LR2-SR: Laplacian Regularized Low-Rank Sparse Representation for Single Image Super-Resolution

In this paper, we propose a single image super-resolution (SR) method based on Laplacian regularized low-rank sparse representation (LR2-SR). Low-rank strategy assumes that similar features should have similar sparse codes in SR. However, it does not make full use of the similarity between features. To overcome this defect, we construct a Laplacian matrix and incorporate a Laplacian regularization into the low-rank sparse representation for SR. The Laplacian matrix measures the similarity between features, and is used to constrain the sparse codes. Thus, we preserve the consistency between features and sparse codes. Furthermore, we utilize the Inexact Augmented Lagrange Multiplier (IALM) and gradient descent algorithm to solve the problem. Extensive experiments demonstrate the effectiveness of the proposed method both quantitatively and qualitatively compared with state-of-the-art sparse-coding based methods.