Self-similarity Regularized Sparse Representation For Image Super-resolution

In our everyday life, images are everywhere and essential. Due to the limitations of imaging hardware, we cannot obtain desired high-resolution images. Improving the imaging hardware system to increase image resolution can be prohibitively expensive. Therefore, using digital image processing technologies to improve image resolution has a very important practical significance. The technique of super-resolution image reconstruction is one of the economical and effective ways to address this issue. Image super-resolution refers to the class of methods that use one or a set of low-resolution images to generate a highresolution image. Image super-resolution has been widely used in military imaging, personal image processing, medical image processing, public security, computer vision and other fields, and it has attracted broad interest from researchers in different communities.Firstly, we introduce the sparse representation model and its basic principles. Several classical matrix decomposition algorithms, dictionary construction methods, as well as the characteristics of various algorithms in sparse representation theory have been discussed and analyzed.Secondly, we analyze the classical image super-resolution algorithm based on sparse representation in detail. In the proposed joint dictionary training, the sparse representation is required to guarantee the reconstruction for both low- and high-resolution image reconstructions. However, in testing, only the low-resolution input is known, and the obtained sparse coefficients can only satisfy the reconstruction requirement for lowresolution input, but there is no guarantee that the coefficients are optimal for high-resolution reconstruction. To address this problem, we propose a novel self-similarity regularized sparse representation for image super-resolution. We use images self-similarity to obtain an approximate high-resolution image patch corresponding to the input low-resolution image patch as a prior, and then we solve the sparse coefficients that satisfies the constraints of prior high- and low-resolution input patches, which is consistent with joint dictionary training and improves the quality of the reconstructed image.Finally, because the image super-resolution algorithm via sparse representation is computationally expensive, we first reduce the complexity of the algorithm by classifying image patches into different categories based on patch variance and process them differently.Then, we propose a fast approximate sparse representation algorithm based on neural network that can greatly reduce the time complexity of the original L1 optimization. We apply our algorithm in several practical applications. It is proved through experiments that the algorithm can notably improve image quality and has great potential value in different practical applications.