Abstract: Face hallucination reconstruction refers to the process of reconstructing high-resolution enhanced face from a low-resolution image.Most of the traditional methods assume that the input image is aligned and noise-free.However,the super resolution performance will decrease when the input facial image is unaligned and affectedby noise.This paper proposed an effective single image super resolution method for unaligned face images,in which the learning-based hierarchical clustering regression approach is used to get better reconstruction model.The proposed face hallucination methodcan be divided into clustering and regression.In the clustering part,a dictionary is trained on the whole face image with tiny size,and the training images are clustered based on the Euclidean distance.Thus,the facial structural prior is fully utilized and the accurate clustering result can be obtained.In the regression part,to reduce the time complexity effectively,only one global dictionary needs to be trained during the entire training phase whose atoms are taken as the anchors.In particular,the learned anchors are shared with all the clusters.For each cluster,the Euclidean distance is used to search the nearest neighbors for each anchor to form the subspace.Moreover,in every subspace,a regression model is learned to map the relationship between low-resolution features and high-resolution samples.The core idea of this method is to utilize the same anchors but different samples for clusters to learn the local mapping more accurately,which can reduce training time and improve reconstruction quality.The results of comparative experiments with other algorithms show that the PSNR can be increased by at least 0.39 dB and the SSIM can be increased by 0.01 to 0.18

Key words: Euclidean distance, Face hallucination, Hierarchical, Regression, Super resolution