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With the term super-resolution we refer to the problem of reconstructing an image of higher resolution than that of unregistered and degraded observations. Typically, the reconstruction is based on the inversion of the observation generation model. In this paper this problem is formulated using a variational Bayesian inference framework and an edge-preserving image prior. A novel super-resolution algorithm is proposed, which is derived using a modification of the constrained variational inference methodology which infers the posteriors of the model variables and selects automatically all the model parameters. This algorithm is very intensive computationally, thus, it is accelerated by harnessing the computational power of a graphics processor unit (GPU). Examples are presented with both synthetic and real images that demonstrate the advantages of the proposed framework as compared to other state-of …