Democratic prior for anti-sparse coding

Clément Elvira (1, 2) , Pierre Chainais (1, 2) , Nicolas Dobigeon (3)

1 Centrale Lille
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 IRIT - Institut de recherche en informatique de Toulouse

Anti-sparse coding aims at spreading the information uniformly over representation coefficients and can be naturally expressed through an ∞-norm regularization. This paper derives a probabilistic formulation of such a problem. A new probability distribution is introduced .This so-called democratic distribution is then used as a prior to promote anti-sparsity in a linear Gaussian inverse problem. A Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of interest. To scale to higher dimension, a proximal Markov chain Monte Carlo algorithm is proposed as an alternative to Gibbs sampling. Simulations on synthetic data illustrate the performance of the proposed method for anti-sparse coding on a complete dictionary. Results are compared with the recent deterministic variational FITRA algorithm.

Mots clés: Anti-sparse representation; democratic distribution; inverse problem

Domaines: Traitement du signal et de l'image [eess.SP]; Statistiques [math.ST]; Machine Learning [stat.ML]; Traitement du signal et de l'image [eess.SP]

Clément Elvira, Pierre Chainais, Nicolas Dobigeon. Democratic prior for anti-sparse coding. IEEE Workshop on Statistical Signal Processing, Jun 2016, Palma de Mallorca, Spain. pp.1 - 4, ⟨10.1109/SSP.2016.7551813⟩. ⟨hal-01433632v1⟩