Extension of emission expectation maximization lookalike algorithms to Bayesian algorithms

We recently developed a family of image reconstruction algorithms that look like the emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this study, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms utilizes a multiplicative update scheme. The extension of these algorithms to Bayesian algorithms is achieved by introducing a new simple factor, which contains the Bayesian information. One of the extended algorithms can be applied to emission tomography and another to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The total-variation norm is employed as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate a stable performance. A simple Bayesian algorithm can be derived for any noise variance function. The proposed algorithms have properties such as multiplicative updating, non-negativity, faster convergence rates for bright objects, and ease of implementation. Our algorithms are inspired by Green's one-step-late algorithm. If written in additive-update form, Green's algorithm has a step size determined by the future image value, which is an undesirable feature that our algorithms do not have.