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., 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. We compute from simulation data the improved image quality obtained by including the time of flight of the coincident quanta.
Imaging and Visualization, Siemens Corporate Research, Princeton, NJ 08540, USA. lparra@sarnoff.com
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D000465:Algorithms; D016477:Artifacts; D003198:Computer Simulation; D005240:Feasibility Studies; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods / Q000706:statistics & numerical data; D016013:Likelihood Functions; D008954:Models, Biological; D016011:Normal Distribution; D019047:Phantoms, Imaging; D016012:Poisson Distribution; D011336:Probability; D014055:Tomography, Emission-Computed / Q000379:methods / Q000706:statistics & numerical data*