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Proceedings Paper

Block circulant preconditioners for 2D deconvolution
Author(s): Raymond K. Chan; James G. Nagy; Robert J. Plemmons
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Paper Abstract

Discretized 2-D deconvolution problems arising, e.g., in image restoration and seismic tomography, can be formulated as 1eas squares compuaions, mm lib— Tx112 where T is often a large-scale rectangular Toeplitz-block matrix. We consider solving such block least squares problems by the preconditioned conjugate gradient algorithm using square nonsingular circulant-block and related preconditioners, constructed from the blocks of the rectangular matrix T. Preconditioning with such matrices allows efficient implementation using the 1-D or 2-D Fast Fourier Transform (FFT). It is well known that the resolution of ill-posed deconvolution problems can be substantially improved by regularization to compensate for their ill-posed nature. We show that regularization can easily be incorporated into our preconditioners, and we report on numerical experiments on a Cray Y-MP. The experiments illustrate good convergence properties of these FET—based preconditioned iterations.

Paper Details

Date Published: 30 November 1992
PDF: 12 pages
Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); doi: 10.1117/12.130917
Show Author Affiliations
Raymond K. Chan, Univ. of Hong Kong (Hong Kong China)
James G. Nagy, Univ. of Minnesota (United States)
Robert J. Plemmons, Wake Forest Univ. (United States)

Published in SPIE Proceedings Vol. 1770:
Advanced Signal Processing Algorithms, Architectures, and Implementations III
Franklin T. Luk, Editor(s)

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