30 November 1992 Block circulant preconditioners for 2D deconvolution
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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.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Raymond K. Chan, Raymond K. Chan, James G. Nagy, James G. Nagy, Robert J. Plemmons, 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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