A proximal approach for constrained cosparse modelling

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 isminimized 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.