Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors

Details Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors Deconvolution under Poisson noise using exact data fidelity and synthesis or analysis sparsity priors

2011-03-11

arxiv.org/abs/1103.2213v1

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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.

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