PERFORMANCE EVALUATION OF AN ITERATIVE IMAGE-RECONSTRUCTION ALGORITHM FOR POSITRON EMISSION TOMOGRAPHY

We discuss an image reconstruction method motivated by positron emission tomography (PET). The measurements tend to be noisy and so the reconstruction method should incorporate the statistical nature of the noise. We set up a discrete model to represent the physical situation and arrive at a nonlinear maximum a posteriori probability (MAP) formulation of the problem. Previously published iterative procedures for this maximization problem involve the solution of 10(4)-10(5) coupled quadratic equations at each iterative step. In this paper an alternative iterative approach, which requires the solution of simple (not coupled) quadratic equations, is motivated and proposed. The method decomposes naturally for parallel computing. We also present a methodology which allows us to experimentally optimize an image reconstruction method for a specific medical task and to evaluate the relative efficacy of two reconstruction methods for a particular task in a manner which meets the high standards set by the methodology of statistical hypothesis testing. We illustrate this by comparing, in the area of PET, the new MAP algorithm to a method which maximizes likelihood and with two variants of the filtered backprojection method. We find that the relative performance of techniques is extremely task dependent, with the new method superior to the others from the point of view of pointwise accuracy, but not from the points of view of two other PET-related figures of merit. In particular, we find that, in spite of the very noisy appearance of the reconstructed images, the maximum likelihood method outperforms the others from the point of view of estimating average activity in individual neurological structures of interest.