A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors

T Hebert; R Leahy

doi:10.1109/42.24868

A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors

IEEE Trans Med Imaging. 1989;8(2):194-202. doi: 10.1109/42.24868.

Authors

T Hebert¹, R Leahy

Affiliation

¹ Signal and Image Process. Inst., Univ. of Southern California, Los Angeles, CA.

PMID: 18230517
DOI: 10.1109/42.24868

Abstract

A generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction, based on locally correlated Markov random-field priors in the form of Gibbs functions and on the Poisson data model. For the M-step of the algorithm, a form of coordinate gradient ascent is derived. The algorithm reduces to the EM maximum-likelihood algorithm as the Markov random-field prior tends towards a uniform distribution. Three different Gibbs function priors are examined. Reconstructions of 3-D images obtained from the Poisson model of single-photon-emission computed tomography are presented.