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Article: Preconditioned iterative methods for algebraic systems from multiplicative half-quadratic regularization image restorations
Title | Preconditioned iterative methods for algebraic systems from multiplicative half-quadratic regularization image restorations |
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Authors | |
Keywords | Preconditioned conjugate gradient method Newton method Eigenvalue bounds Multiplicative half-quadratic regularization Edge-preserving Constraint preconditioner Image restoration |
Issue Date | 2010 |
Citation | Numerical Mathematics, 2010, v. 3, n. 4, p. 461-474 How to Cite? |
Abstract | Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well. © 2010 Global-Science Press. |
Persistent Identifier | http://hdl.handle.net/10722/276903 |
ISSN | 2023 Impact Factor: 1.9 2023 SCImago Journal Rankings: 0.670 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bai, Zhong Zhi | - |
dc.contributor.author | Huang, Yu Mei | - |
dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Yang, Xi | - |
dc.date.accessioned | 2019-09-18T08:35:00Z | - |
dc.date.available | 2019-09-18T08:35:00Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Numerical Mathematics, 2010, v. 3, n. 4, p. 461-474 | - |
dc.identifier.issn | 1004-8979 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276903 | - |
dc.description.abstract | Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edge-preserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations. At each Newton iterate, the preconditioned conjugate gradient method, incorporated with a constraint preconditioner, is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived, which can be used to estimate the convergence speed of the preconditioned conjugate gradient method. We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well. © 2010 Global-Science Press. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Mathematics | - |
dc.subject | Preconditioned conjugate gradient method | - |
dc.subject | Newton method | - |
dc.subject | Eigenvalue bounds | - |
dc.subject | Multiplicative half-quadratic regularization | - |
dc.subject | Edge-preserving | - |
dc.subject | Constraint preconditioner | - |
dc.subject | Image restoration | - |
dc.title | Preconditioned iterative methods for algebraic systems from multiplicative half-quadratic regularization image restorations | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.4208/nmtma.2010.m9014 | - |
dc.identifier.scopus | eid_2-s2.0-80052199043 | - |
dc.identifier.volume | 3 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 461 | - |
dc.identifier.epage | 474 | - |
dc.identifier.eissn | 2079-7338 | - |
dc.identifier.isi | WOS:000284725400005 | - |
dc.identifier.issnl | 1004-8979 | - |