On local convergence of a class of blind separation algorithms

A class of recursive stochastic gradient algorithms for blind separation of dynamically mixed independent source signals are analyzed. The studied methods utilize correlations and high-order moments in order to enforce statistical independence of the separated signals. The local convergence properties of the schemes are investigated, and it is demonstrated that local convergence is tied to positive realness of certain mixing transfer functions.

[1]  P. Loubaton,et al.  Blind deconvolution of multivariate signals: A deflation approach , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

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

[3]  A. Maynard Engebretson,et al.  Acoustic signal separation of statistically independent sources using multiple microphones , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[5]  Nathalie Delfosse,et al.  Adaptive separation of independent sources: a deflation approach , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

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

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

[8]  Esfandiar Sorouchyari,et al.  Blind separation of sources, part III: Stability analysis , 1991, Signal Process..

[9]  T. Wigren Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model , 1994, IEEE Trans. Autom. Control..

[10]  B. Widrow,et al.  Adaptive noise cancelling: Principles and applications , 1975 .

[11]  Jae S. Lim,et al.  A new application of adaptive noise cancellation , 1986, IEEE Trans. Acoust. Speech Signal Process..

[12]  Astrom Computer Controlled Systems , 1990 .

[13]  Lennart Ljung,et al.  Analysis of recursive stochastic algorithms , 1977 .

[14]  Yeheskel Bar-Ness,et al.  A forward/backward bootstrapped structure for blind separation of signals in a multi-channel dispersive environment , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[15]  Meir Feder,et al.  Multi-channel signal separation by decorrelation , 1993, IEEE Trans. Speech Audio Process..

[16]  Lennart Ljung,et al.  On positive real transfer functions and the convergence of some recursive schemes , 1977 .

[17]  Ananthram Swami,et al.  Multichannel ARMA processes , 1994, IEEE Trans. Signal Process..

[18]  Ehud Weinstein,et al.  Iterative and sequential algorithms for multisensor signal enhancement , 1994, IEEE Trans. Signal Process..

[19]  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.