Geometrical Structures of FIR Manifold and Multichannel Blind Deconvolution

In this paper we study geometrical structures of the manifold of Finite Impulse Response (FIR) filters, and develop a natural gradient learning algorithm for blind deconvolution. First, A Lie group structure is introduced to the FIR manifold and the Riemannian metric is then derived by using the isometric property of the Lie group. The natural gradient on the FIR manifold is obtained by introducing a nonholonomic transformation. The Kullback-Leibler divergence is introduced as the measure of mutual independence of the output signals of the demixing model and a feasible cost function is derived for blind deconvolution. An efficient learning algorithm is presented based on the natural gradient approach and its stability analysis is also provided. Finally, we give computer simulations to demonstrate the performance and effectiveness of the proposed natural gradient algorithm.

[1]  Liqing Zhang,et al.  Natural gradient algorithm for blind separation of overdetermined mixture with additive noise , 1999, IEEE Signal Processing Letters.

[2]  Kari Torkkola,et al.  Blind separation of convolved sources based on information maximization , 1996, Neural Networks for Signal Processing VI. Proceedings of the 1996 IEEE Signal Processing Society Workshop.

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

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

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

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

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

[8]  R. W. Lucky,et al.  Techniques for adaptive equalization of digital communication systems , 1966 .

[9]  Andrzej Cichocki,et al.  Hidden image separation from incomplete image mixtures by independent component analysis , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[10]  H. H. Yang,et al.  Serial updating rule for blind separation derived from the method of scoring , 1999, IEEE Trans. Signal Process..

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

[12]  J. Cadzow.  Blind deconvolution via cumulant extrema , 1996, IEEE Signal Process. Mag..

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

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

[15]  Philippe Loubaton,et al.  Subspace methods for blind identification of SIMO-FIR systems , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

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

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

[18]  Yingbo Hua,et al.  Fast maximum likelihood for blind identification of multiple FIR channels , 1996, IEEE Trans. Signal Process..

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

[20]  Andrzej Cichocki,et al.  Information-theoretic approach to blind separation of sources in non-linear mixture , 1998, Signal Process..

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

[22]  Philippe Loubaton,et al.  On subspace methods for blind identification of single-input multiple-output FIR systems , 1997, IEEE Trans. Signal Process..

[23]  J. Treichler,et al.  A new approach to multipath correction of constant modulus signals , 1983 .

[24]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[25]  Shun-ichi Amari,et al.  Novel On-Line Adaptive Learning Algorithms for Blind Deconvolution Using the Natural Gradient Approach , 1997 .

[26]  Andrzej Cichocki,et al.  Multichannel blind deconvolution of non-minimum phase systems using information backpropagation , 1999, ICONIP'99. ANZIIS'99 & ANNES'99 & ACNN'99. 6th International Conference on Neural Information Processing. Proceedings (Cat. No.99EX378).

[27]  Jitendra Tugnait,et al.  Blind identifiability of FIR-MIMO systems with colored input using second order statistics , 2000, IEEE Signal Processing Letters.

[28]  Philippe Loubaton,et al.  Blind identification of MIMO-FIR systems: A generalized linear prediction approach , 1999, Signal Process..

[29]  Y. Sato.  Two Extensional Applications of the Zero-Forcing Equalization Method , 1975, IEEE Trans. Commun..

[30]  Liqing Zhang,et al.  Blind Separation of Filtered Sources Using State-Space Approach , 1998, NIPS.

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

[32]  Jitendra K. Tugnait,et al.  Multistep linear predictors-based blind identification and equalization of multiple-input multiple-output channels , 2000, IEEE Trans. Signal Process..

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

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

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

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

[37]  Erkki Oja,et al.  Independent Component Analysis for Identification of Artifacts in Magnetoencephalographic Recordings , 1997, NIPS.

[38]  Lang Tong,et al.  Blind identification and equalization based on second-order statistics: a time domain approach , 1994, IEEE Trans. Inf. Theory.