depending of the coherent noise properties. Preliminary results show that they consistently better preserve seismic signal of interest embedded in highly energetic directional noises than discrete critically sampled and redundant separable wavelet transforms.
The Short Term Fourier Transform (STFT) is a classical linear time-frequency (T-F) representation. Despites its relative simplicity, it has become a standard tool for the analysis of non-stationary signals. Since it provides a redundant representation, it raises some issues such as (i) \optimal" window choice for analysis, (ii) existence and determination of an inverse transformation, (iii) performance of analysis-modification-synthesis, or reconstruction of selected components of the time-frequency plane and (iv) redundancy controllability for low-cost applications, e.g. real-time computations. We address some of these issues, as well as the less often mentioned problem of transform symmetry in the inverse, through oversampled FBs and their optimized inverse(s) in a slightly more general setting than the discrete windowed Fourier transform.
The complexity of seismic data still challenges signal processing algorithms in several applications. The rediscovery of wavelet transforms by J. Morlet et al. has allowed improvements in addressing several data representation (local analysis, compression) and restoration problems. However, despites their achievements, traditional approaches based on discrete and separable (both for computational purposes) wavelets fail at efficiently representing directional or higher dimensional data features, such as line or plane singularities, especially in severe noise conditions. Subsequent extensions to wavelets (multiscale pyramids, curvelets, contourlets, bandlets) have recently generated tremendous theoretical and practical interests. They feature local and multiscale properties associated with a certain amount of redundancy, which may represent an issue for huge datasets processing. We propose here seismic data processing based on dual-tree M-band wavelet transforms. They combine:
- orthogonal M-band filter banks which better separate frequency bands in seismic data than wavelets, due to the increased degrees of freedom in the filter design,
- Hilbert transform and complex representation of seismic signals which have been effective, especially for attributes definition, with a relatively low redundancy (a factor of two). These transforms have been successfully applied to random noise removal in traditional and remote sensing imagery. We apply them to seismic data and address their potential for local slope analysis and coherent noise (ground-roll) filtering.
Seismic data are subject to different kinds of unwanted perturbations. These random or organised noises, which can be acquisition or processing related for instance, may disturb geophysical interpretations and thwart attempts at automated processing methods. Since the relative features (e.g. amplitude, spectrum) of the signals of interest and the noises may vary locally, signal and noise separation is obtained by a local data-driven filtering with two or three-dimensional oversampled complex filter banks. Filter banks in general decompose the noisy data onto frequency bands and directions on restricted subregions (sub-images or sub-volumes), acting like a local FK with improved properties. The transforms studied in this work present sub-regions smooth overlapping, to avoid tiling effects while allowing signal reconstruction from the transformed domain. The proposed methodology uses limited redundancy filtering that both yield enhanced noise robustness (due to oversampling) and tractable 2D or 3D processing, since they are optimized to limit the redundancy cost. Coupling those redundant transforms with a processing method designed to detect and compute locally dominant directions, and to remove unwanted directions and random noise, leads to good visual results. Tests were performed on 2D and 3D seismic data
Dual-tree wavelet transforms have recently gained popularity since they provide low-redundancy directional analyses of images. In our recent work, dyadic real dual-tree decompositions have been extended to the M-band case, so adding much flexibility to this analysis tool. In this work, we propose to further extend this framework on two fronts by considering (i) biorthogonal and (ii) complex M-band dualtree decompositions. Denoising results are finally provided to demonstrate the validity of the proposed design rules. Keywords: Wavelet transforms, Hilbert transforms, Image analysis, Image processing, Gaussian noise.
