Constrained Maximum Entropy Methods in an Image Reconstruction Problem

Abstract

Maximum entropy and maximum likelihood methods are compared for a simplified version of a medical imaging problem. Iterative reconstructions are tracked by plotting successive values of log-likelihood and entropy, and we find a tradeoff between these two measures of fit. Maximum likelihood is found to fit the data more closely, but maximum entropy creates more reasonable images. We conclude that the former uses the data efficiently, but the latter gives a better choice of image. This reasoning leads to a somewhat Bayesian version of the constrained maximum entropy method of Gull and Daniell (1978). The constraint of that method is interpreted from a Bayesian perspective.

Much of this paper derives from helpful comments by Donald Rubin and Stephen Ansolabehere. This research was supported by a U.S. National Science Foundation graduate fellowship.