Papers by Bruno Torresani
HAL (Le Centre pour la Communication Scientifique Directe), Apr 8, 2002
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright
arXiv (Cornell University), Feb 7, 2020
We develop a timescale synthesis-based probabilistic approach for the modeling of locally station... more 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 timevarying 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.
HAL (Le Centre pour la Communication Scientifique Directe), 1992
L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les ... more L'accès aux archives de la revue « Annales de l'I. H. P., section A » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ 215 Time-frequency representations: wavelet packets and optimal decomposition B. TORRESANI
HAL (Le Centre pour la Communication Scientifique Directe), Jun 23, 2023
This paper introduces a couple of new time-frequency transforms, designed to adapt their scale to... more 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.
Applied and Computational Harmonic Analysis, Apr 1, 1996
We consider implementation of operators via lter banks in the framework of the Multiresolution An... more We consider implementation of operators via lter banks in the framework of the Multiresolution Analysis. Our method is particularly e cient for convolution operators. Although our method of applying operators to functions may be used with any wavelet basis with a su cient number of vanishing moments, we distinguish two particular settings, namely, orthogonal bases, and the autocorrelation shell. We apply our method to evaluate the Hilbert transform of signals and derive a fast algorithm capable of achieving any given accuracy. We consider the case where the wavelet is the autocorrelation function of another wavelet associated with an orthonormal basis and where our method provides a fast algorithm for the computation of the modulus and the phase of signals. Moreover, the resulting wavelet may be viewed as being (approximately, but with any given accuracy) in the Hardy space H 2 (IR).
arXiv (Cornell University), Oct 31, 2013
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a ... more 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.
HAL (Le Centre pour la Communication Scientifique Directe), 1994
Nous décrivons une nouvelle méthode permettant de réaliser des opérateurs en termes de bancs de f... more Nous décrivons une nouvelle méthode permettant de réaliser des opérateurs en termes de bancs de filtres. Nous nous concentrerons plus particulièrement sur la transformée de Hilbert, pour laquelle des filtres approchés (mais aussi précis que l'on veut) peuventêtre construits, produisant des ondelettes "presque progressives". Nous montrerons aussi comment la méthode permet d'obtenir des représentations de signaux par superposition de composantes modulées en amplitude et fréquence.
Uncertainty principles go back to the early years of quantum mechanics. Originally introduced to ... more Uncertainty principles go back to the early years of quantum mechanics. Originally introduced to describe the impossibility for a function to be sharply localized in both the direct and Fourier spaces, localization being measured by variance, it has been generalized to many other situations, including different representation spaces and different localization measures. In this talk we first review classical results on variance uncertainty inequalities (in particular Heisenberg, Robertson and Breitenberger inequalities). We then focus on discrete (and in particular finite-dimensional) situations, where variance has to be replaced with more suitable localization measures. We then present recent results on support and entropic inequalities, describing joint localization properties of vector expansions with respect to two frames. Keywords: uncertainty principle - variance of a function - Heisenberg inequality - support inequalities - entropic inequalities
We study a class of (possibly infinite-dimensional) Lie algebras, called the Quasisimple Lie alge... more We study a class of (possibly infinite-dimensional) Lie algebras, called the Quasisimple Lie algebras (QSLA's), and generalizing semisimple and affine Kac-Moody Lie algebras. They are characterized by the existence of a finite-dimensional Cartan subalgebra, a non-degenerate symmetric ad-invariant Killing form, and nilpotent rootspaces attached to non-isotropic roots. We are then able to derive a classification theorem for the possible quasisimple root systems; moreover, we construct explicit realizations of some of them as current algebras, generalizing the affine loop algebras.
HAL (Le Centre pour la Communication Scientifique Directe), 2014
International audienc
IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005
Current multimedia technologies call for e cient ways of rep resenting signals. We review several... more Current multimedia technologies call for e cient ways of rep resenting signals. We review several e cient methods for signal represen tation, emphasizing potential applications in signal compression and denois ing. We pay special attention to the representations which are adapted to non-stationary features of signals, in particular the classes of bilinear rep resentations, and their approximations using time-frequency atoms (mainly wavelet transforms and Gabor transforms).
