Dictionary Learning with Statistical Sparsity in the Presence of Noise

Shayan Aziznejad (1) , Emmanuel Soubies (2, 3) , Michael Unser (1)

1 Biomedical Imaging Group [Lausanne]
2 IRIT-SC - Signal et Communications
3 CNRS - Centre National de la Recherche Scientifique

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.

Mots clés: Dictionary learning; sparse coding; sparse representation; stable distribution; empirical characteristic function

Domaines: Traitement du signal et de l'image [eess.SP]

Shayan Aziznejad, Emmanuel Soubies, Michael Unser. Dictionary Learning with Statistical Sparsity in the Presence of Noise. 28th European Signal Processing Conference - EUSIPCO 2020, Jan 2021, Amsterdam, Netherlands. pp.2026-2029. ⟨hal-02966135⟩