A Convergence Proof of MLEM and MLEM 3 With Fixed Background
Maximum likelihood expectation maximization (MLEM) is a popular algorithm to reconstruct the activity image in positron emission tomography. This paper introduces a "fundamental equality" for the MLEM complete data from which two key properties easily follow that allows us to: 1) prove in an elegant and compact way the convergence of MLEM for a forward model with fixed background (i.e. counts such as random and scatter coincidences) and 2) generalize this proof for the MLEM 3 algorithm. Moreover, we give necessary and sufficient conditions for the solution to be unique.
IEEE Transactions on Medical Imaging