Face Hallucination via Gradient Constrained Sparse Representation

Face hallucination is an example of the image super-resolution problem, where the higher resolution face images can be obtained from the lower resolution ones. Many methods based on the sparse representation have been proposed to solve this problem. These methods use the position-patch strategy, which divides the input image into several small patches and represents each patch by the patches at the same position in the training set. An effective image prior is critical to improve the quality of the estimated super-resolution images. Thus, we try to exploit the gradient information during the patch representation to achieve better hallucination result. In this paper, we propose a novel face hallucination model based on the sparse representation, called iterative gradient constrained weighted sparse representation method. Our model incorporates both the gradient information of the images and the $l_{1}$ reweighted constraint into the sparse representation to achieve better performance. An iterative algorithm is proposed to refine these reconstructed high-resolution images. The experiments on several face databases show the better performance of our algorithm compared with other baseline algorithms.