Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors
Abstract
In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the Poisson statistics of the noise. On the other hand, as a prior, the images to restore are assumed to be positive and sparsely represented in a dictionary of waveforms such as wavelets or curvelets. Both analysis and synthesis-type sparsity priors are considered. Piecing together the data fidelity and the prior terms, the deconvolution problem boils down to the minimization of non-smooth convex functionals (for each prior). We establish the well-posedness of each optimization problem, characterize the corresponding minimizers, and solve them by means of proximal splitting algorithms originating from the realm of non-smooth convex optimization theory. Experimental results are conducted to demonstrate the potential applicability of the proposed algorithms to astronomical imaging datasets.
Cite
@article{arxiv.1103.2213,
title = {Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors},
author = {François-Xavier Dupé and Jalal Fadili and Jean-Luc Starck},
journal= {arXiv preprint arXiv:1103.2213},
year = {2011}
}