The Application And Research Of The OS-EM Algorithm In SPECT Image Reconstruction

In SPECT, OS-EM algorithm is a better mean to consider physical effect of system model, as well as a very effective method of the image reconstruction. However, because the actual image reconstruction process is affected by noise, the researchers propose a modified OS-EM algorithm by introducing a relaxation parameter. In dealing with reversible problems,bounds for the noise data are usually given in L~2 norm. In this paper, we mainly study the convergence of the OS-EM algorithm for exact data and explore the convergence of the loping algorithm for noisy data in L~2.This thesis is composed of four chapters as follows:· In Chapter 1, we introduce the research background and significance of SPECT, the domestic and foreign current research situation and development trends as well.·In Chapter 2, we introduce the Kullback-Leiber distance, EM algorithm, the continuous version of OS-EM algorithm, list the related lemmas as well.· In Chapter 3, we study the convergence of the OS-EM method for exact data.· In Chapter 4, we research the convergence of the loping OS-EM algorithm for noisy data in L~2.