title: Statistical modeling and reconstruction of randoms precorrected PET data.
abstract: Randoms precorrected positron emission tomography (PET) data is formed as the difference of two Poisson random variables. Its exact probability mass function (PMF) is inconvenient for use in likelihood-based iterative image reconstruction as it contains an infinite summation. The shifted Poisson model is a tractable approximation to this PMF but requires that negative values are truncated, resulting in positively biased reconstructions in low count studies. Here we analyze the properties of the exact PMF and propose a simple but accurate approximation that allows negative valued data. We investigate the properties of this approximation and demonstrate its application to penalized maximum likelihood image reconstruction.
authors.affiliation: Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089 USA.
authors.forename: Quanzheng
authors.initials: Q
authors.lastname: Li
authors.forename: Richard M
authors.initials: RM
authors.lastname: Leahy
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D016208:Databases, Factual; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D049268:Positron-Emission Tomography / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity