A memory gradient algorithm for l2-l0 regularization with applications to image restoration

Emilie Chouzenoux 1 Jean-Christophe Pesquet 1 Hugues Talbot 1 Anna Jezierska 1
1 LIGM - Laboratoire d'Informatique Gaspard-Monge
Abstract : In this paper, we consider a class of differentiable criteria for sparse image recovery problems. The regularization is applied to a linear transform of the target image. As special cases, it includes edge preserving measures or frame analysis potentials. 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 approach is that it allows us to derive an efficient Majorize-Minimize Memory Gradient algorithm. The fast convergence properties of the proposed optimization algorithm are illustrated through image restoration examples.
Keywords : deblurring Non-convex optimization edge preservation sparse representations Majorize-Minimize algorithms inverse problems denoising
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Emilie Chouzenoux, Jean-Christophe Pesquet, Hugues Talbot, Anna Jezierska. A memory gradient algorithm for l2-l0 regularization with applications to image restoration. 18th IEEE International Conference on Image Processing (ICIP 2011), Sep 2011, Bruxelles, Belgium. pp.2717-2720, ⟨10.1109/ICIP.2011.6116230⟩. ⟨hal-00687500⟩

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