Super-resolution of single image aims to reconstruct its high-resolution version from a single low-resolution image. The existing reconstruction methods are inadequate in edge preservation and edge artifact suppression. In this paper, we propose a new SR method based on the sparsity along the directions of image gradients and the similarity of directional features. First, the Directionlet transform is used to extract the directional features of the image; then the directional total variation regular terms and the similarity weight calculation of the non-local mean are applied to the extracted directional features, resulting in that the detailed features of the image can be preserved effectively and the edge artifacts can be suppressed better. Finally, we use a framework of templates for first-order conic solvers with an energy function of minimal error to reconstruct the SR image. Experimental results show that our method that the superiority of our proposed method over the state-of-the-art algorithms.
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