Noise robust face hallucination via locality-constrained representation

Recently, position-patch based approaches have been proposed to replace the probabilistic graph-based or manifold learning-based models for face hallucination. In order to obtain the optimal weights of face hallucination, these approaches represent one image patch through other patches at the same position of training faces by employing least square estimation or sparse coding. However, they cannot provide unbiased approximations or satisfy rational priors, thus the obtained representation is not satisfactory. In this paper, we propose a simpler yet more effective scheme called Locality-constrained Representation (LcR). Compared with Least Square Representation (LSR) and Sparse Representation (SR), our scheme incorporates a locality constraint into the least square inversion problem to maintain locality and sparsity simultaneously. Our scheme is capable of capturing the non-linear manifold structure of image patch samples while exploiting the sparse property of the redundant data representation. Moreover, when the locality constraint is satisfied, face hallucination is robust to noise, a property that is desirable for video surveillance applications. A statistical analysis of the properties of LcR is given together with experimental results on some public face databases and surveillance images to show the superiority of our proposed scheme over state-of-the-art face hallucination approaches.