A hybrid method for deconvolution of Bernoulli-Gaussian processes

We investigate a hybrid method which improves the quality of state inference and parameter estimation in blind deconvolution of a sparse source modeled by a Bernoulli-Gaussian process. In this problem, when both the signal and the filter are jointly estimated, the true posterior is typically highly multimodal. Therefore, when not properly initialized, standard stochastic inference methods, (MCEM, SEM or SAEM), tend to get stuck and suffer from poor convergence. In our approach, we first relax the Bernoulli-Gaussian prior model by a Student-t model. Our simulations suggest that deterministic inference in the relaxed model is not only efficient, but also provides a very good initialization for the Bernoulli-Gaussian model. We provide simulation studies that compare the results obtained with and without our initialization method for several combinations of state inference and parameter estimation methods used for the Bernoulli-Gaussian model.