Face hallucination via weighted sparse representation

By incorporating the priors of image positions, position-patch based face hallucination methods can produce high-quality results and save computation time. These methods represent the test image patch as a linear combination of the same position patches in a training dictionary, and the key issue is how to obtain the optimal coefficients. Due to stability and accuracy issues, methods based on least square estimation or sparse representation (SR) proposed so far are not satisfactory. In this paper, we improve existing SR methods by exploiting similarity between the test and training patches. In particular, we impose a similarity constraint (in terms of the distance between the test patch and bases in the dictionary) on the ℓ₁ minimization regularization term and obtain the coefficients by solving a weighted SR problem. We also provide a new prospective on weighted SR and investigate its robustness to illumination variations. Experiments on commonly used database demonstrate that our method outperforms state of the art.