Résumé en anglais

This paper introduces a novel approach to learn a dictionary in a sparsity-promoting analysis-type prior. The dictionary is opti- mized in order to optimally restore a set of exemplars from their degraded noisy versions. Towards this goal, we cast our prob- lem as a bilevel programming problem for which we propose a gradient descent algorithm to reach a stationary point that might be a local minimizer. When the dictionary analysis operator specializes to a convolution, our method turns out to be a way of learning generalized total variation-type prior. Applications to 1-D signal denoising are reported and potential applicability and extensions are discussed.