Gradient Adaptive Paraunitary Filter Banks for Spatio-Temporal Subspace Analysis and Multichannel Blind Deconvolution

Authors:
Scott C. Douglas;Shun-Ichi Amari;S.-Y. Kung
Affiliations:
Department of Electrical Engineering, Southern Methodist University, Dallas, Texas 75275, USA;Laboratory for Mathematical Neuroscience, RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan;Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
Venue:
Journal of VLSI Signal Processing Systems
Year:
2004

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Abstract

Paraunitary filter banks are important for several signal processing tasks, including coding, multichannel deconvolution and equalization, adaptive beamforming, and subspace processing. In this paper, we consider the task of adapting the impulse response of a multichannel paraunitary filter bank via gradient ascent or descent on a chosen cost function. Our methods are spatio-temporal generalizations of gradient techniques on the Grassmann and Stiefel manifolds, and we prove that they inherently maintain the paraunitariness of the multichannel adaptive system over time. We then discuss the necessary practical approximations, modifications, and simplifications of the methods for solving two relevant signal processing tasks: (i) spatio-temporal subspace analysis and (ii) multichannel blind deconvolution. Simulations indicate that our methods can provide simple, useful solutions to these important problems.