Blind signal separation: statistical principles

Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis that aim to recover unobserved signals or "sources" from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach, but it requires us to venture beyond familiar second order statistics, The objectives of this paper are to review some of the approaches that have been developed to address this problem, to illustrate how they stem from basic principles, and to show how they relate to each other.

[1]  A. Gardner Methods of Statistics , 1941 .

[2]  J. Pfanzagl Asymptotic Expansions Related to Minimum Contrast Estimators , 1973 .

[3]  A. Benveniste,et al.  Robust identification of a nonminimum phase system: Blind adjustment of a linear equalizer in data communications , 1980 .

[4]  Yeheskel Bar-ness,et al.  Bootstrapping adaptive interference cancelers - Some practical limitations , 1982 .

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

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

[7]  R. Liu,et al.  AMUSE: a new blind identification algorithm , 1990, IEEE International Symposium on Circuits and Systems.

[8]  William A. Gardner,et al.  Spectral self-coherence restoral: a new approach to blind adaptive signal extraction using antenna arrays , 1990, Proc. IEEE.

[9]  R. Liu,et al.  An extended fourth order blind identification algorithm in spatially correlated noise , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[10]  L. Tong,et al.  A necessary and sufficient condition for the blind identification of memoryless systems , 1991, 1991., IEEE International Sympoisum on Circuits and Systems.

[11]  Jean-Francois Cardoso,et al.  Super-symmetric decomposition of the fourth-order cumulant tensor. Blind identification of more sources than sensors , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

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

[13]  Thomas M. Cover,et al.  Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing) , 2006 .

[14]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[15]  P. Comon,et al.  ICA-based technique for radiating sources estimation: application to airport surveillance , 1993 .

[16]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .

[17]  Georgios B. Giannakis,et al.  Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors , 1993, Signal Process..

[18]  Lang Tong,et al.  Waveform-preserving blind estimation of multiple independent sources , 1993, IEEE Trans. Signal Process..

[19]  D. Pham,et al.  Séparation aveugle de sources temporellement corrélées , 1993 .

[20]  J. Cardoso On the Performance of Orthogonal Source Separation Algorithms , 1994 .

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

[22]  J. Nadal,et al.  Nonlinear neurons in the low-noise limit: a factorial code maximizes information transfer Network 5 , 1994 .

[23]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[24]  Andrzej Cichocki,et al.  Robust learning algorithm for blind separation of signals , 1994 .

[25]  Proceedings of the IEEE , 2018, IEEE Journal of Emerging and Selected Topics in Power Electronics.

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

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

[28]  L. Lathauwer,et al.  Fetal electrocardiogram extraction by source subspace separation , 1995 .

[29]  K. Anand,et al.  Blind separation of multiple co-channel BPSK signals arriving at an antenna array , 1995, IEEE Signal Processing Letters.

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

[31]  Tzyy-Ping Jung,et al.  Independent Component Analysis of Electroencephalographic Data , 1995, NIPS.

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

[33]  Gustavo Deco,et al.  An information theory based learning paradigm for linear feature extraction , 1996, Neurocomputing.

[34]  Eric Moreau,et al.  High order contrasts for self-adaptive source separation criteria for complex source separation , 1996 .

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

[36]  Terrence J. Sejnowski,et al.  Edges are the Independent Components of Natural Scenes , 1996, NIPS.

[37]  B. Moor,et al.  Independent component analysis based on higher-order statistics only , 1996, Proceedings of 8th Workshop on Statistical Signal and Array Processing.

[38]  Dinh-Tuan Pham,et al.  Blind separation of instantaneous mixture of sources via an independent component analysis , 1996, IEEE Trans. Signal Process..

[39]  Benjamin Friedlander,et al.  Performance analysis of blind signal copy using fourth order cumulants , 1996 .

[40]  Barak A. Pearlmutter,et al.  A Context-Sensitive Generalization of ICA , 1996 .

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

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

[43]  Ruey-Wen Liu,et al.  General approach to blind source separation , 1996, IEEE Trans. Signal Process..

[44]  Pierre Comon,et al.  Decomposition of quantics in sums of powers of linear forms , 1996, Signal Process..

[45]  B. Friedlander,et al.  Blind multi-channel system identification and deconvolution: performance bounds , 1996, Proceedings of 8th Workshop on Statistical Signal and Array Processing.

[46]  Carlos J. Escudero,et al.  An unconstrained single stage criterion for blind source separation , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[47]  J. Cardoso,et al.  On optimal source separation based on second and fourth order cumulants , 1996, Proceedings of 8th Workshop on Statistical Signal and Array Processing.

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

[49]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[50]  Erkki Oja,et al.  A class of neural networks for independent component analysis , 1997, IEEE Trans. Neural Networks.

[51]  Eric Moreau,et al.  Self-adaptive source separation .I. Convergence analysis of a direct linear network controlled by the Herault-Jutten algorithm , 1997, IEEE Trans. Signal Process..

[52]  Jean-François Cardoso,et al.  Estimating equations for source separation , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[53]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[54]  Fabrice Gamboa,et al.  Source separation when the input sources are discrete or have constant modulus , 1997, IEEE Trans. Signal Process..

[55]  Erkki Oja,et al.  Applications of neural blind separation to signal and image processing , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[56]  Shun-ichi Amari,et al.  Adaptive Online Learning Algorithms for Blind Separation: Maximum Entropy and Minimum Mutual Information , 1997, Neural Computation.

[57]  Shun-ichi Amari,et al.  Stability Analysis Of Adaptive Blind Source Separation , 1997 .

[58]  J. Cardoso Infomax and maximum likelihood for blind source separation , 1997, IEEE Signal Processing Letters.

[59]  Andrzej Cichocki,et al.  Stability Analysis of Learning Algorithms for Blind Source Separation , 1997, Neural Networks.

[60]  Andrew D. Back,et al.  A First Application of Independent Component Analysis to Extracting Structure from Stock Returns , 1997, Int. J. Neural Syst..

[61]  G. D'Urso,et al.  Blind identification methods applied to Electricite de France's civil works and power plants monitoring , 1997, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics.

[62]  Terrence J. Sejnowski,et al.  The “independent components” of natural scenes are edge filters , 1997, Vision Research.

[63]  Philippe Garat,et al.  Blind separation of mixture of independent sources through a quasi-maximum likelihood approach , 1997, IEEE Trans. Signal Process..

[64]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[65]  A. V. D. Veen Algebraic methods for deterministic blind beamforming , 1998, Proc. IEEE.

[66]  Daniel Yellin,et al.  Multichannel system identification and deconvolution: performance bounds , 1999, IEEE Trans. Signal Process..

[67]  Ali Mansour,et al.  Blind Separation of Sources , 1999 .

[68]  O. Macchi,et al.  Reply to "Comments on 'self-adaptive source separation, part I: convergence analysis of a direct linear network controled by the Herault-Jutten algorithm" , 2000, IEEE Trans. Signal Process..

[69]  S. Amari Natural Gradient Works Eciently in Learning , 2022 .