A greedy approach to sparse poisson denoising

In this paper we propose a greedy method combined with the Moreau-Yosida regularization of the Poisson likelihood in order to restore images corrupted by Poisson noise. The regularization provides us with a data fidelity term with nice properties which we minimize under sparsity constraints. To do so, we use a greedy method based on a generalization of the well-known CoSaMP algorithm. We introduce a new convergence analysis of the algorithm which extends it use outside of the usual scope of convex functions. We provide numerical experiments which show the soundness of the method compared to the convex l₁-norm relaxation of the problem.