Detector response restoration for high resolution positron emission tomography

A mathematical method was studied to model the detector response of high-spatial-resolution positron emission tomography systems consisting of close-packed small crystals, and to restore the resolution deteriorated due to crystal penetration and/or nonuniform sampling across the field of view (FOV). The simulated detector system has 600 bismuth germanate crystals of 3.14 mm width and 3 cm length packed on a single ring of 60 cm diameter. The space between crystals was filled up with lead (i.e., septa). Each crystal was in coincidence with 200 opposite crystals so that the FOV had a radius of 30 cm. The detector response was modeled based on the attenuating properties of the crystals and the septa, and the geometry of the detector system. The modeled detector response function was used to restore the projections from the sinogram of the ring detector system. The projections had a uniform sampling of 1.57 mm across the FOV and had the crystal penetration and/or the nonuniform sampling compensated. A chest phantom with a few small circular cold objects (≈4 mm diameter) located at the center and near the periphery of the FOV was computer-generated and used to test the restoration. The reconstructed images from the restored projections demonstrated resolution improvement off the FOV center, while preserving the resolution near the center