Denoising, detrending, deconvolution: usual restoration tasks, traditionally decoupled. Coupled formulations entail complex ill-posed inverse problems. We propose PENDANTSS for joint trend removal and blind deconvolution of sparse peak-like signals. It blends a parsimonious prior with the hypothesis that smooth trend and noise can somewhat be separated by low-pass filtering. We combine the generalized quasi-norm ratio SOOT/SPOQ sparse penalties $\ell_p/\ell_q$ with the BEADS ternary assisted source separation algorithm. This results in a both convergent and efficient tool, with a novel Trust-Region block alternating variable metric forward-backward approach. It outperforms comparable methods, when applied to typically peaked analytical chemistry signals. Reproducible code is provided.

MOTIVATION: The cellular system of a living organism is composed of interacting bio-molecules that control cellular processes at multiple levels. Their correspondences are represented by tightly regulated molecular networks. The increase of omics technologies has favored the generation of large-scale disparate data and the consequent demand for simultaneously using molecular and functional interaction networks: gene co-expression, protein-protein interaction (PPI), genetic interaction and metabolic networks. They are rich sources of information at different molecular levels, and their effective integration is essential to understand cell functioning and their building blocks (proteins). Therefore, it is necessary to obtain informative representations of proteins and their proximity, that are not fully captured by features extracted directly from a single informational level. We propose BraneMF, a novel random walk-based matrix factorization method for learning node representation in a multilayer network, with application to omics data integration. RESULTS: We test BraneMF with PPI networks of Saccharomyces cerevisiae, a well-studied yeast model organism. We demonstrate the applicability of the learned features for essential multi-omics inference tasks: clustering, function and PPI prediction. We compare it to the state-of-the-art integration methods for multilayer networks. BraneMF outperforms baseline methods by achieving high prediction scores for a variety of downstream tasks. The robustness of results is assessed by an extensive parameter sensitivity analysis. AVAILABILITY AND IMPLEMENTATION: BraneMF's code is freely available at: https://github.com/Surabhivj/BraneMF, along with datasets, embeddings and result files. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Gene expression is regulated at different molecular levels, including chromatin accessibility, transcription, RNA maturation, and transport. These regulatory mechanisms have strong connections with cellular metabolism. In order to study the cellular system and its functioning, omics data at each molecular level can be generated and efficiently integrated. Here, we propose BRANENET, a novel multi-omics integration framework for multilayer heterogeneous networks. BRANENET is an expressive, scalable, and versatile method to learn node embeddings, leveraging random walk information within a matrix factorization framework. Our goal is to efficiently integrate multi-omics data to study different regulatory aspects of multilayered processes that occur in organisms. We evaluate our framework using multi-omics data of Saccharomyces cerevisiae, a well-studied yeast model organism. RESULTS: We test BRANENET on transcriptomics (RNA-seq) and targeted metabolomics (NMR) data for wild-type yeast strain during a heat-shock time course of 0, 20, and 120 min. Our framework learns features for differentially expressed bio-molecules showing heat stress response. We demonstrate the applicability of the learned features for targeted omics inference tasks: transcription factor (TF)-target prediction, integrated omics network (ION) inference, and module identification. The performance of BRANENET is compared to existing network integration methods. Our model outperforms baseline methods by achieving high prediction scores for a variety of downstream tasks.

Unlike their biological counterparts, simple artificial neural networks are unable to retain information from their past state to influence their behavior. In this contribution, we propose to consider new nonlinear activation functions, whose outputs depend both from the current and past inputs through a hysteresis effect. This hysteresis model is developed in the framework of convolutional neural networks. We then show that, by choosing the nonlinearity in the vast class of rational functions, the identification of the weights amounts to solving a rational optimization problem. For the latter, recent methods are applicable that come with global optimality guarantee, contrary to most optimization methods used in the neural network community. Finally, simulations show that such hysteresis nonlinear activation functions cannot be approximated by traditional ones and illustrate the effectiveness of our weight identification method.

As field seismic data sizes are dramatically increasing toward exabytes, automating the labeling of “structural monads” - corresponding to geological patterns and yielding subsurface interpretation - in a huge amount of available information would drastically reduce interpretation time. Since customary designed features may not account for gradual deformations observable in seismic data, we propose to adapt the wavelet-based scattering network methodology with a tessellation of geophysical images. Its invariances are expected to be able to thwart the effect of the tectonics. The sparse structure of extracted feature vectors suggest to resort to dimension reduction methods before classification. The most promising one is based on a tessellated version of scattering decompositions, combined with a standard affine PCA classifier. Extensive comparative results on a four-class seismic database show the effectiveness of the proposed method in terms of seismic data labeling and object retrieval, in affordable computational time.

