Accelerated strategy for the MLEM algorithm

Article type: Research Article

Authors: Zheng, Xuan | Qu, Gangrong^{; *} | Zhou, Jiajia

Affiliations: School of Science, Beijing Jiaotong University, Beijing, China

Correspondence: [*] Corresponding author: Gangrong Qu, School of Science, Beijing Jiaotong University, Beijing 100044, China. E-mail: grqu@bjtu.edu.cn.

Abstract: BACKGROUND:A statistical method called maximum likelihood expectation maximization (MLEM) is quite attractive, especially in PET/SPECT. However, the convergence rate of the iterative scheme of MLEM is quite slow. OBJECTIVE:This study aims to develop and test a new method to speed up the convergence rate of the MLEM algorithm. METHODS:We introduce a relaxation parameter in the conventional MLEM iterative formula and propose the relaxation strategy on the condition that the spectral radius of the derived iterative matrix from the iterative scheme with the accelerated parameter reaches a minimum value. RESULTS:Experiments with Shepp-Logan phantom and an annual tree image demonstrate that the new computational strategy effectively accelerates computation time while maintains reasonable image quality. CONCLUSIONS:The proposed new computational method involving the relaxation strategy has a faster convergence speed than the original method.

Keywords: MLEM algorithm, convergence rate, relaxation strategy, image reconstruction

DOI: 10.3233/XST-200749

Journal: Journal of X-Ray Science and Technology, vol. 29, no. 1, pp. 135-149, 2021