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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Bibliographic Details
Published in:	BIT Numerical Mathematics Vol. 57; no. 2; pp. 351 - 378
Main Authors:	Huang, G., Lanza, A., Morigi, S., Reichel, L., Sgallari, F.
Format:	Journal Article
Language:	English
Published:	Dordrecht Springer Netherlands 01.06.2017
Subjects:	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
Online Access:	Get full text
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Summary:	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