arXiv subjects

Bruno Torrésani

Publications and source records attributed to Bruno Torrésani.

14 recordsLinked to original sources

arXiv2025

Revisiting CHAMPAGNE: Sparse Bayesian Learning as Reweighted Sparse Coding

This paper revisits the CHAMPAGNE algorithm within the Sparse Bayesian Learning (SBL) framework and establishes its connection to reweighted sparse coding. We demonstrate that the SBL objective can be reformulated as a reweighted $\ell_{21}$-minimization problem, providing a more straightforward interpretation of the sparsity mechanism and enabling the design of an efficient iterative algorithm. Additionally, we analyze the behavior of this reformulation in the low signal-to-noise ratio (SNR) regime, showing that it simplifies to a weighted $\ell_{21}$-regularized least squares problem. Numerical experiments validate the proposed approach, highlighting its improved computational efficiency and ability to produce exact sparse solutions, particularly in simulated MEG source localization tasks.

eess.SP↗

arXiv2025

Stability estimates for adaptive focused time-frequency transforms

This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed function or signal, and that adapts dynamically the time-frequency resolution of the analysis. Sticking to the continuous case setting, this work provides new stability results for the transform (stability with respect with the focus function). It also investigates in some details focus functions based upon regularized R{é}nyi entropies and show corresponding continuity results.

math.CA↗

arXiv2024

A class of non linear adaptive time-frequency transforms

This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to specific features of the analyzed function. Such an adaptation is implemented via so-called focus functions, which control the window scale as a function of the time variable, or the frequency variable. In this respect, these transforms are non-linear, which makes the analysis more complex than usual.Under appropriate assumptions, some norm control can be obtained for both transforms in L^2(R) spaces, which extend the classical continuous frame norm control and guarantees well-definedness on L^2. Given the non-linearity of the transforms, the existence of inverse transforms is not guaranteed anymore, and is an open question. However, the results of this paper represent a first step towards a more general theory.Besides mathematical results, some elementary examples of time and frequency focus functions are provided, which can serve as staring point for concrete applications.

math.CA↗

arXiv2023

Sparse wavelet-based solutions for the M/EEG inverse problem

This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a transformed domain, namely a spatial wavelet domain. Sparsity in the wavelet domain allows to reach ''data compression'' in the cortical sources domain. Spatial wavelets defined on the mesh graph of the triangulated cortical surface are used, in combination with sparse regression techniques, namely LASSO regression or sparse Bayesian learning, to provide localized and compressed estimates for brain activity from sensor data. Numerical results on simulated and real MEG data are provided, which outline the performances of the proposed approach in terms of localization.

eess.SP↗

arXiv2022

Synthesis-based time-scale transforms for non-stationary signals

This paper deals with the modeling of non-stationary signals, from the point of view of signal synthesis. A class of random, non-stationary signals, generated by synthesis from a random timescale representation, is introduced and studied. Non-stationarity is implemented in the timescale representation through a prior distribution which models the action of time warping on a stationary signal. A main originality of the approach is that models directly a timescale representation from which signals can be synthesized, instead of post-processing a pre-computed timescale transform. A maximum a posteriori estimator is proposed for the time warping parameters and the power spectrum of an underlying stationary signal, together with an iterative algorithm, called JEFAS-S, for the estimation, based upon the Expectation Maximization approach. Numerical results show the ability of JEFAS-S to estimate accurately time warping and power spectrum. This is in particular true when time warping involves fast variations, where a similar approach called JEFAS, proposed earlier, fails. In addition, as a by-product, the approach is able to yield extremely sharp timescale representations, also in the case of fast varying non-stationarity, where standard approaches such as synchrosqueezing fail.

cond-mat.soft↗

arXiv2020

Time-scale synthesis for locally stationary signals

We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a function of time by time dependent translations on the scale axis. In a maximum a posteriori approach, we propose an estimator for the model parameters, namely the time-varying scale translation and an underlying power spectrum. The proposed approach is illustrated on a denoising example. It is also shown that the model can handle locally stationary signals with fast frequency variations, and provide in this case very sharp timescale representations more concentrated than synchrosqueezed or reassigned wavelet transform.

