Spike and slab variational inference for blind image deconvolution

In this work, we propose a new variational blind deconvolution method for spike and slab prior models. Soft-sparse or shrinkage priors such as the Laplace and other related Gaussian Scale Mixture priors may not be ideal sparsity promoting priors. They assign zero probability mass to events we may be interested in assigning a probability greater than zero. The truly sparse nature of the spike and slab priors allows us to discard irrelevant information in the blur estimation process, resulting in improved performance. We present an efficient inference algorithm to estimate the unknown blur kernel in the filter space, from which we estimate the final deblurred image. The VB approach we propose in this paper handles the inference in a much more efficient way than MCMC, and is more accurate than the standard mean field variational approximation. We prove the efficacy of our method by means of a series of experiments on both synthetically generated and real images.