The Minimum Entropy and Cumulants Based Contrast Functions for Blind Source Extraction

In this paper we address the problem of blind source extraction of a subset of "interesting" independent sources from a linear convolutive or instantaneous mixture. The interesting sources are those which are independent and, in a certain sense, are sparse and far away from Gaussianity. We show that in the low-noise limit and when none of the desired sources is Gaussian, the minimum entropy and cumulants based approaches can solve the problem. These criteria, with roots in Blind Deconvolution and in Projection Pursuit, will be proposed here for the simultaneous blind extraction of a group of independent sources. Then, we suggest simple algorithms which, working on the Stiefel manifold perform maximization of the proposed contrast functions.

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

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

[3]  D. Donoho.  ON MINIMUM ENTROPY DECONVOLUTION , 1981 .

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

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

[6]  Shun-ichi Amari,et al.  Sequential blind signal extraction in order specified by stochastic properties , 1997 .

[7]  Jitendra K. Tugnait,et al.  Identification and deconvolution of multichannel linear non-Gaussian processes using higher order statistics and inverse filter criteria , 1997, IEEE Trans. Signal Process..

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

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

[10]  Yujiro Inouye,et al.  Iterative algorithms based on multistage criteria for multichannel blind deconvolution , 1999, IEEE Trans. Signal Process..

[11]  Robin Sibson,et al.  What is projection pursuit , 1987 .

[12]  M. Girolami.  Negentropy and Kurtosis as Projection Pursuit Indices Provide Generalised ICA Algorithms , 1996, NIPS 1996.

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

[14]  Sergio Cruces,et al.  Blind source extraction in Gaussian noise , 2000 .

[15]  Terrence J. Sejnowski,et al.  Blind separation and blind deconvolution: an information-theoretic approach , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

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

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

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

[19]  P. Comon,et al.  Contrasts for multichannel blind deconvolution , 1996, IEEE Signal Processing Letters.

[20]  Shun-ichi Amari,et al.  Natural Gradient Learning for Over- and Under-Complete Bases in ICA , 1999, Neural Computation.

[21]  Jean-Francois Cardoso,et al.  Blind signal separation: statistical principles , 1998, Proc. IEEE.

[22]  Shun-ichi Amari,et al.  Adaptive blind signal processing-neural network approaches , 1998, Proc. IEEE.