Convergence of EM image reconstruction algorithms with Gibbs smoothing

P.J. Green has defined an OSL (one-step late) algorithm that retains the E-step of the EM algorithm (for image reconstruction in emission tomography) 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. Convergence is proved under a specific set of sufficient conditions. Several of these conditions concern the potential function of the Gibb's prior, and a number of candidate potential functions are identified. Generalization of the OSL algorithm to transmission tomography is also considered.