A ROW-ACTION ALTERNATIVE TO THE EM ALGORITHM FOR MAXIMIZING LIKELIHOODS IN EMISSION TOMOGRAPHY

The maximum likelihood (ML) approach to estimating the radioactive dis tribution in the body cross section has become very popular among rese archers in emission computed tomography (ECT) since it has been shown to provide very good images compared to those produced with the conven tional filtered backprojection (FBP) algorithm. The expectation maximi zation (EM) algorithm is an often-used iterative approach for maximizi ng the Poisson likelihood in ECT because of its attractive theoretical and practical properties. Its major disadvantage is that, due to its slow rate of convergence, a large amount of computation is often requi red to achieve an acceptable image. In this paper we present a row-act ion maximum likelihood algorithm (RAMLA) as an alternative to the EM a lgorithm for maximizing the Poisson likelihood in ECT. We deduce the c onvergence properties of this algorithm and demonstrate by way of comp uter simulations that the early iterates of RAMLA increase the Poisson likelihood in ECT at an order of magnitude faster that the standard E M algorithm. Specifically, we show that, from the point of view of mea suring total radionuclide uptake in simulated brain phantoms, iteratio ns 1, 2, 3, and 4 of RAMLA perform at least as well as iterations 45, 60, 70, and 80, respectively, of EM. Moreover, we show that iterations 1, 2, 3, and 4 of RAMLA achieve comparable likelihood values as itera tions 45, 60, 70, and 80, respectively, of EM. We also present a modif ied version of a recent fast ordered subsets EM (OS-EM) algorithm and show that RAMLA is a special case of this modified OS-EM. Furthermore, we show that our modification converges to a ML solution whereas the standard OS-EM does not.