Accurate PET Projector Approximations using Ray-Driven Projectors with Image Domain PSF Modeling

Projectors play a critical role in accurate image reconstruction with statistical image reconstruction algorithms in emission tomography. In 3D PET reconstruction, ray-tracing based projectors have gained popularity due to their ease in implementation and speed. Since detection probabilities in PET are governed by solid angles subtended at the detectors by the voxels, there are multiple geometric effects that ray-tracing projectors ignore, and therefore their accuracy suffers. More accurate 2D and 3D projectors have been developed for PET and while they can produce more accurate reconstructions due to better system modeling, they have a much higher computational cost. one of the main reasons for higher computational cost is that many more voxels contribute to a detector pair in accurate projectors compared to ray-tracing based projectors. Image-domain point spread function (PSF) modeling is a widely used technique for resolution recovery at reasonable computational cost and can add contributions from many more voxels to a detector pair similar to what accurate projectors model. In this work, we apply image domain PSF modeling in combination with a 1D Ray-tracing pet projector with the goal of approaching the performance of a more accurate 2D projector. our experimental results show that by properly choosing the PSF kernel size, the fast, less accurate 1-d projector can be made to successfully approximate the much more accurate, overlap-based 2-D projector.