A measure-theoretic variational Bayesian algorithm for large dimensional problems

Aurélia Fraysse (1) , Thomas Rodet (2)

1 L2S - Laboratoire des signaux et systèmes
2 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

In this paper we provide an algorithm allowing to solve the variational Bayesian issue as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. The main advantage of this methodology is that it allows to address large dimensional inverse problems by unsupervised algorithms. The interest of our algorithm is enhanced by its application to large dimensional linear inverse problems involving sparse objects. Finally,we provide simulation results. First we show the good numerical performances of our method by comparing it with classical ones on a small tomographic problem. On a second time we treat a large dimensional dictionary learning problem and compare our method with a wavelet based one.

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

Aurélia Fraysse, Thomas Rodet. A measure-theoretic variational Bayesian algorithm for large dimensional problems. SIAM Journal on Imaging Sciences, 2014, 7 (4), pp.2591-2622. ⟨hal-00702259v2⟩