On Iterative Bayes Algorithms for Emission Tomography

Abstract

In this paper we formulate a new approach to medical image reconstruction from projections in emission tomography. This approach conceptually differs from the traditional methods such as filtered backprojection, maximum likelihood or maximum penalized likelihood. Similar to the Richardson-Lucy algorithm ([1], [2]), our method develops directly from the Bayes formula with the final result being an iterative algorithm, for which the maximum likelihood expectation-maximization of [3] (or [4]) is a special case. Although there are different ways to enforce smoothness in the reconstructions using this method, in this paper we opt to focus only on the way which smoothes the camera bin measurements before reconstruction. In fact, this method can be explicated as maximizing a special penalized log-likelihood function. Its theoretical properties are also analyzed in the paper.

Algorithms for Non-Negatively Constrained Maximum Penalized Likelihood Reconstruction in Tomographic Imaging

“…. , p. It has been pointed out in [23,30] that formula (15) can also be explained by the Bayes conditional probability formula. This EM algorithm possesses the following properties making it attractive for emission tomography; they are:…”