30 November 1992 Block circulant preconditioners for 2D deconvolution
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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.
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Raymond K. Chan, James G. Nagy, Robert J. Plemmons, "Block circulant preconditioners for 2D deconvolution", Proc. SPIE 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III, (30 November 1992); doi: 10.1117/12.130917; https://doi.org/10.1117/12.130917
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