Single Image Super-Resolution With Non-Local Balanced Low-Rank Matrix Restoration

Image super resolution reconstruction is the image processing technology to produce the image of the high-resolution from the low-resolution version which maybe a single or multi-images of the same scenes. Because of its strong practicability, image super resolution reconstruction has been widely used in aerospace, medical, meteorological,criminal investigation and so on. However, it's difficult to obtain multi-images of the same scenes, so single image super resolution will be more important which will reconstruct the high-resolution image from a single low-resolution image. Single image super-resolution reconstruction is an ill-posed inverse problem, and still facing many difficulties and challenges, so It caused great concern in the field of image processing.Up to now, there are still some drawbacks for single image super resolution methods based on non-local self similarity:(1) neglect much structure information in the local patch;(2) the similarity between patches can't be accurately measured;(3) discard the structure similarity which can reconstruct the target structure with similar patches.These papers focus on the characteristics and above problems, and pay more attention on the non-local self similarity, then propose the non-local balanced low rank matrix restoration method. The main research work includes the following aspects:First, for natural images, this paper generalizes a widely used image degradation model, and points out the key factors resulting in low-resolution image. Meanwhile, focus on the non-local means filter(NLM) based methods, this paper find some disadvantages of these methods by analyzing. To overcome these disadvantages, this paper improves the original NLM and proposes patch based NLM based on the local structure in image patches. The patch based NLM takes advantage of the local structure and structural similarity between patches to reconstruct the high-resolution image, and achieves good performances of reconstruction.Second, patch based NLM has a basis hypothesis: the target patch and its similar patches are linear related. While, this hypothesis not universally applicable to low-resolution images, so patch based NLM can't reconstruct the best images. To solve this problem, together with the low rank characteristic, this paper constructs a low rank regularization to enhance the linear correlation between target patch and its similar patches.Theoretical analysis and experiments also showed that the low rank regularization can effectively enhance the linear correlation between the target patch and its similar patchesThird, the data fidelity term together with low rank regularization will be a NP-hard problem. This paper deals with this problem by releasing low rank term with weighted nuclear norm. Then this paper explains proposed model in the MAP framework, together with the prior which indicates the larger singular values will represent more information,gives out the weight's calculation of different singular values. Last, paper test the proposed model with many test images, compared with state-of-the-art methods, the proposed NB-LRM method achieves highly competitive PSNR and SSIM results, while demonstrating better edge and texture preservation performance.