Mathematical Analysis of Stochastic Regularization Approach for Super-Resolution Reconstruction

Traditionally, several distorting processes affect the quality of image sequences or video acquired by commercial digital cameras. Some of the more important distorting effects include warping, blurring, down sampling and additive noise. The term SRR (Super-Resolution Reconstruction) ranges from blur removal by deconvolution in single image to the creation of a single high resolution image from multiple low resolution images having relative sub-pixel displacements. In all cases, the goal of SRR is to remove the effect of possible blurring and noise in the LR images and to obtain images with resolutions that go beyond the conventional limits of the uncompensated imaging system. Thus, the major advantage of this approach is that the cost of implementation is reduced and the existing low resolution (LR) imaging systems can still be utilized. Due to the importance of SRR research and the advantages of the SRR algorithm, this article aims to review the mathematical analysis of the SRR algorithm based on stochastic regularization approaches, one of the most popular techniques introduced by the SRR research community during the last two decades. The mathematical models of SRR algorithm based on classical L1 and L2 norms with several classical regularization functions are comprehensively derived. Finally, the mathematical solutions of each case are obtained by the classical systematical approach.