FAVIER , Gérard

International audience

Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields.This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental...

System identification consists in building mathematical models of dynamical systems from experimental data. Such a methodology was mainly developed for designing model-based control systems. More generally, parameter estimation is at the heart of many signal processing applications aiming to extract information from signals, like radar, sonar,...

À l'ère du Big Data, le traitement de l'information numérique occupe une place centrale dans de nombreux domaines applicatifs. Dans ce contexte, les tenseurs sont aujourd'hui de plus en plus utilisés pour la représentation, la compression, l'analyse, la classification et la fusion de données massives, multidimensionnelles et...

International audience

International audience

Au cours de la dernière décennie, les modèles tensoriels du type CP, appelés aussi décompositions PARAFAC, ont fait l'objet de très nombreuses applications en traitement du signal et de l'image. Depuis les travaux de pionnier de Sidiropoulos, Giannakis et Bro, en 2000 [1], les communications numériques constituent un domaine d'application...

International audience

International audience

In this study, we show that the minimum mean square estimate (MMSE) of the parameters of a fifth-order Volterra model can be obtained in closed-form when the input is independent and identically distributed (i.i.d). The derived closed-form expressions of the kernel coefficients can be used for identifying Volterra systems with arbitrary memory....

Recently, tensor signal processing has received an increased attention, particularly in the context of wireless communication applications. The so-called PARAllel FACtor (PARAFAC) decomposition is certainly the most used tensor tool. In general, the parameter estimation of a PARAFAC decomposition is carried out by means of the iterative ALS...

National audience

International audience

In this paper, we propose a new tensor-based approach to identify the structure of a block-oriented nonlinear system (Hammerstein, Wiener, and Wiener-Hammerstein systems). The proposed method makes use of one time-domain Volterra kernel of an arbitrary order higher than two, which can be viewed as a tensor. We develop a tensor analysis for...

Multilinear analysis provides a powerful mathematical framework for analyzing synthetic aperture radar (SAR) images resulting from the interaction of multiple factors like sky luminosity and viewing angles, while preserving their original shape. In this paper, we propose a multilinear principal component analysis (MPCA) algorithm for target...

Baseband Volterra models are very useful for representing nonlinear communication channels. These models present the specificity to include only odd-order nonlinear terms, with kernels characterized by a double symmetry. The main drawback is their parametric complexity. In this paper, we develop a new class of Volterra models, called baseband...

International audience

International audience

In this paper, we consider the problem of identification of nonlinear communication channels using input-output measurements. The nonlinear channel is structured as a LTI-ZMNL-LTI one, i.e. a zero-memory nonlinearity (ZMNL) sandwiched between two linear time-invariant (LTI) subchannels. Considering Volterra kernels of order higher than two as...

Multilinear analysis provides a powerful mathematical framework for analyzing synthetic aperture radar (SAR) images resulting from the interaction of multiple factors like sky luminosity and viewing angles, while preserving their original shape. In this paper, we propose a multilinear principal component analysis (MPCA) algorithm for target...

In this letter, we present an algorithm for computing the factors of a matrix bilinear decomposition when the factors are constrained to have a Toeplitz and a Vandermonde structure. The proposed algorithm is constituted by a set of recurrence relations derived when the matrix to be decomposed has at least three columns. This algorithm is then...

National audience

International audience

This letter is concerned with the parameter estimation of linear and nonlinear subsystems of parallel-cascade Wiener systems (PCWS). We first present the relationship between a PCWS and its associated Volterra model. We show that the coefficients of the linear subsystems can be obtained using a joint diagonalization of the third-order Volterra...