Bayesian Image Reconstruction: An Application to Emission

A bayesian image reconstruction algorithm is proposed for emission tomography. It incorporates the Poisson nature of the noise in the projection data and characterizes the image to be reconstructed by an homogeneous Gauss-Markov process that can be represented by an autoregressive model. The modelling error is assumed to be a zero mean whitenoise process. The expectation maximization method is applied to find the maximum a posteriori (MAP) estimator. Comparisons between the maximum likelihood (ML) algorithm and the MAP algorithm are carried out with a numerical phantom. The porposed algorithm succeeds in overcoming the noise artefact inherent to ML and gives results superior to the best results reached by ML.