Statistical models for PET and SPECT data

This article outlines the statistical developments that have taken place in emission tomography during the past decade or so. We discuss the statistical aspects of the modelling of the projection data and define the additive Poisson regression model. This leads to the use of the method of maximum likelihood as a means of estimating the underlying isotope concentration within a given region of a patient's body, and to the use of the EM algorithm to compute the reconstruction. The need for the regularization of the maximum likelihood solution is tackled using Bayesian techniques. A number of algorithms for the computation of regularized solutions are outlined. The issue of parameter estimation is discussed and some open issues are mentioned.