This paper describes a new single-image super-resolution algorithm based on sparse representations with image structure constraints. A structure tensor based regularization is introduced in the sparse approximation in order to improve the sharpness of edges. The new formulation allows reducing the ringing artefacts which can be observed around edges reconstructed by existing methods. The proposed method, named Sharper Edges based Adaptive Sparse Domain Selection (SE-ASDS), achieves much better results than many state-of-the-art algorithms, showing significant improvements in terms of PSNR (average of 29.63, previously 29.19), SSIM (average of 0.8559, previously 0.8471) and visual quality perception.