Extension of emission EM look-alike algorithms to Bayesian algorithms

Recently we developed a family of image reconstruction algorithms that look like emission maximum-likelihood expectation-maximization (ML-EM) algorithm. In this paper, we extend these algorithms to Bayesian algorithms. The family of emission-EM-lookalike algorithms uses 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 can be applied to transmission tomography. Computer simulations are performed and compared with the corresponding un-extended algorithms. The totalvariation (TV) norm is used as the Bayesian constraint in the computer simulations. The newly developed algorithms demonstrate stable performance. For any noise variance function, a simple Bayesian algorithm can be derived. The proposed algorithms have properties such as multiplicative update, non-negativity, faster convergence rate for the bright objects, and ease of implementation. Our algorithms are inspired by Green’s one-step-late (OSL) algorithm. “One-step-late” is an undesirable feature. Our algorithms do not have this undesirable one-step-late feature.