Face Hallucination via Trend-Constrained Regularization

Sparse representation based face hallucination methods only utilize generic sparsity prior irrespective of the fact that the near bases in dictionary do make a greater contribution to patch reconstruction. Consequently, they cannot provide satisfactory hallucinated results in terms of accuracy and noise robustness. In this paper, instead of modifying the existing l 1 norm regularization, we propose a completely novel trend-constrained regularization method by exploiting a priori known as shape trend regarding coefficient and similarity curves. In particular, this method explicitly encourages the unknown coefficient curve to follow the shape variation trend of a predetermined similarity curve by means of maximizing their correlation. Owning to the differentiability of the underlying model, both the solution and regularization parameter can be analytically tractable, thus avoiding complex numerical optimization. Based on the observation on distance statistics, we further devise two optimal similarity functions in the form of power and exponential kernel functions. The proposed method boosts face hallucination performance considerably compared with the state-of-the-art methods. Experiments on commonly used face database demonstrate its effectiveness.