Majorization–minimization generalized Krylov subspace methods for ℓp–ℓq optimization applied to image restoration
A new majorization–minimization framework for ℓ p – ℓ q image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized ℓ p – ℓ q functional is provided for both convex a...
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| Veröffentlicht in: | BIT Numerical Mathematics Jg. 57; H. 2; S. 351 - 378 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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| Abstract | A new majorization–minimization framework for
ℓ
p
–
ℓ
q
image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized
ℓ
p
–
ℓ
q
functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed. |
|---|---|
| AbstractList | A new majorization–minimization framework for
ℓ
p
–
ℓ
q
image restoration is presented. The solution is sought in a generalized Krylov subspace that is build up during the solution process. Proof of convergence to a stationary point of the minimized
ℓ
p
–
ℓ
q
functional is provided for both convex and nonconvex problems. Computed examples illustrate that high-quality restorations can be determined with a modest number of iterations and that the storage requirement of the method is not very large. A comparison with related methods shows the competitiveness of the method proposed. |
| Author | Reichel, L. Sgallari, F. Huang, G. Lanza, A. Morigi, S. |
| Author_xml | – sequence: 1 givenname: G. surname: Huang fullname: Huang, G. organization: Geomathematics Key Laboratory of Sichuan, College of Management Science, Chengdu University of Technology – sequence: 2 givenname: A. orcidid: 0000-0002-4904-0682 surname: Lanza fullname: Lanza, A. email: alessandro.lanza2@unibo.it organization: Department of Mathematics, University of Bologna – sequence: 3 givenname: S. surname: Morigi fullname: Morigi, S. organization: Department of Mathematics, University of Bologna – sequence: 4 givenname: L. surname: Reichel fullname: Reichel, L. organization: Department of Mathematical Sciences, Kent State University – sequence: 5 givenname: F. surname: Sgallari fullname: Sgallari, F. organization: Department of Mathematics, University of Bologna |
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| Cites_doi | 10.1016/0167-2789(92)90242-F 10.1109/TIT.2006.871582 10.1137/140967982 10.1007/s11075-007-9136-9 10.1137/140957639 10.1198/0003130042836 10.1016/j.laa.2011.07.019 10.1007/s00041-008-9045-x 10.1162/08997660360581958 10.1109/TNNLS.2013.2286696 10.1007/s10915-015-0129-x 10.1137/110847445 10.1109/TIP.2007.896622 10.1109/TIT.2005.862083 10.1023/A:1021765131316 10.1109/TIP.2008.2008420 10.1016/j.cam.2010.11.003 10.1137/080716542 10.1007/s10107-012-0629-5 10.1137/0909062 10.1023/B:BITN.0000039424.56697.8b 10.1016/j.amc.2013.10.063 10.1007/978-3-642-54774-4_4 10.1007/s00211-016-0842-x |
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| Keywords | Majorization–minimization algorithm – Image restoration minimization Generalized Krylov subspace |
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| Snippet | A new majorization–minimization framework for
ℓ
p
–
ℓ
q
image restoration is presented. The solution is sought in a generalized Krylov subspace that is build... |
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| Title | Majorization–minimization generalized Krylov subspace methods for ℓp–ℓq optimization applied to image restoration |
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