Regularity and sparsity for inverse problems in imaging

This article is a survey on regularization techniques for inverse problems based on l1 criteria. We split these criteria in two categories: those which promote regularity of the signal (e.g. total variation) and those which express the fact that a signal is sparse in some dictionnary. In the first part of the paper, we give guidelines to choose a prior and propose a comparative study of these two priors on standard transforms such as total variation, redundant wavelets, and curvelets. In the second part of the paper, we give a sketch of different first order algorithms adpated to the minimization of these l1-terms. © 2010 Lavoisier, Paris.