Fast Algorithms For Compressive Sensing Image Restoration Based On Total Variation Model

In order to improve the quality of the image, the task of image reconstruction isto construct model, use some numerical methods, restore or recovery the original image.In this thesis, we propose alternating minimization algorithm and alternating directionalgorithm for recovering the compressive sensing image based on total variation regular-ization optimization model. We analyze the algorithms’ convergence properties and dosome numerical experiments to show the efciency of each algorithm.In chapter1, we introduce the background and signifcance of the thesis. We briefyreview the theory of compressive sensing and total variation, and recall some recent algo-rithm for solving1-norm and total variation regularized minimization problems. More-over, we give the preliminaries of alternating direction algorithm for convex separableminimization problems, and list some notations which used in this thesis.In chapter2, based on the total variation model, we proposed double algorithms forthe compressive sensing image restoration. Both algorithms minimize the penalty functionand augmented Lagrangian function respectively. We linearize the ftting term and adda proximal point term to ensure that both subproblems have closed-form solutions. Theiterative form of both algorithms is very simple and requires a shrinkage and two matrix-vector produce at each iteration. With some mild conditions, we show that both algorithmconverges globally. Moreover, we also do some numerical experiments which show thatboth proposed algorithm are promising.In Chapter3, combining the Xiao-Yang-Yuan’s algorithm with the proposed algo-rithm in the previous chapter, we develop a hybrid linearized algorithm. At each iteration,the proposed algorithm alternatively linearized the quadratic ftting term of the aug-mented Lagrangian function. The performance comparisons illustrate that the proposedalgorithm is superior to the algorithm in the previous section.In Chapter4, we give a summary of this thesis and list some further research topics.