1. A system for generating higher resolution output face images from input face images, the system comprising: a convolutional neural network (CNN) that generates a face representation of an input face image, the CNN including convolution, non-linearity and down-sampling; a face hallucinator that generates a hallucinated face image from the face representation, the hallucinated face image having a higher resolution than the input face image; a coefficient estimator that generates a coefficient from the face representation; and a face combiner that combines the hallucinated face image with an up-sampled version of the input face image to produce an output face image, wherein the face combiner generates the output face image as a linear combination of the hallucinated face image and the up-sampled version of the input face image, and the coefficient determines the linear combination, wherein the output face image has more texture than the hallucinated face image.