List-mode likelihood: EM algorithm and image quality estimation demonstrated on 2-D PET

Using a theory of list-mode maximum-likelihood (ML) source reconstruction presented recently by Barrett et al. (1997), this paper formulates a corresponding expectation-maximization (EM) algorithm, as well as a method for estimating noise properties at the ML estimate. List-mode ML is of interest in cases where the dimensionality of the measurement space impedes a binning of the measurement data. It can be advantageous in cases where a better forward model can be obtained by including more measurement coordinates provided by a given detector. Different figures of merit for the detector performance can be computed from the Fisher information matrix (FIM). This paper uses the observed FIM, which requires a single data set, thus, avoiding costly ensemble statistics. The proposed techniques are demonstrated for an idealized two-dimensional (2-D) positron emission tomography (PET) [2-D PET] detector. The authors compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta.