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Super-resolution from a single image plays an important role in many computer vision systems. However, it is still a challenging task, especially in preserving local edge structures. To construct high-resolution images while preserving the sharp edges, an effective edge-directed super-resolution method is presented in this paper. An adaptive self-interpolation algorithm is first proposed to estimate a sharp high-resolution gradient field directly from the input low-resolution image. The obtained high-resolution gradient is then regarded as a gradient constraint or an edge-preserving constraint to reconstruct the high-resolution image. Extensive results have shown both qualitatively and quantitatively that the proposed method can produce convincing super-resolution images containing complex and sharp features, as compared with the other state-of-the-art super-resolution algorithms.