A survey of uncertainty principles and some signal processing applications

The goal of this paper is to review the main trends in the domain of uncertainty principles and localization, emphasize their mutual connections and investigate practical consequences. The discussion is strongly oriented towards, and motivated by signal processing problems, from which significant advances have been made recently. Relations with sparse approximation and coding problems are emphasized

Pyramidal Algorithms for Littlewood-Paley Decompositions

International audienceIt is well known that with any usual multiresolution analysis of L 2 (IR) is associated a pyramidal algorithm for the computation of the corresponding wavelet coefficients. It is shown that an approximate pyramidal algorithm may be associated with more general Littlewood-Paley decompositions. Accuracy estimates are provided for such approximate algorithms. Finally, some explicit examples are studie

Wavelets and Binary Coalescences Detection

International audienceGravitational waves generated by coalescing binary systems of neutron stars or black holes are expected to behave like chirps, i.e. amplitude and frequency modulated signals, buried into strongly correlated noise, with very low signal to noise ratio. This note presents a wavelet based algorithm for on line processing and detection of such signals, from interferometric detectors which are currently being constructed , and discusses a few examples. The details of the method and more complete simulations can be found in [6]. The detection of gravitational waves, predicted by general relativity but never observed so far, is a major challenge in today's experimental physics. Several projects are currently being developed, among which one may quote the LIGO [1], GEO [4] and VIRGO [2] laser in-terferometric detectors. Among the potential sources for gravitational waves, the most promising are presumably pulsars, and coalesc-ing binary systems of black holes or neutron stars. Such systems are expected to produce " simple " signals, for which available models are considered reliable. We focus here on the case of coalescing binary systems. The corresponding gravitational waves take the form of chirps, i.e. amplitude and frequency modulated signals. The detection problem may be formulated as follows. The signal takes the form f (x) = h θ (x − x 0) + n(x) (1

Multi-Ridge Detection and Time-Frequency Reconstruction

International audienceThe ridges of the wavelet transform, the Gabor transform or any time-frequency representation of a signal contain crucial information on the characteristics of the signal. Indeed they mark the regions of the time-frequency plane where the signal concentrates most of its energy. We introduce a new algorithm to detect and identify these ridges.The procedure is based on an original form of Markov Chain Monte Carlo algorithm specially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multi-ridge transforms. It is a common practice among practitioners to reconstruct a signal from the skeleton of a transform of the signal (i.e. the restriction of the transform to the ridges). After reviewing several known procedures we introduce a new reconstruction algorithm and we illustrate its efficiency on speech signals

Characterization of signals by the ridges of their wavelet transforms

International audienceWe present a couple of new algorithmic procedures for the detection of ridges in the modulus of the (continuous) wavelet transform of one-dimensional signals. These detection procedures are shown to be robust to additive white noise. We also derive and test a new reconstruction procedure. The latter uses only information from the restriction of the wavelet transform to a sample of points from the ridge. This provides with a very efficient way to code the information contained in the signal

Optimal Window and Lattice in Gabor Transform Application to Audio Analysis

This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation technique for non-stationary signals. We illustrate our approach and the earlier one by addressing three time-frequency analysis problems to show the improvements achieved by the use of optimal lattice and window: close frequencies distinction, frequency estimation and SNR estimation. The results are presented, when possible, with real world audio signals

FINDING EEG SPACE-TIME-SCALE LOCALIZED FEATURES USING MATRIX-BASED PENALIZED DISCRIMINANT ANALYSIS

International audienceThis paper proposes a new method for constructing and selecting of discriminant space-time-scale features for electroencephalogram (EEG) signal classification, suitable for Error Related Potentials (ErrP)detection in brain-computer interface (BCI). The method rests on a new variant of matrix-variate Linear Discriminant Analysis (LDA), and differs from previously proposed approaches in mainly three ways. First, a discrete wavelet expansion is introduced for mapping time-courses to time-scale coefficients, yielding time-scale localized features. Second, the matrix-variate LDA is modified in such a way that it yields an interesting duality property, that makes interpretation easier. Third, a space penalization is introduced using a surface Laplacian, so as to enforce spatial smoothness. The proposed approaches, termed D-MLDA and D-MPDA are tested on EEG signals, with the goal of detecting ErrP. Numerical results show that D-MPDA outperforms D-MLDA and other matrix-variate LDA techniques. In addition this method produces relevant features for interpretation in ErrP signals

Identification de signaux parcimonieux dans un dictionnaire hybride

Nous proposons et étudions une nouvelle famille d'algorithmes de décomposition de signaux sur des systèmes hybrides (par exemple, une unions de bases), basés sur une modélisation probabiliste. La modélisation repose sur deux ingrédients : un modèle pour les coefficients de la décomposition, et un modèle de carte de signifiance, décrivant les positions des coefficients significatifs dans l'espace des indices. Deux types de modélisation des cartes de signifiance sont proposées. La première, suivant un modèle de Bernoulli et appelée non structurée, ne privilégie aucune relation de dépendance entre coefficients significatifs. La seconde, qui repose sur un modèle de Bernoulli-hiérarchique, favorise certaines structures dans le domaine des indices. Les algorithmes sont comparés et illustrés par des applications de débruitage