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Conference Paper: Generalization of Strang's preconditioner with applications to iterative deconvolution
Title | Generalization of Strang's preconditioner with applications to iterative deconvolution |
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Authors | |
Issue Date | 1994 |
Citation | SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, San Diego, CA, 24-29 July 1994. In Proceedings of SPIE - The International Society for Optical Engineering, 1994, v. 2296, p. 528-539 How to Cite? |
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. |
Persistent Identifier | http://hdl.handle.net/10722/276473 |
ISSN | 2023 SCImago Journal Rankings: 0.152 |
DC Field | Value | Language |
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dc.contributor.author | Chan, Raymond H. | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Plemmons, Robert J. | - |
dc.date.accessioned | 2019-09-18T08:33:42Z | - |
dc.date.available | 2019-09-18T08:33:42Z | - |
dc.date.issued | 1994 | - |
dc.identifier.citation | SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, San Diego, CA, 24-29 July 1994. In Proceedings of SPIE - The International Society for Optical Engineering, 1994, v. 2296, p. 528-539 | - |
dc.identifier.issn | 0277-786X | - |
dc.identifier.uri | http://hdl.handle.net/10722/276473 | - |
dc.description.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. | - |
dc.language | eng | - |
dc.relation.ispartof | Proceedings of SPIE - The International Society for Optical Engineering | - |
dc.title | Generalization of Strang's preconditioner with applications to iterative deconvolution | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1117/12.190864 | - |
dc.identifier.scopus | eid_2-s2.0-0028737406 | - |
dc.identifier.volume | 2296 | - |
dc.identifier.spage | 528 | - |
dc.identifier.epage | 539 | - |
dc.identifier.issnl | 0277-786X | - |