Majorize-Minimize adapted metropolis-hastings algorithm. Application to multichannel image recovery

Yosra Marnissi, Amel Benazza-Benyahia, Émilie Chouzenoux, Jean-Christophe Pesquet

Abstract: One challenging task in MCMC methods is the choice of the proposal density. It should ideally provide an accurate approximation of the target density with a low computational cost. In this paper, we are interested in Langevin diffusion where the proposal accounts for a directional component. We propose a novel method for tuning the related drift term. This term is preconditioned by an adaptive matrix based on a Majorize-Minimize strategy. This new procedure is shown to exhibit a good performance in a multispectral image restoration example.