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

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.

Mots clés: Non-convex optimization; edge preservation; sparse representations; Majorize-Minimize algorithms; inverse problems; denoising; deblurring

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

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⟩