A Study On Algorithms Of Image Superresolution Based On Sparse Regularization Theory

This dissertation is a study on the image super-resolution al-gorithms. The super-resolution aims to estimate a high-resolution imagefrom one or several low-resolution observation images. The task of imagesuper-resolution is to achieve the inverse process of low-resolution imagegeneratedprocess. Thatis, itfusestheinformationoflow-resolutionimageto reconstruct the high-resolution image based on the assumption or priorknowledge of the low-resolution image generation model. However, be-cause of the lost information of input image, the super-resolution problemis an undetermined problem and the solution is not uniqueness.In this dissertation, we mainly study the interpolation-based and learn-ing based super-resolution methods, the sparse representation based, andlow-rank recovery based super-resolution methods in especial. The maincontents are as follows:1. Improve the model of solving the sparse representation coefficientsfor low-resolution image patch. This dissertation presents a new approachto recover high-resolution image based upon p(0<p <1) non-convexoptimization because the p∈(0,1) norm can yield sparser solution than1norm. Moreover, for different input image patch, the value of p and λaffect the reconstruction results. This dissertation selects the best choiceof p in (0,1) and appropriate λ for each image patch. The experimentsfurther show that the proposed p(0<p <1) regularization non-convexoptimization method outperforms the convex optimization method and cangenerate higher-quality image.2. Present a new approach to reduce the computation complexity ofclassical sparse representation based on image super-resolution method,via local structural similarity and collaborative representation. It seeks the linear representation coefficients for the low-resolution image patches by2norm regularization model. The2norm based objective function inthis paper implies an analytical solution and it does not involve local min-ima. Hence, it costs a lower complexity compared to1sparsity constraintmodel. The experimental results demonstrate that the proposed method isfeasible and effective for small size image super-resolution. Further re-search shows that the proposed method can also perform well for the largemagnification factors and noisy data.3. Research on image super-resolution methods suggests that whenthe blurring kernel is the Dirac delta function, the image super-resolutionbecomes an image interpolation problem. In this dissertation we put for-ward an efficient method to determine the order of linear model implicityby formulating the super-resolution problem as a low rank matrix comple-tion and recovery problem. In addition, the proposed method can deal withthe noisy data and random perturbation robustly. The experimental resultsshow that the proposed method is effective and competitive compared withsome other methods.