Abstract
Row-action algorithms were developed as faster alternative to the conventional expectation-maximization (EM) algorithm for maximizing the Poisson likelihood function of statistical image reconstruction in positron emission tomography. The major advantage of row-action algorithms is the use of a relaxation parameter that controls the amount of image updates during reconstruction process. This unique characteristic makes row-action algorithm sharing the similar convergence rate as ordered subset expectation-maximization (OSEM) algorithm, while maintaining better stability. However, the selection of appropriate relaxation parameter depends on many physical factors. In this research, we propose a novel flexible number generation scheme for relaxation parameter. The idea is to incorporate a pre-conditioned matrix, approximating the Hessian matrix of the objective function, into the original reconstruction algorithm so that the original likelihood function will become more well-condition. This step can also alleviate the difficulty in selecting initial value of the relaxation parameter. We then adopt the relaxation sequence suggested by Tanaka and Kudo for stable convergence. Experimental results indicate that the proposed relaxation scheme for row-action algorithms can achieve stable convergence for larger subsets, while the corresponding OSEM algorithms fail to converge.