A greedy approach to sparse poisson denoising

Abstract

International audienceIn 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 1 -norm relaxation of the problem

A Review on CT and X-Ray Images Denoising Methods

“…The Poisson denoising based on greedy approach of Dupe and Anthoine [36]. The goal of this method is combination of a greedy method with Moreau-Yosida regularization of the Poisson likelihood.…”

Sparse and redundant signal representations for x-ray computed tomography

“…Suppose that x 0 [i] is the i th patch of the true underlying image and x[i] is the measured patch under Poisson noise. If we wish to recover x 0 [i] from x[i] via sparse representation in a dictionary D, we need to solve a problem that has the following form [165]:…”

Patch-based models and algorithms for image processing: a review of the basic principles and methods, and their application in computed tomography

“…The reason why only one atom was used for representation of each patch was the difficulties in sparse coding under the Poisson noise. These difficulties have been discussed in [29,34], and greedy sparse coding algorithms have been proposed for solving this problem. The authors of [29] applied their algorithm for denoising of images with Poisson noise with a wavelet dictionary and achieved impressive results.…”