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Blind Source Separation in Nonlinear Mixtures


Directeur de thèse :     Christian JUTTEN

Co-encadrant :     Bertrand RIVET

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Signal, image, parole, télécoms

Structure de rattachement : UJF

Établissement d'origine : Sharif University of Technology

Financement(s) : Erc


Date d'entrée en thèse : 01/11/2014

Date de soutenance : 30/04/2018


Composition du jury :
M. Farrokh Marvasti, Professeur, Universiteì de Technologie de Sharif
M. Yannick Deville, Professeur, Universiteì Paul Sabatier Toulouse 3
M. Reza Sameni, HDR, Universiteì de Shiraz
M. Mohammad Bagher Shamsollahi, Professeur, Universiteì de Technologie de Sharif
M. Hamid Soltanian-Zadeh, Professeur, Universiteì de Teìheìran


Résumé : In this study, nonlinear BSS problem is tackled using a novel approach utilizing temporal information of the signals. The original idea followed in this purpose is to study a linear time-varying source separation problem deduced from the initial nonlinear problem by derivations. It is shown that already-proposed counter-examples showing inefficiency of Independent Component Analysis (ICA) for nonlinear mixtures, loose their validity, considering independence in the sense of stochastic processes instead of simple random variables. Based on this approach, both nice theoretical results and algorithmic developments are provided. Even though these achievements are not claimed to be a mathematical proof for the separability of nonlinear mixtures, it is shown that given a few assumptions, which are satisfied in most practical applications, they are separable. Moreover, nonlinear BSS for two useful sets of source signals is also addressed: (1) spatially sparse sources and (2) Gaussian processes. Distinct BSS methods are proposed for these two cases, each of which has been widely studied in the literature and has been shown to be quite beneficial in modeling many practical applications.

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