Robust Blind Source Separation Utilizing Second and Fourth Order Statistics

We introduce identifiability conditions for the blind source separation (BSS) problem, combining the second and fourth order statistics. We prove that under these conditions, well known methods (like eigen-value decomposition and joint diagonalization) can be applied with probability one, i.e. the set of parameters for which such a method doesn't solve the BSS problem, has a measure zero.

[1]  A. Cichocki,et al.  Robust whitening procedure in blind source separation context , 2000 .

[2]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

[3]  Lang Tong,et al.  A finite-step global convergence algorithm for the parameter estimation of multichannel MA processes , 1992, IEEE Trans. Signal Process..

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

[5]  Lang Tong,et al.  Indeterminacy and identifiability of blind identification , 1991 .

[6]  Jean-Franois Cardoso High-Order Contrasts for Independent Component Analysis , 1999, Neural Computation.

[7]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[8]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[9]  Chunqi Chang,et al.  Uncorrelated component analysis for blind source separation , 1999 .

[10]  Zhi Ding,et al.  A matrix-pencil approach to blind separation of colored nonstationary signals , 2000, IEEE Trans. Signal Process..

[11]  Aapo Hyvärinen,et al.  Topographic Independent Component Analysis , 2001, Neural Computation.

[12]  Adel Belouchrani,et al.  JOINT CUMULANT AND CORRELATION BASED SIGNAL SEPARATION WITH APPLICATION TO EEG DATA ANALYSIS � , 2001 .

[13]  Erkki Oja,et al.  Independent Component Analysis , 2001 .

[14]  Andrzej Cichocki,et al.  On-line Algorithm for Blind Signal Extraction of Arbitrarily Distributed, but Temporally Correlated Sources Using Second Order Statistics , 2000, Neural Processing Letters.

[15]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .