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An Adaptive Constraint Method for Paraunitary Filter Banks with Applications to Spatiotemporal Subspace Tracking

Abstract

This paper presents an adaptive method for maintaining paraunitary constraints on direct-form multichannel finite impulse response (FIR) filters. The technique is a spatiotemporal extension of a simple iterative procedure for imposing orthogonality constraints on nearly unitary matrices. A convergence analysis indicates that it has a large capture region, and its convergence rate is shown to be locally quadratic. Simulations of the method verify its capabilities in maintaining paraunitary constraints for gradient-based spatiotemporal principal and minor subspace tracking. Finally, as the technique is easily extended to multidimensional convolution forms, we illustrate such an extension for two-dimensional adaptive paraunitary filters using a simple image sequence encoding example.

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Correspondence to Scott C. Douglas.

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Douglas, S.C. An Adaptive Constraint Method for Paraunitary Filter Banks with Applications to Spatiotemporal Subspace Tracking. EURASIP J. Adv. Signal Process. 2007, 080301 (2006). https://doi.org/10.1155/2007/80301

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Keywords

  • Convolution
  • Convergence Rate
  • Quantum Information
  • Image Sequence
  • Iterative Procedure