The EM algorithm in medical imaging

This article outlines the statistical developments that have taken place in the use of the EM algorithm in emission and transmission tomography during the past decade or so. We discuss the statistical aspects of the modelling of the projection data for both the emission and transmission cases and define the relevant probability models. This leads to the use of the method of maximum likelihood as a means of estimating the relevant unknown parameters within a given region of a patient's body and to the use of the EM algorithm to compute the reconstruction. Various different types of EM algorithm are discussed, including the SAGE algorithms of Fessler and Hero. The limitations of the EM algorithm, per se, are covered and the need for regularization is stressed. A number of different methods for penalizing the likelihood are described and a number of algorithms for the computation of the penalized EM reconstruction are discussed