A Class Of Methods Based On LLT Model For Super-resolution Image Reconstruction

In many digital imaging applications, images with high resolution are desired and often required. However, confined by the available technicals, imaging systems pro-duce images always with a limited resolution. Low images can not meet needs. Super-resolution image reconstruction is using many low-resolution images containing differ-ent information to reconstruct the high resolution image. The pioneer work of super-resolution reconstruction may go back to 1984 by Tsai and Huang. Since then, many researchers have devoted themselves to the work in this area. The research is focused on a few points, such as high precision sub-resolution registration algorithm; robust and ef-ficient reconstruction; real-time processing techniques. The focus of this paper is robust and efficient reconstruction.In 1992, Rudin, Osher and Fatemi presented the total variation-based image restora-tion model, which is called ROF model. It can be utilized to obtain the restored image with a good quality and remove noise while preserving the edges of an image. The vari-ational partial differential equation-based image restoration methods began their rapid development process. However, the ROF model has also some shortcomings such as " staircase effects" and more complicated computation, so a lot of modified or extended models and fast calculation methods are proposed to overcome these deficiencies.In this dissertation, we mainly study how to combine a class of models with good nature-LLT model and a class of fast optimization algorithms to reconstruct a super-resolution image so that we obtain robust and efficient algorithm for reconstruction. This thesis is composed of the following four chapters.In the first chapter, the basic knowledge of super-resolution image restoration and the correlative algorithms, and the advantage of the variational PDE-based image restora-tion are briefly presented.The second chapter is devoted to introducing some basic mathematical knowledge which are theoretical foundation of the variational PDE-based super-resolution image reconstruction and the tools of calculation.In the third chapter, we first introduce Bregman iterative methods, and then propose a super resolution image reconstruction method by combining split Bregman iterative method and the LLT model. We prove the convergence of the proposed method. The numerical experiments are implemented. Experimental resluts show that the proposed method is robust and efficient. In the fourth chapter, we propose a super resolution image reconstruction method by combining the augmented Lagrangian method and the LLT model. We prove the convergence of the proposed method, and show the connection between the augmented Lagrangian method and the split Bregman method. The numerical experiments are im-plemented. Experimental resluts show that the proposed method is robust and efficient too.