Rééchantillonnage de l’échelle dans les algorithmes MCMC pour les problèmes inverses bilinéaires

This article presents an efficient method for improving the behavior of the MCMC sampling algorithm involved in the resolution of bilinear inverse problems. Blind deconvolution and source separation are among the applications that benefit from this improvement. The proposed method addresses the scale ambiguity inherent to bilinear inverse problems. Solving this type of problem within a Bayesian framework lifts the ambiguity but the MCMC involved is badly mixing. Introducing an additional sampling step on the scale parameter drastically improves the behavior of the MCMC. The main advantage of this method, compared to other attempts to correct the pathological behavior of the MCMC, is that it is theoretically sound. The additional computational cost is negligible.