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Super-resolution (SR) is a technique to enhance the resolution of an image without changing the camera resolution, through using software algorithms. In this context, this paper proposes a fully automatic SR algorithm, using a recent nonparametric Bayesian inference method based on numerical integration, known in the statistical literature as integrated nested Laplace approximation (INLA). By applying such inference method to the SR problem, this paper shows that all the equations needed to implement this technique can be written in closed form. Moreover, the results of several simulations (three of them are here presented) show that the proposed algorithm performs better than other SR algorithms recently proposed. As far as the authors know, this is the first time that the INLA is used in the area of image processing, which is a meaningful contribution of this paper.