AN EXPECTATION MAXIMIZATION RECONSTRUCTION ALGORITHM FOR EMISSION TOMOGRAPHY WITH NONUNIFORM ENTROPY PRIOR

A Bayesian image reconstruction algorithm is proposed for emission tom ography. It incorporates the Poisson nature of the noise in the projec tion data and uses a non-uniform entropy as an a priori probability di stribution of the image in a maximum a posteriori (MAP) approach. The expectation maximization (EM) method was applied to find the MAP estim ator. The Newton-Raphson numerical method whose convergence and positi ve solutions are proven, was used to solve the EM problem. The prior m ean at iteration k was determined by smoothing the image obtained at i teration k-1. Comparisons between the ML and the MAP algorithm were ca rried out with a numerical phantom that contains a narrow valley regio n. The ML solution after 50 iterations was chosen as the initial solut ion for the MAP algorithm, since the global performance of the ML algo rithm deteriorates with increasing number of iterations while its loca l performance in the valley region is always improving. The resulting algorithm is a compromise between ML who has the best local performanc e in the valley region and the MAP who has the best global performance .