Sparse signal recovery using a Bernoulli generalized Gaussian prior

Lotfi Chaari (1, 2) , Jean-Yves Tourneret (3, 2) , Caroline Chaux (4)

1 IRIT-TCI - Traitement et Compréhension d’Images
2 Toulouse INP - Institut National Polytechnique (Toulouse)
3 IRIT-MINDS - CoMputational imagINg anD viSion
4 I2M - Institut de Mathématiques de Marseille

Bayesian sparse signal recovery has been widely investigated during the last decade due to its ability to automatically estimate regularization parameters. Prior based on mixtures of Bernoulli and continuous distributions have recently been used in a number of recent works to model the target signals , often leading to complicated posteriors. Inference is therefore usually performed using Markov chain Monte Carlo algorithms. In this paper, a Bernoulli-generalized Gaussian distribution is used in a sparse Bayesian regularization framework to promote a two-level flexible sparsity. Since the resulting conditional posterior has a non-differentiable energy function , the inference is conducted using the recently proposed non-smooth Hamiltonian Monte Carlo algorithm. Promising results obtained with synthetic data show the efficiency of the proposed regularization scheme.

Mots clés: Sparse Bayesian regularization; MCMC; ns-HMC; restoration

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

Lotfi Chaari, Jean-Yves Tourneret, Caroline Chaux. Sparse signal recovery using a Bernoulli generalized Gaussian prior. EUSIPCO 2015 23rd European Signal Processing Conference, Aug 2015, Nice, France. ⟨10.1109/EUSIPCO.2015.7362676⟩. ⟨hal-01278488⟩