This paper addresses the implementation and comparison of algorithms for real-time knock detection. Knock is an unwanted abnormal combustion process that may damage engines and limit their efficiency. For series vehicles, knock detection is generally obtained from knock sensors that capture other noise sources, thus requiring robust algorithms. In order to estimate the performance of time-frequency and Kalman filter based algorithms, a knock signal model is proposed and the algorithms are tested under various noise conditions. Experiments on modelled and real signals show the superiority of the recently developed S-method with respect to extended Kalman filtering. Keywords: Knock, Real time systems, Time-Frequency Analysis, Kalman filtering, Wigner distributions
When an oversampled FIR filter bank structure is used for signal analysis, a main problem is to guarantee its invertibility and to be able to determine an inverse synthesis filter bank. As the analysis scheme corresponds to a redundant decomposition, there is no unique inverse filter bank and some of the solutions can lead to artifacts in textured image filtering applications. In this paper, the flexibility in the choice of the inverse filter bank is exploited to find the best-localized impulse responses. The design is performed by solving a constrained optimization problem which is reformulated in a smaller dimensional space. Application to seismic data clearly shows the improvements brought by the optimization process. Keywords: FIR digital filters, Transforms, Redundancy, Optimization methods, Seismic signal processing
Signals and images in industrial applications are often subject to strong disturbances and thus require robust methods for their analysis. Since these data are often non-stationary, time-scale or time-frequency tools have demonstrated effectiveness in their handling. More specifically, wavelet transforms and other filter bank generalizations are particularly suitable, due to their discrete implementation. We have recently investigated a specific family of filter banks, the M-band dual-tree wavelet, which provides state of the art performance for image restoration. It generalizes an Hilbert pair based decomposition structure, first proposed by N. Kingsbury and further investigated by I. Selesnick. In this work, we apply this frame decomposition to the analysis of two examples of signals and images in an industrial context: detection of structures and noises in geophysical images and the comparison of direct and indirect measurements resulting from engine combustion. Keywords: M-band wavelets, Hilbert transform, Dual-tree, Image denoising, Direction analysis.
In a previous work, we proposed a relatively simple method to build non separable perfect reconstruction oversampled lapped transforms. The main drawback of this method was that the redundancy factor was constrained to be equal to the overlapping one. This constitutes a strong limitation for applications such as seismic processing involving three-dimensional data sets. The memory requirements may indeed become hard to meet if the redundancy is not reduced. In this paper, we propose an approach to guarantee that a given lapped transform is invertible by a finite length filter bank. We show how to compute a corresponding synthesis filter bank. The proposed analysis/ synthesis filter bank system is applied to directional filtering of noisy three-dimensional seismic data.
Surface wave attenuation is a difficult problem to address in foothills areas due to the high variability of their typology. Such recorded events can indeed be non linear and even mimic reflection hyperbolas. We present two innovative approaches that exploit the combination of different criteria so as to discriminate be- tween effective signal and noise. The first one makes use of both apparent velocity and polarisation. Its ability to detect noise is demonstrated on a synthetic multi-component data set inspired from South American foothills. The second one combines apparent velocity and a decomposition on different time and space scales. Im- provements over classical FK filtering are shown on a sin- gle component real data set from Canadian foothills
In this work, we study the properties of an additive noise undergoing a dual-tree M-band wavelet analysis. We express the relationships governing noise coefficients both in the primal and the dual tree. The knowlegde of the noise statistical properties is particularly useful for the design of efficient denoising methods in the framework of a dual-tree wavelet analysis. Our main contribution consists in the computation of the resulting cross-correlation functions for several M-band wavelet families. More specifically, we show that pairwise coefficients, from the primal and the dual-tree resulting from a white noise decomposition, are uncorrelated. Yet, there exists a significant local correlation, whose extent depends on the choice of the wavelet pair.
Second poster presentation award to Aurélie Pirayre et al., "Incorporating structural a priori in Gene Regulatory Network Inference using Graph cuts" [Poster, Awarded 2nd best poster], European Student Council Symposium 2014 (ESCS'14), Strasbourg, France
Best student paper award to Caroline Chaux et al., ICASSP 2005
2000-2001 SEG Student Sections Award of merit with Tage Røsten, NTNU (now Statoil)
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