CONVERGENCE OF EM IMAGE-RECONSTRUCTION ALGORITHMS WITH GIBBS SMOOTHING

Recent modifications of the EM emission reconstruction algorithm to include a Gibbs prior promise smoother, more appealing images. These priors incorporate nearest neighbor interactions that penalize large deviations in parameter estimates for adjacent pixels. In this context, Green has defined an OSL (one step late) algorithm that retains the E-step of the EM algorithm, but provides an approximate solution to the M-step. Further modifications of the OSL algorithm guarantee convergence to the unique maximum of the log posterior function. The present paper proves convergence under a specific set of sufficient conditions. Several of these conditions concern the potential functions of the Gibbs prior, and a number of new, candidate potential functions are identified. Generalization of the OSL algorithm to transmission tomography is also considered.