Single Image Super Resolution Based On Rank Minimization Theory

Currently，image super resolution recovery is one of the most challenging andactive area in image processing field. Because of the inherent limitations of imagesensors and the process of generating images，the image we get cannot obtain andreserve all the information of the scene. The main idea of image super resolution is togenerate high resolution images with one or several low resolution images based onsignal processing methods.Recently, motivated by the Compressive Sensing theory, a large amount ofpapers based on sparse representation are proposed in image super resolution recovery.We mainly apply matrix minimization theory to recover a high resolution image froma given single low resolution image. The main content of the paper are as follows:First, based on rank minimization theory, we propose the Compressive PrincipalComponent Pursuit model for single image super resolution recovery. This model issolved by the Augmented Lagrange Multiplier Algorithm. The nonlocal meansalgorithm used in image denoising is employed to generate approximate low rankmatrix, then the low rank matrix obtained by ALM is taken as the high resolutionimage.Second, due to the drawback of the above-mentioned model, we develop a newOutlier Pursuit model which utilizes the low rank matrix and the sparse matrixsimultaneously. The Outlier Pursuit model is solved by Accelerated ProximalGradient Algorithm. The low rank matrix and the sparse matrix obtained through thealgorithm are used as the high resolution image.Last, experimental results show the validity of the model based on rankminimization theory. Moreover, the performance of the model including the low rankmatrix and the sparse matrix simultaneously is better than the one considering the lowrank matrix only.