Data-adaptive low-rank modeling and external gradient prior for single image super-resolution

Image super-resolution (SR) is a challenging task which aims to recover the high-resolution (HR) images from the degraded low-resolution (LR) observations. To address this ill-posed problem, properly exploiting the image prior is of great importance. In this paper, we propose a data-adaptive low-rank (DLR) model. Rather than directly assuming that the rank of a group of similar patches is low, the DLR model imposes the low-rank property on the residual of the grouped patches. In addition, the shape of the patches in our DLR model is adapted to the contents of images, so that the dissimilar pixels in a group of patches can be largely reduced. In order to further boost the performance, an external gradient prior (EGP), which is learned externally to capture gradient information, is combined with DLR to form a joint prior. When solving the DLR-based and the joint-prior-based minimization problems, the split Bregman method is adopted to speed up the convergence. The extensive experimental results show that our algorithms outperform many state-of-the-art single image SR methods in terms of both objective and subjective qualities.