A multistage representation of the Wiener filter based on orthogonal projections

  • Authors:

  • J. S. Goldstein;I. S. Reed;L. L. Scharf

  • Affiliations:

  • Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

The Wiener filter is analyzed for stationary complex Gaussian signals from an information theoretic point of view. A dual-port analysis of the Wiener filter leads to a decomposition based on orthogonal projections and results in a new multistage method for implementing the Wiener filter using a nested chain of scalar Wiener filters. This new representation of the Wiener filter provides the capability to perform an information-theoretic analysis of previous, basis-dependent, reduced-rank Wiener filters. This analysis demonstrates that the cross-spectral metric is optimal in the sense that it maximizes mutual information between the observed and desired processes. A new reduced-rank Wiener filter is developed based on this new structure which evolves a basis using successive projections of the desired signal onto orthogonal, lower dimensional subspaces. The performance is evaluated using a comparative computer analysis model and it is demonstrated that the low-complexity multistage reduced-rank Wiener filter is capable of outperforming the more complex eigendecomposition-based methods