Single image super-resolution (SR) aims at generating a plausible and visually pleasing high-resolution (HR) image from a low-resolution (LR) input. In this paper, we propose an effective single image SR algorithm by using collaborative representation and exploiting non-local self-similarity of natural images. In particular, the collaborative-representation-based method is applied to build the so-called self-projection matrices from a training set of HR images. Then the learned self-projection matrices are used to establish the collaborative-representation-based regularization (CRR), which is responsible for introducing the external HR information. Furthermore, to guarantee a reliable estimation of the HR image, the non- local low-rank regularization (NLR) which exploits internal prior of images is also taken into consideration. Since the CRR term and NLR term are complementary, they are assembled together to form a new reconstruction-based framework for SR recovery. Finally, to implement the proposed framework, an iterative algorithm is designed to gradually improve the quality of the SR results. Extensive experimental results indicate that the proposed approach is capable of delivering higher quality of SR results than several state-of-the-art SR methods.<\/strong><\/p>\n\n\n\n Index Terms\u2014Super-resolution, Collaborative representation, Non-local self-similarity Regularization.<\/strong><\/p>\n\n\n\nSource Code<\/h3>\n\n\n\n