Preconditioners for linear systems arising in image reconstruction

Kyle Riley; Curtis R. Vogel

doi:10.1117/12.325697

2 October 1998 Preconditioners for linear systems arising in image reconstruction

Kyle Riley, Curtis R. Vogel

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325697
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

For the numerical solution of large linear systems, the preconditioned conjugate gradient algorithm can be very effective if one has a good preconditioner. Two distinctly different approaches to preconditioning are discussed for solving systems derived from continuous linear operators of the form K + (alpha) L, where K is a convolution operator, L is a regularization operator, and (alpha) is a small positive parameter. The first approach is circulant preconditioning. The second, less standard, approach is based on a two-level decomposition of the solution space. A comparison of the two approaches is given for a model problem arising in atmospheric image deblurring.

Citation Download Citation

Kyle Riley and Curtis R. Vogel "Preconditioners for linear systems arising in image reconstruction", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325697

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