Face Hallucination From New Perspective of Non-Linear Learning Compressed Sensing

The past decade has witnessed a prosperity of sparsity-inspired face hallucination methods that use sparse prior and instances to generate High-Resolution (HR) faces. However, they need numerous Low-Resolution (LR) and HR instance pairs and adopt approximate sparse coding, which will bring bias to the recovery and suffer from high computational burden. In this paper we advance a Single Face Image Hallucination (SFIH) method from a new perspective of Non-linear Learning Compressive Sensing (NLCS), which can recover HR faces from a surprisingly small number of HR faces. The nonlinear sparse coding of facial images is explored, and a Deep AutoEncoder (DAE) network is constructed for learning a kernel function from a single HR instance set. SFIH is then reduced to an analytic compressive recovery problem by reformulating linear sparse coding as a nonlinear DAE model. By exploring the nonlinear sparsity in the feature space, NLCS can accurately and rapidly recover HR facial images with large magnification factor and exhibit robustness to LR-HR instance pairs mapping. Some experiments are taken on realizing 3X, 6X, 9X amplification of face images, and the results prove its efficiency and superiority to its counterparts.