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Learning-based super-resolution (SR) methods are popular in many applications recently. In these methods, the high-frequency details are usually found or combined through patch matching from training database. However, the representation ability of small patch is limited and it is difficult to guarantee that the super-resolved image is the best under the global view. To this end, the authors propose a statistical learning method for SR with both global and local constraints. More specifically, they introduce a mixture model into maximum a posteriori (MAP) estimation, which combines a global parametric constraint with a patch-based local non-parametric constraint. The global parametric constraint guarantees the super-resolved global image to agree with the sparse property of natural images, and the local non-parametric constraint is used to infer the residues between the image derived from the global constraint and the ground truth high-resolution (HR) image. Compared with the traditional patch-based learning methods without the global constraint, our method can not only preserve global image structure, but also restore the local details more effectively. Experiments verify the effectiveness of the proposed method.