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 a system 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.

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.

We propose a new compression method devoted to large structured hexahedral meshes having discontinuities. It is dedicated to applications such as visualization or physical simulations whose management by any workstation or mobile device with limited memory and bandwidth is critical. Our method relies on a multiresolution analysis that generates a hierarchy of meshes at increasing resolutions. Our technique also uses a discontinuity tracking feature for their preservation, whatever the resolution, and consequently maintains a coherent geometry with respect to the original mesh. Experimental results emphasize the quality of our compression, in terms of both geometrical distortion and compression ratio.

With the advent of microarrays, arose the need to analyze gene expression data. Tools for building gene regulation networks are indeed of high interest for regulatory relationship sketching and gene interaction prediction. Given all pairwise gene regulation information available, we propose to determine the presence of edges in the final gene regulatory network by adopting a convex optimization formulation. Our energy minimization strategy includes a regularization term accounting for the difference of connectivity of particular genes (i.e. transcription factors), and we employ proximal methods to compute the optimal solution. The resulting algorithm, called “Brane relax”, outperforms state-of-the-art methods while keeping a reduced computational cost.

This paper proposes a novel approach for echo-like multiple removal in two-dimensional seismic images. It is based on constrained adaptive filtering associated with geometric wavelets. Approximate templates of multiple reflections are assumed to be available and they are matched to multiple reflections throughout estimated finite impulse response filters. The problem is formulated under a constrained convex optimization form where the data of interest and filters are estimated jointly. Proximal approaches are used to perform the minimization of the derived criterion. The effectiveness of the proposed approach is demonstrated with various noise levels on realistic simulated data and on field seismic data.

BACKGROUND: Inferring gene networks from high-throughput data 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. METHODS: 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 by the state-of-the-art GENIE3, winner of the DREAM4 multifactorial challenge. RESULTS: 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. CONCLUSIONS: BRANE Cut is a weighted graph thresholding method. Using biologically sound penalties and data-driven parameters, it improves three state-of-the art GRN inference methods. It is applicable as a generic network inference post-processing, due to its computational efficiency.

The ℓ1/ℓ2ratio 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/ℓ2function 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/ℓ2function. 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/ℓ2term, on an application to seismic data blind deconvolution.

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation is obtained through time-varying filtering, compensating inaccuracies in given approximate templates. The under-determined problem can then be formulated as a convex optimization one, providing estimates of both filters and primaries. Within this framework, the criterion to be minimized mainly consists of two parts: a data fidelity term and hard constraints modeling a priori information. This formulation may avoid, or at least facilitate, some parameter determination tasks, usually difficult to perform in inverse problems. Not only classical constraints, such as sparsity, are considered here, but also constraints expressed through hyperplanes, onto which the projection is easy to compute. The latter constraints lead to improved performance by further constraining the space of geophysically sound solutions.

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.

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.

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.

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 dual-tree decompositions. Denoising results are finally provided to demonstrate the validity of the proposed design rules.

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.

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 the extended Kalman filtering.

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 over-complete 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 behavior 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.

We propose a new estimator for image denoising using a 2D dual-tree M-band wavelet transform. Our work extends existing block-based wavelet thresholding methods by exploiting simultaneously coefficients in the two M-band wavelet trees. The contributions of this paper are two-fold. Firstly, we perform a statistical analysis of the noise in the considered redundant decomposition. Secondly, we propose an efficient method to remove the noise. Our approach relies on an extension of Stein's formula which allows us to take into account the specific correlations of the noise components. Simulation results are then presented to validate the proposed method

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

We propose a two-dimensional generalization to the M-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.

We propose a 2D generalization to the M-band case of the dual-tree structure (initially proposed by N.G. Kingsbury and further investigated by I.W. Selesnick) based on a Hilbert pair of wavelets. We particularly address the construction of the dual basis and the resulting directional analysis. We revisit the necessary preprocessing 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 image denoising comparisons.

