Detector response restoration in image reconstruction of 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 had 600 bismuth germanate crystals of 3.14 mm width and 30 mm 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, as well as 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 restored projections had a uniform sampling of 1.57 mm across the FOV. The crystal penetration and/or the nonuniform sampling were compensated in the projections. A penalized maximum-likelihood algorithm was employed to accomplish the restoration. The restored projections were then filtered and backprojected to reconstruct the image. A chest phantom with a few small circular "cold" objects ( approximately 4 mm diameter) located at the center and near the periphery of 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.