Block circulant preconditioners for 2D deconvolution

Raymond K. Chan; James G. Nagy; Robert J. Plemmons

doi:10.1117/12.130917

30 November 1992 Block circulant preconditioners for 2D deconvolution

Raymond K. Chan, James G. Nagy, Robert J. Plemmons

Proceedings Volume 1770, Advanced Signal Processing Algorithms, Architectures, and Implementations III; (1992) https://doi.org/10.1117/12.130917
Event: San Diego '92, 1992, San Diego, CA, United States

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.

Citation Download Citation

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

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available