Maximum-likelihood reconstruction of transmission images in emission computed tomography via the EM algorithm

The expectation-maximization (EM) algorithm for computing maximum-likelihood estimates of transmission images in positron-emission tomography (PET) (see K. Lange and R. Carson, J. Comput. Assist. Tomogr., vol.8, no.2, p.306-16, 1984) is extended to include measurement error, accidental coincidences and Compton scatter. A method for accomplishing the maximization step using one step of Newton's method is proposed. The algorithm is regularized with the method of sieves. Evaluations using both Monte Carlo simulations and phantom studies on the Siemens 953B scanner suggest that the algorithm yields unbiased images with significantly lower variances than filtered-backprojection when the images are reconstructed to the intrinsic resolution. Large features in the images converge in under 200 iterations while the smallest features required up to 2,000 iterations. All but the smallest features in typical transmission scans converge in approximately 250 iterations. The initial implementation of the algorithm requires 50 sec per iteration on a DECStation 5000.