Dictionary Learning with Statistical Sparsity in the Presence of Noise

We consider a new stochastic formulation of sparse representations that is based on the family of symmetric alpha-stable (S alpha S) distributions. Within this framework, we develop a novel dictionary-learning algorithm that involves a new estimation technique based on the empirical characteristic function. It finds the unknown parameters of an S alpha S law from a set of its noisy samples. We assess the robustness of our algorithm with numerical examples.