The Use of Sieves to Stabilize Images Produced with the EM Algorithm for Emission Tomography

Abstract

Images produced in emission tomography with the expectation-maximization (EM) algorithm have been observed to become more 'noisy' as the algorithm converges towards the maximum-likelihood estimate. We argue in this paper that there is an instability which is fundamental to maximum-likelihood estimation as it is usually applied and, therefore, is not a result of using the EM algorithm, which is but one numerical implementation for producing maximum-likelihood estimates. We show how Grenader's method of sieves can be used with the EM algorithm to remove the instability and thereby decrease the 'noise' artifact introduced into the images with little or no increase in computational complexity.