Analysis And Research About The Iterative Algorithm In Image Reconstruction

The ordered subsets expectation maximization algorithm is a very important iterativemethod in image reconstruction. The advantage is that the algorithm is easy to implement.It can be used to reconstruct good image quality when the projection data are fewer. However,if the projection data contain excessive noise and the number of the subsets are divided intolarge, the blurred image is obtained by means of the algorithm and the algorithm is divergent.For this problem, we obtain a loping OSEM algorithm by introducing the relaxation parametersand apply the algorithm to the circular Radon transform operator equation in the inverse prob-lem. Numerical simulation shows that the loping OSEM algorithm is a convergent regularizationmethod for solving the inverse problem.The organization of this thesis is as follows:In Chapter1we systematically introduce the background and signifcance on studying theiterative algorithm in imaging reconstruction, discuss the status of the study and develop-ment trends in future.In Chapter2we introduce and discuss some relevant contents of the EM algorithm andthe OSEM algorithm.In Chapter3we obtain the loping OSEM algorithm and apply it to the equation whichthe operator is the circular Radon transform, we also prove weak convergence and stabilityof the loping OSEM algorithm.In Chapter4we make summary of the work as well as the prospect of the work.