Single image super-resolution with non-local balanced low-rank matrix restoration

Single image super-resolution (SR) has gained popularity to construct a high-resolution (HR) image from a single low-resolution (LR) version. More recently, non-local self similarity (NSS) has been attracted enormous interests in the field of SR, and the non-local means (NLM)-based methods are classical NSS-based SR methods. However, NLM-based methods neglect the structure information in the patches and structural similarity between patches, so it will be prone to introduce unexpected details into resultant HR images. In this paper, we propose a non-local balanced low rank matrix restoration model (NB-LRM) to improve the performance of SR which will overcome the drawbacks of NLM-based methods and take full advantage of the NSS prior. The proposed algorithm formulates the constrained optimization problem for HR image recovery. First, to take advantage of the local structure in the patch and the structural similarity between the non-local similar patches, we propose a measurement of the similarity based on both Euclidean distance and Pearson distance, then reconstruct the target patch by weighted average the similar patches. Second, to guarantee the structural similarity and linear correlation between the target patch and similar patches, we propose a new low rank regular term. Third, we introduce the iterative low rank regular algorithm to solve our model. Addition, this method doesn't need other image priors and can produce more robust reconstruction of image local structures. Compared with state-of-the-art SR methods, the proposed NB-LRM method achieves highly competitive PSNR and SSIM result, while demonstrating better edge and texture preservation performance.