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-273

“Statistical Modeling and Fast Bayesian Reconstruction in Positron Tomography”

by Erkan Ünal Mumcuoglu

October 1994

Conjugate gradient algorithms are described for reconstruction of transmission and emission PET images. The reconstructions are based on a Bayesian formulation where the data are modeled as a collection of independent Poisson random variables and the image is modeled using a Markov random field. A conjugate gradient algorithm is used to compute a maximum a posteriori (MAP) estimate of the image by maximizing over the posterior density. To ensure non-negativity of the solution a penalty function method and an active set type method are developed. Preconditioners are used to enhance convergence rates. These methods generally achieve effective convergence in 15-25 iterations.

A novel statistical forward PET model is presented which includes all physical characteristics of the tomographic measurement. That model also includes contributions from random and scattered coincidences. An independent maximum likelihood (ML) method to estimate mean of the randoms and a fast Klien-Nishina formula based method to estimate the mean of the scattered coincidences are developed.

Reconstructions are presented of an 18FDG whole body scan from data collected using a Siemens/CTI ECAT931 whole body system. These results indicate significant improvements in emission image quality using the Bayesian approach, in comparison to filtered backprojection, particularly when reprojections of the MAP transmission image are used in place of the standard attenuation correction factors.

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