Detector response models for statistical iterative image reconstruction in high resolution PET

One limitation in a practical implementation of statistical iterative image reconstruction is to compute a transition matrix accurately modeling the relationship between projection and image spaces. Detector response function (DRF) in positron emission tomography (PET) is broad and spatially-variant, leading to large transition matrices taking too much space to store. In this work, we investigate the effect of simpler DRF models on image quality in maximum likelihood expectation maximization reconstruction. We studied 6 cases of modeling projection/image relationship: tube/pixel geometric overlap with tubes centered on detector face; same as previous with tubes centered on DRF maximum; two different fixed-width Gaussian functions centered on DRF maximum weighing tube/pixel overlap; same as previous with a Gaussian of the same spectral resolution as DRF; analytic DRF based on linear attenuation of gamma-rays in detector arrays weighing tube/pixel overlap. We found that DRF oversimplification may affect visual image quality and image quantification dramatically, including artefact generation. We showed that analytic DRF yielded images of excellent quality for a small animal PET system with long, narrow detectors and generated a transition matrix for 2-D reconstruction that could be easily fitted into the memory of current stand-alone computers.