Blind separation of sources : Methods, assumptions and applications

The blind separation of sources is a recent and important problem in signal processing. Since 1984 \cite{herault-cr-84}, it has been studied by many authors whilst many algorithms have been proposed. In this paper, the description of the problem, its assumptions, its currently applications and some algorithms and ideas are discussed. keywords: independent component analysis (ICA), contrast function, Kullback-Leibner divergence, prediction error, sub-space methods, decorrelation, high order statistics, whitening, Mutual-Information, likelihood maximization, conjoint diagonalization.

[1]  Ehud Weinstein,et al.  New criteria for blind deconvolution of nonminimum phase systems (channels) , 1990, IEEE Trans. Inf. Theory.

[2]  L. Scharf,et al.  Statistical Signal Processing: Detection, Estimation, and Time Series Analysis , 1991 .

[3]  Philippe Loubaton,et al.  Subspace based techniques for second order blind separation of convolutive mixtures with temporally correlated sources , 1997 .

[4]  Allan Kardec Barros,et al.  Blind Separation for Convolutive Mixtures of Non-stationary Signals , 1998, ICONIP.

[5]  Véronique Capdevielle,et al.  Séparation de sources large bande à l'aide des moments d'ordre supérieur , 1995 .

[6]  Dirk Van Compernolle,et al.  Signal separation by symmetric adaptive decorrelation: stability, convergence, and uniqueness , 1995, IEEE Trans. Signal Process..

[7]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[8]  Charkani El Hassani,et al.  Séparation auto-adaptative de sources pour des mélanges convolutifs : application à la téléphonie mains-libres dans les voitures , 1996 .

[9]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[10]  B. Noble.  Applied Linear Algebra , 1969 .

[11]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[12]  A. Mansour,et al.  Subspace adaptive algorithm for blind separation of convolutive mixtures by conjugate gradient method , 1998 .

[13]  Kiyotoshi Matsuoka,et al.  A neural net for blind separation of nonstationary signals , 1995, Neural Networks.

[14]  Nathalie Delfosse,et al.  Adaptive blind separation of convolutive mixtures , 1996, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[15]  Comon.  5 - Analyse en composantes indépendantes et identification aveugle , 1990 .

[16]  Andreas G. Andreou,et al.  Current-mode subthreshold MOS implementation of the Herault-Jutten autoadaptive network , 1992 .

[17]  Nadege Thirion.  Séparation d'ondes en prospection sismique , 1995 .

[18]  Juha Karhunen,et al.  Generalizations of principal component analysis, optimization problems, and neural networks , 1995, Neural Networks.

[19]  Philippe Loubaton,et al.  Adaptive subspace algorithm for blind separation of independent sources in convolutive mixture , 2000, IEEE Trans. Signal Process..

[20]  A. Belouchrani,et al.  Séparation aveugle au second ordre de sources corrélées , 1993 .

[21]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[22]  Yves Deville,et al.  Application of blind source separation techniques to multi-tag contactless identification systems , 1995 .

[23]  Eric Moulines,et al.  Subspace methods for the blind identification of multichannel FIR filters , 1995, IEEE Trans. Signal Process..

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[25]  S.C. Douglas,et al.  Multichannel blind deconvolution and equalization using the natural gradient , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[26]  B. Ans,et al.  Simulation de réseaux neuronaux (SIRENE). II: Hypothése de décodage du message de mouvement porté par les afférences fusoriales IA et II par un mécanisme de plasticité synaptique , 1983 .

[27]  Noboru Ohnishi,et al.  Multichannel blind separation of sources algorithm based on cross-cumulant and the Levenberg-Marquardt method , 1999, IEEE Trans. Signal Process..

[28]  Philippe Loubaton,et al.  A subspace algorithm for certain blind identification problems , 1997, IEEE Trans. Inf. Theory.

[29]  Alberto Prieto,et al.  A Geometrical Based Procedure for Source Separation Mapped to a Neural Network , 1995, IWANN.

[30]  Pierre Priouret,et al.  Adaptive Algorithms and Stochastic Approximations , 1990, Applications of Mathematics.

