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
Hauptverfasser: Huang, G., Lanza, A., Morigi, S., Reichel, L., Sgallari, F.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Netherlands 01.06.2017
Schlagworte:
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Majorization–minimization algorithm
–
Image restoration
minimization
Generalized Krylov subspace
ISSN:0006-3835, 1572-9125
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Zusammenfassung: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.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-016-0643-8