Positron emission tomography (PET) provides insight into the physiology of living subjects and is an invaluable tool for the detection and staging of cancer. A PET scanner detects photons emitted from targeted regions inside the body and reconstructs them into images. These emission measurements are inherently noisy due to the limitations of the detection system and the physics of the decay. Consequently, this noise causes poor representations of the region of interest and ultimately complicates diagnoses. One primary method for reducing the influence of the noise is to improve the models used in the image reconstruction. This dissertation defends that the statistics of the PET measurements provide valuable information for improving the system and data model.; In particular, this work develops a successful method for estimating geometric system parameters directly from data measurements. These parameters are then used to accurately describe the system model. Along with refining the system model, this research improves the data model for rebinned PET measurements. Rebinning represents an approach for simplifying high sensitivity 3D PET data into a form that can be quickly reconstructed into a meaningful image. The proposed improved data models are incorporated into direct and statistical reconstruction algorithms, leading to techniques tailored for the statistics of rebinned measurements. Results prove that some of the new tailored methods significantly outperform conventional 2D reconstruction algorithms.
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