Two-channel constrained least squares problems: solutions using power methods and connections with canonical coordinates
Date
2005
Authors
Azimi-Sadjadi, Mahmood R., author
Scharf, Louis L., author
Pezeshki, Ali, author
Hua, Yingbo, 1960-, author
IEEE, publisher
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Abstract
The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering and transform methods for resolving channel measurements into canonical or half-canonical coordinates. Based on this connection, a unified framework for reduced-rank Wiener filtering is presented. Then, various representations of reduced-rank Wiener filters in canonical and half-canonical coordinates are introduced. An alternating power method is proposed to recursively compute the canonical coordinate and half-canonical coordinate mappings. A deflation process is introduced to extract the mappings associated with the dominant coordinates. The correctness of the alternating power method is demonstrated on a synthesized data set, and conclusions are drawn.
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Subject
generalized eigenvalue problem
constrained least squares
canonical coordinates
alternating power method
half-canonical coordinates
reduced-rank Wiener filtering
rank reduction
SVD
two-channel least squares