Single Image Super Resolution Based On Sparse Regularization And Iterative Refinement

Image super-resolution is one of the important problems in the field of digital image processing and computer vision, and its purpose is to recover the high-resolution images via a low-resolution image or a group of image sequences. Among the image superresolution field, we focus on the single-frame image super-resolution problem. In practical applications, it usually occurs blur and jagged effect after image zooming on display devices. To solve these problems, many scholars have done much work for single-frame image super-resolution.This thesis mainly introduces the development of some classic single-frame image super-resolution methods, and analyzes these image super-resolution algorithms at first.Here, we focus on the single image super-resolution algorithm based on approximated Heaviside functions. This model first utilizes some characteristics of the approximated Heaviside functions to solve the image super-resolution problem, which uses two classes of approximated Heaviside functions as a basis to denote the smooth component and non-smooth component, respectively. And then we compute corresponding coefficients.Finally, we can get the high super-resolution image by combing these coefficients with the corresponding high super-resolution basis. The advantage of this model is that it has simple calculations and it is completely single image super-resolution method without using other training data. However, only two classes of approximated Heaviside functions can not depict the whole image information completely, such as more smooth components or more sharp components.Based on that, we propose one model which use different classes of approximated Heaviside functions to represent smooth components and non-smooth components, respectively. Likewise, taking into account the sparsity of the non-smooth components, we apply l1 regularization to every sparse coefficient. And then we solve the model via the block-wise ADMM. In addition, the new method incorporates an iterative refinement to the residuals between the original low-resolution input and the downsampled resulted image, aiming to pick up more image details. And the iterative refinement model is solved by ADMM. Finally, a large number of numerical experiments show that our methods provide more accurate when compared with some existing competitive methods.