PET image reconstruction with a Bayesian projector for multi-electronic collimation schemes

We evaluated a new image reconstruction algorithm using a Bayesian projector for multi-collimation PET systems. We are developing a PET system using high spatial and energy resolution 3-D detectors made from cadmium zinc telluride with cross-strip anodes and cathodes. This PET system can collimate photon pairs by coincidence timing and can collimate single photons by the kinematics of Compton scatter within the detector (Compton collimation). Compton collimation of single photons can dramatically increase overall photon sensitivity by making use of events that are discarded by conventional PET systems. However, single photon events offer lower spatial resolution than coincidence measurements. Previously, we showed that conventional maximum likelihood reconstruction by the list- mode ordered subset expectation-maximization (OS-EM) algorithm for these "multi-collimation" data sets yields no measurable improvement over images reconstructed using high- resolution coincidence collimation alone. We also studied a Bayesian projector function with non-uniform emission probability along the line of response weighted by an image prior generated from the low-resolution (Compton collimation) channel, to reconstruct the high-resolution (coincidence) channel. In this work, we investigated a novel approach using priors generated by reconstructing images from the high-spatial resolution coincidence data followed by post-reconstruction smoothing with a new spatially varying 3-D filter function and the Perona-Malik gradient anisotropic diffusion filter.