Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations

Abstract : Interpreting the celebrated Rudin-Osher-Fatemi (ROF) model in a Bayesian framework has led to interesting new variants for Total Variation image denoising in the last decade. The Posterior Mean variant avoids the so-called staircasing artifact of the ROF model but is computationally very expensive. Another recent variant, called TV-ICE (for Iterated Conditional Expectation), delivers very similar images but uses a much faster fixed-point algorithm. In the present work, we consider the TV-ICE approach in the case of a Poisson noise model. We derive an explicit form of the recursion operator, and show linear convergence of the algorithm, as well as the absence of staircasing effect. We also provide a numerical algorithm that carefully handles precision and numerical overflow issues, and show experiments that illustrate the interest of this Poisson TV-ICE variant.
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SSVM 2015, 5th International Conference on Scale Space and Variational Methods in Computer Vision, May 2015, Lège Cap Ferret, France. Proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 9087, pp.178-190, 2015, Lecture Notes in Computer Science. <http://link.springer.com/book/10.1007/978-3-319-18461-6>. <10.1007/978-3-319-18461-6_15>
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Rémy Abergel, Cécile Louchet, Lionel Moisan, Tieyong Zeng. Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations. SSVM 2015, 5th International Conference on Scale Space and Variational Methods in Computer Vision, May 2015, Lège Cap Ferret, France. Proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), 9087, pp.178-190, 2015, Lecture Notes in Computer Science. <http://link.springer.com/book/10.1007/978-3-319-18461-6>. <10.1007/978-3-319-18461-6_15>. <hal-01275813>

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