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- Publisher Website: 10.1016/S0024-3795(99)00274-8
- Scopus: eid_2-s2.0-0034415728
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Article: Cosine transform preconditioners for high resolution image reconstruction
Title | Cosine transform preconditioners for high resolution image reconstruction |
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Authors | |
Keywords | Discrete cosine transform Image reconstruction Toeplitz matrix Neumann boundary condition |
Issue Date | 2000 |
Citation | Linear Algebra and Its Applications, 2000, v. 316, n. 1-3, p. 89-104 How to Cite? |
Abstract | This paper studies the application of preconditioned conjugate gradient methods in high resolution image reconstruction problems. We consider reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The resulting blurring matrices are spatially variant. The classical Tikhonov regularization and the Neumann boundary condition are used in the reconstruction process. The preconditioners are derived by taking the cosine transform approximation of the blurring matrices. We prove that when the L2 or H1 norm regularization functional is used, the spectra of the preconditioned normal systems are clustered around 1 for sufficiently small subpixel displacement errors. Conjugate gradient methods will hence converge very quickly when applied to solving these preconditioned normal equations. Numerical examples are given to illustrate the fast convergence. © 2000 Elsevier Science Inc. |
Persistent Identifier | http://hdl.handle.net/10722/276722 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Chan, Raymond H. | - |
dc.contributor.author | Chan, Tony F. | - |
dc.contributor.author | Yip, Andy M. | - |
dc.date.accessioned | 2019-09-18T08:34:27Z | - |
dc.date.available | 2019-09-18T08:34:27Z | - |
dc.date.issued | 2000 | - |
dc.identifier.citation | Linear Algebra and Its Applications, 2000, v. 316, n. 1-3, p. 89-104 | - |
dc.identifier.issn | 0024-3795 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276722 | - |
dc.description.abstract | This paper studies the application of preconditioned conjugate gradient methods in high resolution image reconstruction problems. We consider reconstructing high resolution images from multiple undersampled, shifted, degraded frames with subpixel displacement errors. The resulting blurring matrices are spatially variant. The classical Tikhonov regularization and the Neumann boundary condition are used in the reconstruction process. The preconditioners are derived by taking the cosine transform approximation of the blurring matrices. We prove that when the L2 or H1 norm regularization functional is used, the spectra of the preconditioned normal systems are clustered around 1 for sufficiently small subpixel displacement errors. Conjugate gradient methods will hence converge very quickly when applied to solving these preconditioned normal equations. Numerical examples are given to illustrate the fast convergence. © 2000 Elsevier Science Inc. | - |
dc.language | eng | - |
dc.relation.ispartof | Linear Algebra and Its Applications | - |
dc.subject | Discrete cosine transform | - |
dc.subject | Image reconstruction | - |
dc.subject | Toeplitz matrix | - |
dc.subject | Neumann boundary condition | - |
dc.title | Cosine transform preconditioners for high resolution image reconstruction | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1016/S0024-3795(99)00274-8 | - |
dc.identifier.scopus | eid_2-s2.0-0034415728 | - |
dc.identifier.volume | 316 | - |
dc.identifier.issue | 1-3 | - |
dc.identifier.spage | 89 | - |
dc.identifier.epage | 104 | - |
dc.identifier.isi | WOS:000089045600007 | - |
dc.identifier.issnl | 0024-3795 | - |