Parameter estimation in spike and slab variational inference for blind image deconvolution.

Most current state of the art blind image deconvolution methods model the underlying image (either in the image or filter space) using sparsity promoting priors and perform inference, that is, image, blur, and parameter estimation using variational approximation. In this paper we propose the use of the spike-and-slab prior model in the filter space and a variational posterior approximation more expressive than mean field. The spike-and-slab prior model, which is the "gold-standard" in sparse machine learning, has the ability to selectively shrink irrelevant variables while relevant variables are mildly regularized. This allows to discard irrelevant information while preserving important features for the estimation of the blur which results in more precise and less noisy blur kernel estimates. In this paper we present a variational inference algorithm for estimating the blur in the filter space, which is both more efficient than MCMC and more accurate than the standard mean field variational approximation. The parameters of the prior model are automatically estimated together with the blur. Once the blur is estimated, a non-blind image restoration algorithm is used to obtain the sharp image. We prove the efficacy of our method on both synthetically generated and real images.