Superiorization of EM algorithm and its application in Single-Photon Emission Computed Tomography(SPECT)

Abstract

In this paper,we presented an efficient algorithm to implement the regularization reconstruction of SPECT.Image reconstruction with priori assumptionsis usually modeled as a constrained optimization problem.However, there is no efficient algorithm to solve it due to the large scale of the problem.In this paper, we used thesuperiorization of the expectation maximization (EM) iteration toimplement the regularization reconstruction of SPECT.We first investigated the convergent conditions of the EM iteration in the presence of perturbations.Secondly, we designed the superiorized EM algorithm based on the convergent conditions, and thenproposed a modified version of it.Furthermore, we gave two methods to generate desired perturbations for two special objective functions.Numerical experiments for SPECT image reconstruction were conducted to validate theperformance of the proposed algorithms.The experiments show that the superiorized EM algorithms are more stable and robust fornoised projection data and initial image than the classic EM algorithm,and outperform the classic EM algorithm interms of mean square error and visual quality of the reconstructed images.