[31]  Reinhold Orglmeister,et al.  Blind source separation of real world signals , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[32]  Ali Mansour,et al.  A simple cost function for instantaneous and convolutive sources separation , 1995 .

[33]  L. Lathauwer,et al.  Blind source separation by higher-order singular value decomposition , 1994 .

[34]  J. Lacoume,et al.  Statistiques d'ordre supérieur pour le traitement du signal , 1997 .

[35]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[36]  Yannick Deville,et al.  A unified stability analysis of the Hérault-Jutten source separation neural network , 1996, Signal Process..

[37]  Eric A. Vittoz,et al.  CMOS Integration of Herault-Jutten Cells for Separation of Sources , 1989, Analog VLSI Implementation of Neural Systems.

[38]  Pierre-Olivier Amblard,et al.  Adaptive estimation of the fourth-order cumulant of a white stochastic process , 1995, Signal Process..

[39]  Joos Vandewalle,et al.  Blind source separation by simultaneous third-order tensor diagonalization , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[40]  Allan Kardec Barros,et al.  independent , 2006, Gumbo Ya Ya.

[41]  Yannick Deville,et al.  Analysis of the stability of time-domain source separation algorithms for convolutively mixed signals , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[42]  Beate H. Laheld,et al.  Séparation adaptative de sources en aveugle. Implantation complexe sans contraintes , 1993 .

[43]  Te-Won Lee,et al.  Blind Separation of Delayed and Convolved Sources , 1996, NIPS.

[44]  J. Hérault,et al.  Réseau de neurones à synapses modifiables: décodage de messages sensoriels composites par apprentissage non supervisé et permanent , 1984 .

[45]  Pierre Comon,et al.  Séparation de mélanges de signaux , 1989 .

[46]  Christian Jutten,et al.  What should we say about the kurtosis? , 1999, IEEE Signal Processing Letters.

[47]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[48]  M. Gaeta,et al.  4 - Estimateurs du maximum de vraisemblance étendus à la séparation de sources non gaussiennes , 1990 .

[49]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[50]  J. Cardoso,et al.  COMPARAISONS DE METHODES DE SEPARATION DE SOURCES , 1991 .

[51]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[52]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[53]  Masahiro Oya,et al.  Blind Separation of Sources Using Temporal Correlation of the Observed Signals , 1997 .

[54]  Pierre Comon,et al.  Application of ICA to airport surveillance , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.

[55]  E. Moreau.  Apprentissage et adaptativite. Separation auto-adaptative de sources independantes , 1995 .

[56]  Christian Jutten,et al.  Fourth-order criteria for blind sources separation , 1995, IEEE Trans. Signal Process..

[57]  Blind source separation and multichannel deconvolution , 1999 .

[58]  Gérard Favier,et al.  Recursive estimation of fourth-order cumulants with application to identification , 1998, Signal Process..

[59]  Shun-ichi Amari,et al.  Neural Learning in Structured Parameter Spaces - Natural Riemannian Gradient , 1996, NIPS.

[60]  P. McCullagh.  Tensor Methods in Statistics , 1987 .

[61]  Lang Tong,et al.  A new approach to blind identification and equalization of multipath channels , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[62]  D. Pham.  Séparation aveugle de sources via une analyse en composantes indépendantes , 1995 .

[63]  Nathalie Delfosse,et al.  Séparation adaptative de sources indépendantes par une approche de déflation , 1993 .

[64]  Jean-Louis Lacoume,et al.  Statistiques d'ordres supérieurs pour le traitement du signal , 1997 .

[65]  M. Krob,et al.  Fonction de contraste pour l'identification aveugle d'un modele lineaire quadratique , 1993 .

[66]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

[67]  Lagunas Hernandez,et al.  A general adaptive algorithm for nonGaussian source separation without any constraint , 1994 .

[68]  Nathalie Delfosse,et al.  Adaptive blind separation of independent sources: A deflation approach , 1995, Signal Process..

