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A Majorize-Minimize subspace approach for l2-l0 image regularization

Abstract : In this work, we consider a class of differentiable criteria for sparse image computing problems, where a non-convex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes edge preserving measures or frame analysis potentials commonly used in image processing. As shown by our asymptotic results, the l2-l0 penalties we consider may be employed to provide approximate solutions to l0-penalized optimization problems. One of the advantages of the proposed approach is that it allows us to derive an efficient Majorize-Minimize subspace algorithm. The convergence of the algorithm is investigated by using recent results in non-convex optimization. The fast convergence properties of the proposed optimization method are illustrated through image processing examples. In particular, its effectiveness is demonstrated on several data recovery problems.
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https://hal.archives-ouvertes.fr/hal-00789962
Contributor : Emilie Chouzenoux <>
Submitted on : Tuesday, February 19, 2013 - 10:31:30 AM
Last modification on : Wednesday, February 26, 2020 - 7:06:06 PM

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Emilie Chouzenoux, Anna Jezierska, Jean-Christophe Pesquet, Hugues Talbot. A Majorize-Minimize subspace approach for l2-l0 image regularization. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2013, 6 (1), pp.563-591. ⟨10.1137/11085997X⟩. ⟨hal-00789962⟩

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