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

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.