A proximal approach for constrained cosparse modelling

Giovanni Chierchia (1) , Nelly Pustelnik (2) , Jean-Christophe Pesquet (3) , Béatrice Pesquet-Popescu (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 LIGM - Laboratoire d'Informatique Gaspard-Monge

The concept of cosparsity has been recently introduced in the arena of compressed sensing. In cosparse modelling, the ℓ0 (or ℓ1) cost of an analysis-based representation of the target signal is minimized under a data fidelity constraint. By taking benefit from recent advances in proximal algorithms, we show that it is possible to efficiently address a more general framework where a convex block sparsity measure is minimized under various convex constraints. The main contribution of this work is the introduction of a new epigraphical projection technique, which allows us to consider more flexible data fidelity constraints than the standard linear or quadratic ones. The validity of our approach is illustrated through an application to an image reconstruction problem in the presence of Poisson noise.

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

Giovanni Chierchia, Nelly Pustelnik, Jean-Christophe Pesquet, Béatrice Pesquet-Popescu. A proximal approach for constrained cosparse modelling. Acoustics, Speech and Signal Processing (ICASSP), 2012 IEEE International Conference on, Mar 2012, Kyoto, Japan. pp.3433 - 3436, ⟨10.1109/ICASSP.2012.6288654⟩. ⟨hal-00826002⟩