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Equivariant Adaptive Source Separation
 IEEE Trans. on Signal Processing
, 1996
"... Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Eq ..."
Abstract

Cited by 385 (10 self)
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Source separation consists in recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation which implements an adaptive version of equivariant estimation and is henceforth called EASI (Equivariant Adaptive Separation via Independence) . The EASI algorithms are based on the idea of serial updating: this specific form of matrix updates systematically yields algorithms with a simple, parallelizable structure, for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions and interference rejection levels depend only on the (normalized) distributions of the source signals. Close form expressions of these quantities are given via an asymptotic performance analysis. This is completed by some numerical experiments illustrating the effectiveness of the proposed ap...
On the Performance of Orthogonal Source Separation Algorithms
, 1994
"... . Source separation consists in recovering a set of n independent signals from m n observed instantaneous mixtures of these signals, possibly corrupted by additive noise. Many source separation algorithms use second order information in a whitening operation which reduces the non trivial part of th ..."
Abstract

Cited by 46 (4 self)
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. Source separation consists in recovering a set of n independent signals from m n observed instantaneous mixtures of these signals, possibly corrupted by additive noise. Many source separation algorithms use second order information in a whitening operation which reduces the non trivial part of the separation to determining a unitary matrix. Most of them further show a kind of invariance property which can be exploited to predict some general results about their performance. Our first contribution is to exhibit a lower bound to the performance in terms of accuracy of the separation. This bound is independent of the algorithm and, in the i.i.d. case, of the distribution of the source signals. Second, we show that the performance of invariant algorithms depends on the mixing matrix and on the noise level in a specific way. A consequence is that at low noise levels, the performance does not depend on the mixture but only on the distribution of the sources, via a function which is charac...
Properties Of The Empirical Characteristic Function And Its Application To Testing For Independence
 Proceedings of 3rd International Conference on Independent Component Analysis and Signal Separation
, 2001
"... In this article, the asymptotic properties of the empirical characteristic function are discussed. The residual of the joint and marginal empirical characteristic functions is studied and the uniform convergence of the residual in the wider sense and the weak convergence of the scaled residual to a ..."
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Cited by 8 (0 self)
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In this article, the asymptotic properties of the empirical characteristic function are discussed. The residual of the joint and marginal empirical characteristic functions is studied and the uniform convergence of the residual in the wider sense and the weak convergence of the scaled residual to a Gaussian process are investigated. Taking into account of the result, a statistical test for independence against alternatives is considered.
Date of Defense: 22/10/2013 Jury:
, 2013
"... The French “HDR ” diploma (Habilitation à Diriger des Recherches) is necessary to be the principal supervisor of PhD theses in French Universities. The candidate must write a dissertation that is defended in front of an international Jury. Typically, a collection of published articles with accessory ..."
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The French “HDR ” diploma (Habilitation à Diriger des Recherches) is necessary to be the principal supervisor of PhD theses in French Universities. The candidate must write a dissertation that is defended in front of an international Jury. Typically, a collection of published articles with accessory information may suffice as content of the manuscript. For my HDR I decided to write from scratch a coherent manuscript with a considerable amount of unpublished content. Since my contributions in scientific journals as first author concern mainly methodological works (see chapter I), I decided to compile a manuscript reminding the structure of a small handbook of advanced methods for EEG data analysis. As a matter of fact all methods presented in this manuscript may be understood as a way to study the latent variables hidden in EEG recordings, what we name here generically source analysis, concept that will be precised as the reading progresses. Such a work is meant to be expanded and enriched in the future. It is addressed to students and peers approaching the field of quantitative EEG
Author manuscript, published in "N/P" DOI: 10.1016/j.clinph.2008.09.007 On the Blind Source Separation of Human Electroencephalogram by Approximate Joint Diagonalization of Second Order Statistics
"... helpful comments and suggestions about this paper. BSS of Human EEG by SOS AJD – Congedo et al. 2008 Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimatin ..."
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helpful comments and suggestions about this paper. BSS of Human EEG by SOS AJD – Congedo et al. 2008 Over the last ten years blind source separation (BSS) has become a prominent processing tool in the study of human electroencephalography (EEG). Without relying on head modeling BSS aims at estimating both the waveform and the scalp spatial pattern of the intracranial dipolar current responsible of the observed EEG. In this review we begin by placing the BSS linear instantaneous model of EEG within the framework of brain volume conduction theory. We then review the concept and current practice of BSS based on secondorder statistics (SOS) and on higherorder statistics (HOS), the latter better known as independent component analysis (ICA). Using neurophysiological