Space-variant and anisotropic resolution modeling in list-mode EM reconstruction

One issue common to PET scanners is the space-variance of the point spread function (PSF): manifesting itself as resolution degradation as one moves away from the center of the fleld-of-view (FOV). This effect occurs due to a higher probability of inter-crystal penetration with higher angles of radiation incident on crystal fronts. Depth-of-interaction (DOI) encoding is known to improve this problem, but has not reached complete space-invariance. In this work, a space-variant PSF has been incorporated into the system matrix of a list-mode EM algorithm. Furthermore, in an effort to further extend generality and accuracy of the model, anisotropicity of the PSF has also been considered: finite resolution effects at any position in the FOV are allowed to have distinct values along the axial and the two transaxial directions, and are allowed to degrade differently with increasing distance from the center of the FOV. The spatial distribution of image resolution has been measured and fit using exponential and inverse-Gaussian functions. It is shown that the proposed modeling of the PSF, compared to space-invariant and isotropic modeling, improves resolution recovery across the FOV.