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In this paper we present a new Bayesian model for the blind image deconvolution (BID) problem. The main novelties of this model are three. The first one is the use of a sparse kernel-based model for the point spread function (PSF) that allows estimation of both PSF shape and support. The second one is a robust distribution of the BID model errors and the third novelty is an image prior that preserves edges of the reconstructed image. Sparseness, robustness and preservation of edges is achieved by using priors that are based on the Student-t probability density function (pdf). The Variational methodology is used to solve the corresponding Bayesian model. Numerical experiments are presented that demonstrate the advantages of this model as compared to previous Gaussian based ones.