Heavy-Tailed Self-Similarity Modeling for Single Image Super Resolution

Self-similarity is a prominent characteristic of natural images that can play a major role when it comes to their denoising, restoration or compression. In this paper, we propose a novel probabilistic model that is based on the concept of image patch similarity and applied to the problem of Single Image Super Resolution. Based on this model, we derive a Variational Bayes algorithm, which super resolves low-resolution images, where the assumed distribution for the quantified similarity between two image patches is heavy-tailed. Moreover, we prove mathematically that the proposed algorithm is both an extended and superior version of the probabilistic Non-Local Means (NLM). Its prime advantage remains though, which is that it requires no training. A comparison of the proposed approach with state-of-the-art methods, using various quantitative metrics shows that it is almost on par, for images depicting rural themes and in terms of the Structural Similarity Index (SSIM) with the best performing methods that rely on trained deep learning models. On the other hand, it is clearly inferior to them, for urban themed images and in terms of all metrics, especially for the Mean-Squared-Error (MSE). In addition, qualitative evaluation of the proposed approach is performed using the Perceptual Index metric, which has been introduced to better mimic the human perception of the image quality. This evaluation favors our approach when compared to the best performing method that requires no training, even if they perform equally in qualitative terms, reinforcing the argument that MSE is not always an accurate metric for image quality.