Parallel ProXimal Algorithm for Image Restoration Using Hybrid Regularization -- Extended version

Abstract : Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, namely how to find a good regularizer. While total variation introduces staircase effects, wavelet domain regularization brings other artefacts, e.g. ringing. However, a trade-off can be made by introducing a hybrid regularization including several terms non necessarily acting in the same domain (e.g. spatial and wavelet transform domains). While this approach was shown to provide good results for solving deconvolution problems in the presence of additive Gaussian noise, an important issue is to efficiently deal with this hybrid regularization for more general noise models. To solve this problem, we adopt a convex optimization framework where the criterion to be minimized is split in the sum of more than two terms. For spatial domain regularization, isotropic or anisotropic total variation definitions using various gradient filters are considered. An accelerated version of the Parallel Proximal Algorithm is proposed to perform the minimization. Some difficulties in the computation of the proximity operators involved in this algorithm are also addressed in this paper. Numerical experiments performed in the context of Poisson data recovery, show the good behaviour of the algorithm as well as promising results concerning the use of hybrid regularization techniques.
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Contributor : Nelly Pustelnik <>
Submitted on : Saturday, October 22, 2011 - 5:17:52 PM
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  • HAL Id : hal-00574531, version 2


Nelly Pustelnik, Caroline Chaux, Jean-Christophe Pesquet. Parallel ProXimal Algorithm for Image Restoration Using Hybrid Regularization -- Extended version. 2011. ⟨hal-00574531v2⟩



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