In this work, we introduce a novel variational model for image restoration. In particular, we study the suitability of exploiting self-similarity of natural images in the fidelity term. Traditionally, this cue has been used for the regularization term, promoting to align similarities in the degraded image with similarities in the restored one. In contrast, our proposed nonlocal data-fidelity term penalizes deviations of patches after having suffered from the degradation process if they are similar in the degraded image. Experiments on super-resolution, denoising and depth filtering show the competitiveness of this new formulation with respect to traditional nonlocal regularization terms and recent learning-based methods.

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