math.ST↗

arXiv2018

Spectral analysis for nonstationary audio

A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random signals. The focus is on time warping and amplitude modulation, and an approximate maximum-likelihood approach based on suitable approximations in the wavelet transform domain is developed. This paper provides theoretical analysis of the approximations, and introduces JEFAS, a corresponding estimation algorithm. The latter is tested and validated on synthetic as well as real audio signal.

eess.AS↗

arXiv2015

A Bayesian model for microarray datasets merging

The aggregation of microarray datasets originating from different studies is still a difficult open problem. Currently, best results are generally obtained by the so-called meta-analysis approach, which aggregates results from individual datasets, instead of analyzing aggre-gated datasets. In order to tackle such aggregation problems, it is necessary to correct for interstudy variability prior to aggregation. The goal of this paper is to present a new approach for microarray datasets merging, based upon explicit modeling of interstudy variability and gene variability. We develop and demonstrate a new algorithm for microarray datasets merging. The underlying model assumes normally distributed intrinsic gene expressions, distorted by a study-dependent nonlinear transformation, and study dependent (normally distributed) observation noise. The algorithm addresses both parameter estimation (the parameters being gene expression means and variances, observation noise variances and the nonlinear transformations) and data adjustment, and yields as a result adjusted datasets suitable for aggregation. The method is validated on two case studies. The first one concerns E. Coli expression data, artificially distorted by given nonlinear transformations and additive observation noise. The proposed method is able to correct for the distortion, and yields adjusted datasets from which the relevant biological effects can be recovered, as shown by a standard differential analysis. The second case study concerns the aggregation of two real prostate cancer datasets. After adjustment using the proposed algorithm, a differential analysis performed on adjusted datasets yields a larger number of differentially expressed genes (between control and tumor data). The proposed method has been implemented using the statistical software R 1, and Bioconductor packages 2. The source code (valid for merging two datasets), as well as the datasets used for the validation, and some complementary results, are made available on the web site

stat.ME↗

arXiv2015

Analyse discriminante matricielle descriptive. Application a l'étude de signaux EEG

We focus on the descriptive approach to linear discriminant analysis for matrix-variate data in the binary case. Under a separability assumption on row and column variability, the most discriminant linear combinations of rows and columns are determined by the singular value decomposition of the difference of the class-averages with the Mahalanobis metric in the row and column spaces. This approach provides data representations of data in two-dimensional or three-dimensional plots and singles out discriminant components. An application to electroencephalographic multi-sensor signals illustrates the relevance of the method.

stat.AP↗

arXiv2013

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples.

math.NA↗

arXiv2013

Estimation of frequency modulations on wideband signals; applications to audio signal analysis

The problem of joint estimation of power spectrum and modulation from realizations of frequency modulated stationary wideband signals is considered. The study is motivated by some specific signal classes from which departures to stationarity can carry relevant information and has to be estimated. The estimation procedure is based upon explicit modeling of the signal as a wideband stationary Gaussian signal, transformed by time-dependent, smooth frequency modulation. Under such assumptions, an approximate expression for the second order statistics of the transformed signal's Gabor transform is obtained, which leads to an approximate maximum likelihood estimation procedure. The proposed approach is validated on numerical simulations.

math.ST↗

arXiv2013

A hybrid scheme for encoding audio signal using hidden Markov models of waveforms

This paper reports on recent results related to audiophonic signals encoding using time-scale and time-frequency transform. More precisely, non-linear, structured approximations for tonal and transient components using local cosine and wavelet bases will be described, yielding expansions of audio signals in the form tonal + transient + residual. We describe a general formulation involving hidden Markov models, together with corresponding rate estimates. Estimators for the balance transient/tonal are also discussed.

math.ST↗

arXiv2013

Determining Local Transientness of Audio Signals

We describe a new method for estimating the degree of "transientness" and "tonality" of a class of compound signals involving simultaneously transient and harmonic features. The key assumption is that both transient and tonal layers admit sparse expansions, respectively in wavelet and local cosine bases. The estimation is performed using particular form of entropy (or theoretical dimension) functions. We provide theoretical estimates on the behavior of the proposed estimators, as well as numerical simulations. Audio signal coding provides a natural field of application.

math.ST↗

arXiv2012

Refined support and entropic uncertainty inequalities

Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing a generalization of the coherence. In the finite dimensional case and under certain conditions, minimizers of this inequalities are given as constant functions on their support. In addition, $\ell^p$-norms inequalities are introduced as byproducts of the entropic inequalities.

cs.IT↗