Face hallucination is to synthesize a high-resolution facial image from a low-resolution input.A novel two-step approach to hallucinating faces based on the MAP criterion is presented in this paper.First

a linear relationship between high-resolution and low-resolution facial images is established by applying PCA on both of them

and the global image

which is similar to the original high-resolution image

is reconstructed based on the MAP criterion.Second

a linear model between the residual image (the difference between the original image and the global image) and the low-resolution residual image (the difference between the low-resolution input and the manually down-sampled global image) is built

and

following a MRF prior

the optimal residual image is estimated based on the MAP criterion again.Experiments demonstrate that our approach can be applied to yield 4-8 fold super-resolution with high-quality hallucinated results.