The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-130

“A Generalized EM Algorithm for 3-D Bayesian Reconstruction from Poisson Data Using Gibbs Priors”

by Tom Hebert and Richard Leahy

June 1988

For independent Poisson observations having a complete/incomplete data representation, a generalized expectation-maximization (GEM) algorithm is developed for Bayesian reconstruction based upon locally correlated Markov random field priors in the form of Gibbs functions. For the M-step of the algorithm, a form of coordinate gradient ascent with an initial step-size resembling that of the EM likelihood algorithm is employed. Implementation closely follows that of the EM likelihood algorithm. In addition, as the prior tends towards a uniform distribution, this algorithm reduces to the EM likelihood algorithm. Three different Gibbs function priors are examined. The generalized EM Bayesian approach is applied to estimating the 3-D image parameters in the Poisson model of single photon emission computer tomography (SPECT).

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