Accelerated Iterative Reconstruction for Positron Emission Tomography Based on the EM Algorithm for Maximum Likelihood Estimation

Abstract

The EM method that was originally developed for maximum likelihood estimation in the context of mathematical statistics may be applied to a stochastic model of positron emission tomography (PET). The result is an iterative algorithm for image reconstruction that is finding increasing use in PET, due to its attractive theoretical and practical properties. Its major disadvantage is the large amount of computation that is often required, due to the algorithm's slow rate of convergence. This paper presents an accelerated form of the EM algorithm for PET in which the changes to the image, as calculated by the standard algorithm, are multiplied at each iteration by an overrelaxation parameter. The accelerated algorithm retains two of the important practical properties of the standard algorithm, namely the selfnormalization and nonnegativity of the reconstructed images. Experimental results are presented using measured data obtained from a hexagonal detector system for PET. The likelihood function and the norm of the data residual were monitored during the iterative process. According to both of these measures, the images reconstructed at iterations 7 and 11 of the accelerated algorithm are similar to those at iterations 15 and 30 of the standard algorithm, for two different sets of data. Important theoretical properties remain to be investigated, namely the convergence of the accelerated algorithm and its performance as a maximum likelihood estimator.