title: Single Image Superresolution via Directional  Group Sparsity and Directional Features.
abstract: Single image superresolution (SR) aims to construct a high-resolution version from a single low-resolution (LR) image. The SR reconstruction is challenging because of the missing details in the given LR image. Thus, it is critical to explore and exploit effective prior knowledge for boosting the reconstruction performance. In this paper, we propose a novel SR method by exploiting both the directional group sparsity of the image gradients and the directional features in similarity weight estimation. The proposed SR approach is based on two observations: 1) most of the sharp edges are oriented in a limited number of directions and 2) an image pixel can be estimated by the weighted averaging of its neighbors. In consideration of these observations, we apply the curvelet transform to extract directional features which are then used for region selection and weight estimation. A combined total variation regularizer is presented which assumes that the gradients in natural images have a straightforward group sparsity structure. In addition, a directional nonlocal means regularization term takes pixel values and directional information into account to suppress unwanted artifacts. By assembling the designed regularization terms, we solve the SR problem of an energy function with minimal reconstruction error by applying a framework of templates for first-order conic solvers. The thorough quantitative and qualitative results in terms of peak signal-to-noise ratio, structural similarity, information fidelity criterion, and preference matrix demonstrate that the proposed approach achieves higher quality SR reconstruction than the state-of-the-art algorithms.
authors.forename: Xiaoyan
authors.initials: X
authors.lastname: Li
authors.forename: Hongjie
authors.initials: H
authors.lastname: He
authors.forename: Ruxin
authors.initials: R
authors.lastname: Wang
authors.forename: Dacheng
authors.initials: D
authors.lastname: Tao