Contrast properties of entropic criteria for blind source separation

A unifying framework based on information-theoretic inequalities
Première édition

In the recent years, Independent Component Analysis has become a fundamental tool in signal and data processing, especially in the field of Blind Source Separation (BSS); under mild conditions, independent source signals can be recovered from mixtures of them by maximizing a so-called contrast function. Neither the mixing system nor the original sources are needed for that purpose, justifying the "blind" term. Among the existing BSS methods is the class of approaches maximizing Information-Theoretic Criteria (ITC), that rely on Rényi's entropies, including the well-known Shannon and Hartley entropies. These ITC are maximized via adaptive optimization schemes. Two major issues in this field are the following: i) Are ITC really contrast functions? and ii) As most of the algorithms look in fact for a local maximum point, what about the relevance of these local optima from the BSS point of view? Even though there are some partial answers to these questions in the literature, most of them are based on simulations and conjectures; formal developments are often lacking. This thesis aims at filling this lack as well as providing intuitive justifications, too. The BSS problem is stated in Chapter 1, and viewed under the information theory angle. The two next chapters address specifically the above questions: Chapter 2 discusses the contrast function property of ITC while the possible existence of spurious local maximum points in ITC is the purpose of Chapter 3. Finally, Chapter 4 deals with a range-based criterion, the only “entropy-based” contrast function which is discriminant, i.e. free from spurious local maxima. The interest of this approach is confirmed by testing the proposed technique on various examples, including the MLSP 2006 data analysis competition benchmark; our method outperforms the previously obtained results on large-scale and noisy mixture samples obtained through ill-conditioned mixing matrices.


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Spécifications


Éditeur
Presses universitaires de Louvain
Partie du titre
Numéro 138
Auteur
Frédéric Vrins,
Collection
Thèses de l'École polytechnique de Louvain
Langue
anglais
Catégorie (éditeur)
Sciences appliquées
BISAC Subject Heading
TEC000000 TECHNOLOGY & ENGINEERING
Code publique Onix
06 Professionnel et académique
CLIL (Version 2013-2019 )
3069 TECHNIQUES ET SCIENCES APPLIQUEES
Date de première publication du titre
01 janvier 2007
Type d'ouvrage
Thèse
Langue originale
anglais

Livre broché


Date de publication
01 janvier 1999
ISBN-13
9782870160534
Ampleur
Nombre de pages de contenu principal : 135
Code interne
9782870160534
Poids
3040 grammes
Prix
55,00 €
ONIX XML
Version 2.1, Version 3

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Sommaire


Sommaire des tomes 1. Introduction. Législation (belge et européenne). Application pratique des étapes du système HACCP : Généralités - Description des produits - Diagramme de fabrication - Bonnes pratiques d'hygiène Analyses des dangers, Mesures préventives - Identification des CCP - Etablissement des limites critiques - Systèmes de surveillance et enregistrements de ces surveillances - Plan d'actions correctives et responsabilités Systèmes de documentions et d'enregistrements - Vérification du système HACCP Renseignements utiles généraux.