HAL (Le Centre pour la Communication Scientifique Directe), 2012
HAL (Le Centre pour la Communication Scientifique Directe), Jun 22, 2022
-Nous abordons le problème du filtrage des composantes temps-fréquence localisées dans les signau... more -Nous abordons le problème du filtrage des composantes temps-fréquence localisées dans les signaux. Nous le formulons comme un problème de minimisation d'une forme quadratique appropriée, qui implique un terme d'attache aux données sur la transformée de Fourier à court terme en dehors du support de la composante indésirable et un terme de pénalisation de l'énergie à l'intérieur du support. Nous étudions deux méthodes de résolution : une méthode spectrale et une méthode de type quasi-Newton (BFGS). Ces dernières font intervenir des opérateurs appelés multiplicateurs de Gabor. Nous exploitons les techniques de projections aléatoires pour approcher ces opérateurs. Nous étudions et comparons la complexité théorique d'un BFGS classique à un BFGS combiné aux projections aléatoires. Nous comparons le temps de calcul de ces deux méthodes sur plusieurs signaux audio. Nous comparons également leur temps de calcul à celui de la méthode spectrale. Les performances de toutes ces approches sont évaluées et comparées sur plusieurs signaux audio.
HAL (Le Centre pour la Communication Scientifique Directe), 2023
arXiv (Cornell University), Oct 27, 2015
The aggregation of microarray datasets originating from different studies is still a difficult op... more 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 aggregated 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 www.latp.univ-mrs.fr/∼mcroubau/MicroarrayMerging
Nous décrivons une nouvelle approche pour l'analyse de données issues du transcriptome, basée sur... more Nous décrivons une nouvelle approche pour l'analyse de données issues du transcriptome, basée sur les techniques de séparation de sources en aveugle. Cette approche fournit en sortie des "profils d'expression élémentaires", ou "sources", éventuellement interprétables comme de possibles voies de régulation. Une analyse plus fine des sources ainsi obtenues montre qu'elles sont généralement caractérisées par une sur-expression (resp. sous-expression) significative d'un petit nombre de gènes, parfois accompagnée d'une sous-expression (resp. surexpression) d'une famille complémentaire de gènes. Les résultats obtenus sur deux jeux de données d'expression montrent que certaines des familles ainsi détectées correspondent à des familles connues de gènes co-régulés, ce qui valide l'approche.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 9, 2002
Nous décrivons une nouvelle approche pour l'analyse de données issues du transcriptome, basée sur... more Nous décrivons une nouvelle approche pour l'analyse de données issues du transcriptome, basée sur les techniques de séparation de sources en aveugle. Cette approche fournit en sortie des "profils d'expression élémentaires", ou "sources", éventuellement interprétables comme de possibles voies de régulation. Une analyse plus fine des sources ainsi obtenues montre qu'elles sont généralement caractérisées par une sur-expression (resp. sous-expression) significative d'un petit nombre de gènes, parfois accompagnée d'une sous-expression (resp. surexpression) d'une famille complémentaire de gènes. Les résultats obtenus sur deux jeux de données d'expression montrent que certaines des familles ainsi détectées correspondent à des familles connues de gènes co-régulés, ce qui valide l'approche.
HAL (Le Centre pour la Communication Scientifique Directe), 1992
We describe some geometric aspects of wavelet systems leading to time-frequency representations o... more We describe some geometric aspects of wavelet systems leading to time-frequency representations of signals. These aspects are illustrated by the use of wavelets for local frequencies characterization in signals.
Applied and Computational Harmonic Analysis, Jul 1, 2023
This paper deals with the modeling of non-stationary signals, from the point of view of signal sy... more 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.
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Papers by Bruno Torresani