submitted to Physics in Medicine and Biology An Accelerated Convergent Ordered Subsets Algorithm for Emission Tomography

Abstract. We propose an algorithm, E-COSEM (Enhanced Complete-Data Ordered Subsets Expectation-Maximization) for fast maximum likelihood (ML) reconstruction in emission tomography. E-COSEM is founded on an incremental EM approach. Unlike the familiar OSEM (ordered subsets EM) algorithm which is not convergent, we show that E-COSEM converges to the ML solution. Alternatives to OSEM include RAMLA, and for the related maximum a posteriori (MAP) problem, the BSREM and OS-SPS algorithms. These are fast and convergent, but require a judicious choice of a user-specified relaxation schedule. E-COSEM itself uses a sequence of iterationdependent parameters (very roughly akin to relaxation parameters) to control a tradeoff between a greedy, fast but non-convergent update and a slower but convergent update. These parameters are computed automatically at each iteration and require no user specification. For the ML case, our simulations show that E-COSEM is nearly as fast as RAMLA