Block circulant preconditioners for 2D deconvolution

Raymond H. CHAN*, James G. NAGY, Robert J. PLEMMONS

*Corresponding author for this work

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationProceedings Volume 1770: Advanced Signal Processing Algorithms, Architectures, and Implementations III
EditorsFranklin T. LUK
Number of pages12
ISBN (Print)9780819409430
Publication statusPublished - 30 Nov 1992
Externally publishedYes
EventSPIE's 1992 International Symposium on Optics, Imaging, and Instrumentation - San Diego, United States
Duration: 19 Jul 199221 Jul 1992

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceSPIE's 1992 International Symposium on Optics, Imaging, and Instrumentation
Country/TerritoryUnited States
CitySan Diego


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