A PRIMAL-DUAL ITERATIVE ALGORITHM FOR A MAXIMUM-LIKELIHOOD-ESTIMATION PROBLEM

The duality between maximum likelihood and entropy maximization problems is used to provide a primal-dual method for solving a maximum likelihood estimation problem arising from Positron Emission Tomography. We prove convergence of our algorithm from the fact that the sequence it generates can be seen as the dual sequence produced by the hybrid version of Bregman's method when applied to a linearly constrained convex program with a Burg's entropy type objective function. This algorithm is shown to be closely connected to the so called Expectation Maximization (EM) algorithm.