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

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

2011-12-29

arxiv.org/abs/1112.6272v1

Mathematics

Optimization and Control

Scientific paper

In this article, 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 considered l2-l0 penalties may be employed to 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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