Bayesian Estimator for Angle Recovery: Event Classification and Reconstruction in Positron Emission Tomography

PET at the highest level is an inverse problem: reconstruct the location of the emission (which localize biological function) from detected photons. Ideally, one would like to directly measure an annihilation photon's incident direction on the detector In the developed algorithm, Bayesian Estimation for Angle Recovery (BEAR), we utilized the increased information gathered from localizing photon interactions in the detector and developed a Bayesian estimator for a photon's incident direction. Probability distribution functions (PDFs) were filled using an interaction energy weighted mean or center of mass (COM) reference space, which had the following computational advantages: (1) a significant reduction in the size of the data in measurement space, making further manipulation and searches faster (2) the construction of COM space does not depend on measurement location, it takes advantage of measurement symmetries, and data can be added to the training set without knowledge and recalculation of prior training data, (3) calculation of posterior probability map is fully parallelizable, it can scale to any number of processors. These PDFs were used to estimate the point spread function (PSF) in incident angle space for (i) algorithm assessment and (ii) to provide probability selection criteria for classification. The algorithm calculates both the incident 0 and (/> angle, with -^16 degrees RMS in both angles, limiting the incoming direction to a narrow cone. Feature size did not improve using the BEAR algorithm as an angle filter, but the contrast ratio improved 40% on average.