On Convergence of the EMML Algorithm for PET Reconstruction

The EM-ML (expectation-maximization, maximum-likelihood) algorithm for PET rec onstruction is an iterative method. Sequence convergence to a fixed point that satisfies the Karush-Kuhn-Tucker conditions for optimality has previously been established [1, 2, 3]. This cor respondence first gives an alternative proof of sequence convergence and optimality based on d irect expansion of certain Kullback discrimination functions and a standard result in optimization theory. U sing results in series convergence, we then show that several sequences converge to 0 f as er thank → ∞, i.e., the sequences areo(k).