| Positron emission tomography (PET) is a medical imaging method used to access physiology and patho-physiology of living organisms by determining the distribution of positron-emitting pharmaceuticals. This distribution is determined by detecting anti-colinear annihilation (coincidence) photons through the light produced by the interaction of the annihilation photons with a pixelated scintillation crystal.;Current PET systems are capable of providing high-resolution (less than 5 mm) images. Efficient algorithms are needed to process the increasingly larger data sets in a timely manner, while improving the quantitative accuracy.;We develop efficient analytic and Monte-Carlo simulators of PET data. Simulation enables one to perform controlled experiments with known truth to validate newly-developed data processing algorithms. Statistical algorithms are developed to accurately estimate the interaction positions of the coincidence photons in the PET detector modules. We also develop an extremely efficient analytical image reconstruction algorithm.;We provide a discussion of the physical models, the mathematical development, and the implementation of our simulation, image reconstruction, and interaction position algorithms. Performance metrics are measured with each of the algorithms we develop and are compared to previously-developed methods with both simulated and real measured data. |