Hidden Markov tree (HMT) wavelet models have demonstrated superior performance in image filtering, by their ability to capture features across scales. Recently, we proposed to extend the HMT framework to the lapped transform domain, where lapped transforms (LT) are M-channel linear phase filterbanks. When the number of channels is a power of 2, the block partition provided by LT is remapped to an octave-like representation, where an HMT is able to model the statistical dependencies between intra- and interband coefficients. Due to better energy compaction and reduced aliasing properties, LT outperforms discrete wavelet transforms at moderate noise levels, both subjectively and objectively. However, critically-decimated LT suffers from a lack of shift-invariance, resulting in a degraded performance. We study the improvement of HMT modeling in the LT domain (HMT-LT), combined with a redundant decomposition, in order to increase its performance for image denoising.

It is reported that the use of multiple subband transforms for thresholding based denoising gains performance in the mean square error sense. In traditional thresholding-based methods, a noisy image is decomposed by linear transformations such as wavelets, FFT and so on and the transformed coefficients are hard/soft-thresholded. In particular, it is well-known that wavelets work well for denoising. From the viewpoint that wavelets are in a class of subband transforms, we propose a strategy in which multiple subband transforms are switched region by region, i.e. block by block. For reconstruction, the projection-based iterative method is used. Experimental results are pretty good and promising.

In several applications such as denoising, when signal expansion is not crucial, oversampled filter banks may outperform critically decimated filter banks. We study the performance of the recently proposed GLPBT (Generalized Lapped Pseudo-Biorthogonal Transform), a class of oversampled filter banks, on noise removal in seismic data, using controlled redundancy. We also investigate heuristics for the choice of an optimal threshold, which appears to depend non-trivially on the noise variance. Tests indicate that carefully designed oversampled filter banks are able to outperform critically sampled ones.

Algorithms based on wavelet-domain hidden Markov tree (HMT) have demonstrated excellent performance for image denoising. The HMT model is able to capture image features across the scales, in contrast to classical shrinkage that thresholds subbands independently. In this work, we extend the aforementioned results to a lapped transform domain. Lapped transforms (LT) are M-channel linear phase filter banks. Their use is motivated by their good energy compaction properties and robustness to oversmoothing. It is also observed that LT preserve better oscillatory image components, such as textures. Since LT are applied as block transforms, the transforms coefficients are rearranged into an octave-like decomposition, and their statistics are modeled by the same HMT structure as in the wavelet case. At moderate noise levels, the proposed algorithm is able to improve the results obtained with wavelets, subjectively and objectively.

Compression and denoising are two of the most successful applications of wavelets to signals and natural images. Both techniques have also been successfully applied to seismic signals, but compression is not widely accepted yet, since it is often believed to harm seismic information.

Previous work has shown that GenLOT coding is a very effective technique for compressing seismic data. The role of a transform in a coder is to concentrate information and reduce statistical redundancy. When used with embedded zerotree coding, GenLOTs often provide superior performance to traditional block oriented algorithms or to wavelets. In this work we investigate the use of generalized unequal length lapped orthogonal transforms (GULLOT). Their shorter bases for high-frequency components are suitable for reducing ringing artifacts in images. While GULLOTs yield comparable performance to GenLOTs on smooth seismic signals like stacked sections, they achieve improved performance on less smooth signals such as shot gathers.

Summary form only given. Seismic data compression is desirable in geophysics for both storage and transmission stages. Wavelet coding methods have generated interesting developments, including a real-time field test trial in the North Sea in 1995. Previous work showed that GenLOT with basic optimization also outperforms state-of-the-art biorthogonal wavelet coders for seismic data. In this paper, we focus on the problem of filter bank optimization using various properties of seismic data. It is often desirable to evaluate the compression performance of a transform on a set of data using a priori objective measures, to reduce extensive testings by selecting only good a priori transforms, and to tailor transforms to the statistical properties of the data set. In the scope of this work, we use symmetric AR models up to order 4 to obtain an average model of the horizontal and vertical signals of a seismic stack section. Rosten et al. (1999), have already shown that order 1 or 2 models give good results in filter bank optimization for non-unitary filter banks, using coding gain optimization. Several other criteria may be used for transform optimization. Following the theory in Tran and Nguyen (1999), we use a weighted combination of C/sub o/=k/sub C/C/sub C/+k/sub S/C/sub S/+k/sub d/C/sub D/ of coding gain, stopband attenuation and DC leakage minimization functions.

GenLOT coding has been shown an effective technique for seismic data compression, especially when compared to block-based algorithms (such as JPEG), or to wavelets. The transforms remove statistical redundancy and permit efficient compression, when used with advanced encoding techniques, such as the embedded zerotree coding framework. We derive a model for seismic data based on auto-regressive processes. This model is used to design GenLOT filter banks optimized for seismic data, using objective optimization criteria.