@inproceedings{c7ea793985b04cc6854ec1eff8999b50,

title = "Block circulant preconditioners for 2D deconvolution",

abstract = "Discretized 2-D deconvolution problems, arising e.g., in image restoration and seismic tomography, can be formulated as least squares computations, min∥b - Tx∥ 2, 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 FFT-based preconditioned iterations.",

author = "CHAN, {Raymond H.} and NAGY, {James G.} and PLEMMONS, {Robert J.}",

year = "1992",

month = nov,

day = "30",

doi = "10.1117/12.130917",

language = "English",

isbn = "9780819409430",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

publisher = "SPIE",

pages = "60--71",

editor = "LUK, {Franklin T.}",

booktitle = "Proceedings Volume 1770: Advanced Signal Processing Algorithms, Architectures, and Implementations III",

address = "United States",

note = "SPIE's 1992 International Symposium on Optics, Imaging, and Instrumentation ; Conference date: 19-07-1992 Through 21-07-1992",

}