Adaptive paraunitary filter banks for principal and minor subspace analysis

Paraunitary filter banks are important for several signal processing tasks. We consider the task of adapting the coefficients of a multichannel FIR paraunitary filter bank via gradient ascent or descent on a chosen cost function. The proposed generalized algorithms inherently adapt the system's parameters in the space of paraunitary filters. Modifications and simplifications of the techniques for spatio-temporal principal and minor subspace analysis are described. Simulations verify one algorithm's useful behavior in this task.

[1]  Qin Lin,et al.  A unified algorithm for principal and minor components extraction , 1998, Neural Networks.

[2]  E. Stiefel.  Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten , 1935 .

[3]  B. Farhang-Boroujeny,et al.  Adaptive phase equalization using all-pass filters , 1991, ICC 91 International Conference on Communications Conference Record.

[4]  Teng Joon Lim,et al.  Adaptive allpass filtering for nonminimum-phase system identification , 1994 .

[5]  Georgios B. Giannakis,et al.  Principal component filter banks for optimal multiresolution analysis , 1995, IEEE Trans. Signal Process..

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

[7]  Lei Xu,et al.  Least mean square error reconstruction principle for self-organizing neural-nets , 1993, Neural Networks.

[8]  Roberto H. Bamberger,et al.  FIR principal component filter banks , 1998, IEEE Trans. Signal Process..

[9]  Andrzej Cichocki,et al.  Relationships between instantaneous blind source separation and multichannel blind deconvolution , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[10]  S.C. Douglas,et al.  On the relationship between blind deconvolution and blind source separation , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[11]  D. Fuhrmann.  A geometric approach to subspace tracking , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[12]  Pierre Moulin,et al.  Theory and design of signal-adapted FIR paraunitary filter banks , 1998, IEEE Trans. Signal Process..

[13]  Scott C. Douglas,et al.  Kuicnet Algorithms for Blind Deconvolution , 1998, Neural Networks for Signal Processing VIII. Proceedings of the 1998 IEEE Signal Processing Society Workshop (Cat. No.98TH8378).

[14]  S.C. Douglas,et al.  Multichannel blind deconvolution and equalization using the natural gradient , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

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

[16]  R. Lambert.  Multichannel blind deconvolution: FIR matrix algebra and separation of multipath mixtures , 1996 .

[17]  S. Amari,et al.  A self-stabilized minor subspace rule , 1998, IEEE Signal Processing Letters.

[18]  B. Widrow,et al.  Adaptive inverse control , 1987, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[19]  S. Amari,et al.  Quasi-Newton filtered-error and filtered-regressor algorithms for adaptive equalization and deconvolution , 1997, First IEEE Signal Processing Workshop on Signal Processing Advances in Wireless Communications.

[20]  E. Oja,et al.  On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix , 1985 .

[21]  P. P. Vaidyanathan,et al.  Theory and design of optimum FIR compaction filters , 1998, IEEE Trans. Signal Process..

[22]  Andrzej Cichocki,et al.  Self-whitening algorithms for adaptive equalization and deconvolution , 1999, IEEE Trans. Signal Process..

[23]  U. Helmke,et al.  Optimization and Dynamical Systems , 1994, Proceedings of the IEEE.

[24]  S. Amari,et al.  Gradient adaptation under unit-norm constraints , 1998, Ninth IEEE Signal Processing Workshop on Statistical Signal and Array Processing (Cat. No.98TH8381).

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