Abstract Face super-resolution refers to inferring the high-resolution face image from its low-resolution one. In this paper, we propose a parts-based face hallucination framework which consists of global face reconstruction and residue compensation. In the first phase, correlation-constrained non-negative matrix factorization (CCNMF) algorithm combines non-negative matrix factorization and canonical correlation analysis to hallucinate the global high-resolution face. In the second phase, the High-dimensional Coupled NMF (HCNMF) algorithm is used to compensate the error residue in hallucinated images. The proposed CCNMF algorithm can generate global face more similar to the ground truth face by learning a parts-based local representation of facial images; while the HCNMF can learn the relation between high-resolution residue and low-resolution residue to better preserve high frequency details. The experimental results validate the effectiveness of our method.