Stochastic gradient adaptive algorithms for blind source separation

The aim in blind source separation is to separate linear mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. In this paper we propose a new family of adaptive algorithms that recursively compute the optimum separa...

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Vydáno v:	Signal processing Ročník 75; číslo 1; s. 11 - 27
Hlavní autoři:	Dapena, Adriana, Castedo, Luis
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 01.01.1999 Elsevier Science
Témata:	Adaptive algorithms Applied sciences Blind source separation Exact sciences and technology Higher-order statistics Information, signal and communications theory Signal and communications theory Signal, noise Telecommunications and information theory Adaptive algorithms Blind source separation Higher-order statistics Signal mixing Stability Separation Adaptive algorithm Gaussian noise Computer simulation Signal processing Cost function Image restoration Modeling Signal to noise ratio
ISSN:	0165-1684, 1872-7557
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Abstract	The aim in blind source separation is to separate linear mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. In this paper we propose a new family of adaptive algorithms that recursively compute the optimum separating system. The algorithms are of the gradient ascent type and maximize a statistical criterion that involves only second- and fourth-order cumulants. We present a complete analysis of all the stationary points in the proposed criterion for an arbitrary number of complex sources. We demonstrate that the algorithms can only converge to points where perfect separation is achieved provided that the mixing system is a square invertible matrix and all the sources have the same kurtosis sign. We also prove that the criterion is free of undesirable maxima. Das Ziel einer blinden Quellseparation ist es, lineare Überlagerungen stochastisch unabhängiger, nicht gaußverteilter Signale zu trennen, ohne daß auf a priori Kenntnisse über die Quellen oder über das Überlagerungssystem zurückgegriffen werden muß. In diesem Artikel schlagen wir eine neue Familie von adaptiven Algorithmen vor, die ein optimales Separationssystem rekursiv berechnen. Die Algorithmen sind vom Typ des Gradientenanstiegs und maximierem ein statistisches Kriterium, das ausschließlich Kumulanten zweiter und vierter Ordnung beinhaltet. Wir stellen eine vollständige Analyse aller stationären Punkte des vorgeschlagenen Kriteriums vor, wobei eine beliebige Anzahl komplexer Quellen vorliegen kann. Wir zeigen, daß die Algorithmen nur zu denjenigen Punkten konvergieren können, bei denen perfekte Separation vorliegt, vorausgesetzt, bei dem Überlagerungssystem handelt es sich um eine quadratinvertierbare Matrix und alle Quellen besitzen dasselbe Kurtosisvorzeichen. Wir zeigen ebenfalls, daß das Kriterium keine unerwünschten Maxima besitzt. Le but de la séparation de sources aveugle est de séparer des mélanges linéaires de signaux non gaussiens statistiquement indépendants sans se recourir à une connaissance a priori des sources ou du système de mélange. Dans cet article, nous proposons une nouvelle famille d'algorithmes adaptatifs qui calculent récursivement le système de séparation optimal. Les algorithmes sont du type “montée de gradient” et maximisent un critère statistique qui ne fait intervenir que des cumulants des second et quatrième ordres. Nous présentons une analyse complète de tous les points stationnaires du critère proposé, pour un nombre arbitraire de sources complexes. Nous démontrons que les algorithmes ne peuvent converger que vers des points où une séparation parfaite est atteinte, pourvu que le système de mélange ait une matrice carrée inversible et que toutes les sources aient le même signe du kurtoris. Nous prouvons aussi que ce critère ne présente pas de maxima indésirables.
AbstractList	The aim in blind source separation is to separate linear mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. In this paper we propose a new family of adaptive algorithms that recursively compute the optimum separating system. The algorithms are of the gradient ascent type and maximize a statistical criterion that involves only second- and fourth-order cumulants. We present a complete analysis of all the stationary points in the proposed criterion for an arbitrary number of complex sources. We demonstrate that the algorithms can only converge to points where perfect separation is achieved provided that the mixing system is a square invertible matrix and all the sources have the same kurtosis sign. We also prove that the criterion is free of undesirable maxima. The aim in blind source separation is to separate linear mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. In this paper we propose a new family of adaptive algorithms that recursively compute the optimum separating system. The algorithms are of the gradient ascent type and maximize a statistical criterion that involves only second- and fourth-order cumulants. We present a complete analysis of all the stationary points in the proposed criterion for an arbitrary number of complex sources. We demonstrate that the algorithms can only converge to points where perfect separation is achieved provided that the mixing system is a square invertible matrix and all the sources have the same kurtosis sign. We also prove that the criterion is free of undesirable maxima. Das Ziel einer blinden Quellseparation ist es, lineare Überlagerungen stochastisch unabhängiger, nicht gaußverteilter Signale zu trennen, ohne daß auf a priori Kenntnisse über die Quellen oder über das Überlagerungssystem zurückgegriffen werden muß. In diesem Artikel schlagen wir eine neue Familie von adaptiven Algorithmen vor, die ein optimales Separationssystem rekursiv berechnen. Die Algorithmen sind vom Typ des Gradientenanstiegs und maximierem ein statistisches Kriterium, das ausschließlich Kumulanten zweiter und vierter Ordnung beinhaltet. Wir stellen eine vollständige Analyse aller stationären Punkte des vorgeschlagenen Kriteriums vor, wobei eine beliebige Anzahl komplexer Quellen vorliegen kann. Wir zeigen, daß die Algorithmen nur zu denjenigen Punkten konvergieren können, bei denen perfekte Separation vorliegt, vorausgesetzt, bei dem Überlagerungssystem handelt es sich um eine quadratinvertierbare Matrix und alle Quellen besitzen dasselbe Kurtosisvorzeichen. Wir zeigen ebenfalls, daß das Kriterium keine unerwünschten Maxima besitzt. Le but de la séparation de sources aveugle est de séparer des mélanges linéaires de signaux non gaussiens statistiquement indépendants sans se recourir à une connaissance a priori des sources ou du système de mélange. Dans cet article, nous proposons une nouvelle famille d'algorithmes adaptatifs qui calculent récursivement le système de séparation optimal. Les algorithmes sont du type “montée de gradient” et maximisent un critère statistique qui ne fait intervenir que des cumulants des second et quatrième ordres. Nous présentons une analyse complète de tous les points stationnaires du critère proposé, pour un nombre arbitraire de sources complexes. Nous démontrons que les algorithmes ne peuvent converger que vers des points où une séparation parfaite est atteinte, pourvu que le système de mélange ait une matrice carrée inversible et que toutes les sources aient le même signe du kurtoris. Nous prouvons aussi que ce critère ne présente pas de maxima indésirables.
Author	Dapena, Adriana Castedo, Luis
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Keywords	Adaptive algorithms Blind source separation Higher-order statistics Signal mixing Stability Separation Adaptive algorithm Gaussian noise Computer simulation Signal processing Cost function Image restoration Modeling Signal to noise ratio
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SubjectTerms	Adaptive algorithms Applied sciences Blind source separation Exact sciences and technology Higher-order statistics Information, signal and communications theory Signal and communications theory Signal, noise Telecommunications and information theory
Title	Stochastic gradient adaptive algorithms for blind source separation
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