GEM algorithm for edge-preserving reconstruction in transmission tomography from Gaussian data

The problem of edge-preserving tomographic reconstruction from Gaussian data is considered. The problem is formulated in a Bayesian framework, where the image is modeled as a pair of Markov Random Fields: a continuous-valued intensity process and a binary line process. The solution, defined as the maximizer of the posterior probability, is obtained using a Generalized Expectation-Maximization (GEM) algorithm in which both the intensity and the line processes are iteratively updated. The simulation results show that when suitable priors are assumed for the line configurations, the reconstructed images are better than those obtained without a line process, even when the number of observed data is lower. A comparison between the GEM algorithm and an algorithm based on mixed-annealing is made.