Gradient Scan Gibbs Sampler: an efficient algorithm for high-dimensional Gaussian distributions

Olivier Féron (1) , François Orieux (2) , Jean-François Giovannelli

1 EDF R&D OSIRIS - Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie
2 L2S - Laboratoire des signaux et systèmes

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set of directions. The algorithm is proved to converge, i.e. the drawn samples are asymptotically distributed according to the target distribution. Our main motivation is in inverse problems related to general linear observation models and their solution in a hierarchical Bayesian framework implemented through sampling algorithms. It finds direct applications in semi-blind / unsupervised methods as well as in some non-Gaussian methods. The paper provides an illustration focused on the unsupervised estimation for super-resolution methods.

Domaines: Traitement des images [eess.IV]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Applications [stat.AP]

Olivier Féron, François Orieux, Jean-François Giovannelli. Gradient Scan Gibbs Sampler: an efficient algorithm for high-dimensional Gaussian distributions. IEEE Journal of Selected Topics in Signal Processing, 2016, 10 (2), pp.343-352. ⟨10.1109/JSTSP.2015.2510961⟩. ⟨hal-01252598⟩