[69]  Jean-Francois Cardoso,et al.  Source separation using higher order moments , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[70]  Allan Kardec Barros,et al.  Comparison among Three Estimators for High Order Statistics , 1998, ICONIP.

[71]  Henrik Sahlin,et al.  Source separation using second order statistics , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[72]  Eric Moreau,et al.  Separation auto-adaptative de sources sans blanchiment prealable , 1993 .

[73]  P. Garat.  Approche statistique pour la séparation aveugle de sources , 1994 .

[74]  Christian Jutten,et al.  A Geometrical algorithm for blind separation of sources , 1995 .

[75]  Christian Jutten,et al.  A direct solution for blind separation of sources , 1996, IEEE Trans. Signal Process..

[76]  John Carlin,et al.  Bootstrapping adaptive cross pol cancelers for satellite communications , 1982 .

[77]  Pierre Comon.  Quelques développements récents en traitement du signal , 1995 .

[78]  Ehud Weinstein,et al.  Criteria for multichannel signal separation , 1994, IEEE Trans. Signal Process..

[79]  Philippe Loubaton,et al.  Second order blind identification of convolutive mixtures with temporally correlated sources: A subspace based approach , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[80]  C. L. Nikias,et al.  Signal processing with higher-order spectra , 1993, IEEE Signal Processing Magazine.

[81]  Christian Jutten,et al.  Blind source separation for convolutive mixtures , 1995, Signal Process..

[82]  Dirk Van Compernolle,et al.  Feedforward and feedback in a symmetric adaptive noise canceler : “stability analysis in a simplified case” , 1992 .

[83]  Christian Jutten,et al.  Kurtosis: Definition and Properties , 1998 .

[84]  C. Jutten,et al.  Subspace method for blind separation of sources and for a convolutive mixture model , 1996 .

[85]  Christian Jutten,et al.  Independent components analysis versus principal components analysis , 1988 .

[86]  Pierre Comon,et al.  Blind separation of sources, part II: Problems statement , 1991, Signal Process..

[87]  Allan Kardec Barros,et al.  A fast algorithm for blind separation of sources based on the cross-cumulant and Levenberg-Marquardt method , 1998, ICSP '98. 1998 Fourth International Conference on Signal Processing (Cat. No.98TH8344).

[88]  C. Jutten,et al.  Robustesse des hypothèses dans une méthode sous-espace pour la séparation de sources , 1997 .

[89]  Adel Belouchrani,et al.  A new composite criterion for adaptive and iterative blind source separation , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[90]  C. Jutten.  Calcul neuromimétique et traitement du signal : analyse en composantes indépendantes , 1987 .

[91]  Eric Moreau,et al.  New self-adaptative algorithms for source separation based on contrast functions , 1993, [1993 Proceedings] IEEE Signal Processing Workshop on Higher-Order Statistics.

[92]  Pierre Comon,et al.  Separation Of Sources Using Higher-Order Cumulants , 1989, Optics & Photonics.

[93]  Jean-Francois Cardoso,et al.  Performances en séparation de sources , 1993 .

[94]  Jean-Louis Lacoume,et al.  Blind separation of wide-band sources: Application to rotating machine signals , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[95]  Ali Mansour,et al.  The blind separation of non-stationary signals by only using the second order statistics , 1999, ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359).

[96]  M. Gaeta.  Les statistiques d'ordre supérieur appliquées à la séparation de sources , 1991 .

[97]  Julio Ortega Lopera,et al.  Separation of sources: A geometry-based procedure for reconstruction of n-valued signals , 1995, Signal Process..

[98]  A. Mansour,et al.  Discussion of Simple Algorithms and Methods to Separate Non-stationary Signals. , 2000 .

[99]  Christian Jutten,et al.  Detection de grandeurs primitives dans un message composite par une architecture de calcul neuromime , 1985 .

[100]  Nathalie Delfosse,et al.  Séparation aveugle adaptative de mélanges convolutifs , 1995 .

[101]  Ali Mansour,et al.  Adaptive blind elimination of artifacts in ECG signals , 1998 .