Generalization of Strang's preconditioner with applications to iterative deconvolution

Raymond H. CHAN*, Michael K. NG, Robert J. PLEMMONS

*Corresponding author for this work

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

Abstract

In this paper, we proposed a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The [n/2]th column of our circulant preconditioner Sn is equal to the [n/2]th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as (S*nSn) 1/2 . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. Comparisons of our preconditioner Sn with other circulant-based preconditioners are carried out for some 1D Toeplitz least squares problems: min||b - Ax||2. Preliminary numerical results show that S n performs quite well. Test results are also reported for a 2D deconvolution problem arising in ground-based atmospheric imaging.

Original languageEnglish
Title of host publicationProceedings volume 2296: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation
EditorsFranklin T. Luk
PublisherSPIE
Pages528-539
Number of pages12
ISBN (Print)0819416207
DOIs
Publication statusPublished - 28 Oct 1994
Externally publishedYes
EventSPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation - San Diego, United States
Duration: 24 Jul 199427 Jul 1994

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume2296
ISSN (Print)0277-786X

Conference

ConferenceSPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation
Country/TerritoryUnited States
CitySan Diego
Period24/07/9427/07/94

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