A Reversible Jump MCMC in Bayesian Blind Deconvolution With a Spherical Prior

Blind deconvolution (BD) is the recovery of a scene of interest convolved with an unknown impulse response function. Within a Bayesian context, prior distributions are assigned to both unknowns to regularize the BD problem. A common approach is to use Gaussian priors. Nonetheless, the latter do not alleviate the so-called scale ambiguity that prevents from efficiently sampling the joint posterior distribution and building appropriate estimators. In this paper, we instead use a Von-Mises prior that removes scale ambiguity and we focus on the design of a sampling scheme of the joint posterior. The latter may exhibit multiple modes. We propose accordingly a reversible jump Markov chain Monte Carlo method that prevents samples from lingering in local modes. Compared to state-of-the-art techniques, the algorithm shows an improved within- and between-mode mixing property with synthetic data. This paves the way for the design of Bayesian estimators naturally deprived of scale ambiguity.