Count-level Dependent Image Domain PSF Kernel Width Selection for Fully 3D PET Image Reconstruction

we present an image-domain point spread function (PSF) modeling approach for resolution recovery where spatially varying PSF kernel widths are adjusted based on data quality. This approach attempts to maximize contrast recovery while minimizing edge artifacts (ringing) associated with PSF modeling. We choose broader PSF kernels for noisier datasets where the extent of ringing is comparable to noise standard deviation levels and therefore result in minimal visible ringing artifacts. Similarly, we choose narrower, under-modeled PSF kernels for high count datasets to avoid edge artifacts associated with broader kernels which would have been visible at low image noise levels. We quantify ringing by measuring the difference between the highest overshoot and lowest undershoot levels around the mean background activity level. We define "visible ringing" by the difference between ringing and twice the background standard deviation and use it as our primary metric for measuring artifact levels. We show through simulations that broader PSF kernels can be used for noisier datasets with minimal visible ringing for improved contrast recovery. We use these results to determine the broadest PSF kernel widths to be used at each count level to achieve the highest level of contrast recovery with minimal visible ringing.