A new MCMC algorithm for blind Bernoulli-Gaussian deconvolution

This paper proposes a new algorithm for Bernoulli-Gaussian (BG) blind deconvolution in the Markov chain Monte Carlo (MCMC) framework. To tackle such a problem, the classical Gibbs sampler is usually adopted, as proposed by Cheng et al. [1]. However, as already pointed out by Bourguignon and Carfantan [2], it fails to explore the state space efficiently. In principle, a more efficient exploration technique could be obtained by integrating the Gaussian amplitudes out of the target distribution. Unfortunately, some of the sampling steps then become intractable. Therefore, our solution mixes steps in which the amplitudes are integrated out with others where they are not. The invariant condition is shown to hold, and simulations indicate that it behaves much more satisfactorily than the reference Gibbs sampler.