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Proceedings Paper

Generalization of Strang's preconditioner with applications to iterative deconvolution
Author(s): Raymond Hon-fu Chan; Michael Kwok-po Ng; Robert J. Plemmons
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Paper Abstract

In this paper, we proposed a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The [n/2]th column of our circulant preconditioner Sn is equal to the [n/2]th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as (S*nSn)1/2. This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. Comparisons of our preconditioner Sn with other circulant-based preconditioners are carried out for some 1D Toeplitz least squares problems: minb - Ax2. Preliminary numerical results show that Sn performs quite well. Test results are also reported for a 2D deconvolution problem arising in ground-based atmospheric imaging.

Paper Details

Date Published: 28 October 1994
PDF: 12 pages
Proc. SPIE 2296, Advanced Signal Processing: Algorithms, Architectures, and Implementations V, (28 October 1994); doi: 10.1117/12.190864
Show Author Affiliations
Raymond Hon-fu Chan, Chinese Univ. of Hong Kong (Hong Kong)
Michael Kwok-po Ng, Chinese Univ. of Hong Kong (Hong Kong)
Robert J. Plemmons, Wake Forest Univ. (United States)

Published in SPIE Proceedings Vol. 2296:
Advanced Signal Processing: Algorithms, Architectures, and Implementations V
Franklin T. Luk, Editor(s)

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