Edge‐preserving tomographic reconstruction from gaussian data using a gibbs prior and a generalized expectation‐maximization algorithm

The problem of edge‐preserving tomographic reconstruction from Gaussian data is considered. The problem is formulated within 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 a priori information considered here enforces constraints both on the local regularity of the image and on the line configurations. 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 introducing suitable priors on the line configurations improves the quality of the reconstructed images, and is particularly useful when the data record is small. The relationships with other approaches for managing discontinuities are outlined. A comparison between the GEM algorithm and an algorithm based on mixed‐annealing is made on the basis of computer simulations.©1994 John Wiley & Sons Inc