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In this work, we consider a class of differentiable criteria for sparse imagecomputing problems, where a nonconvex regularization is applied to an arbitrarylinear transform of the target image. As special cases, it includesedge-preserving measures or frame-analysis potentials commonly used in imageprocessing. As shown by our asymptotic results, the l2-l0 penalties we considermay be employed to provide approximate solutions to l0-penalized optimizationproblems. One of the advantages of the proposed approach is that it allows usto derive an efficient Majorize-Minimize subspace algorithm. The convergence ofthe algorithm is investigated by using recent results in nonconvexoptimization. The fast convergence properties of the proposed optimizationmethod are illustrated through image processing examples. In particular, itseffectiveness is demonstrated on several data recovery problems.

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