Dictionary Learning with Statistical Sparsity in the Presence of Noise
Abstract
We consider a new stochastic formulation of sparse representations that is based on the family of symmetric α-stable (SαS) 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 SαS law from a set of its noisy samples. We assess the robustness of our algorithm with numerical examples.
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