I. Introduction
A major problem in positron emission tomographic imaging is the parallax error caused by the necessarily thick scintillator crystals when no depth of interaction (DOI) information is provided. It leads to event mispositioning and degrades spatial resolution for points located at large radial distances from the scanner's central axis [1]. For existing -ray imaging systems, the image quality can be improved potentially, when sufficiently good estimates for the DOI is provided by the detector [2], [3]. While other effects, for instance, mispositioning due to Compton scattering inside the scintillator, a finite positron travelling path and residual non-collinearity of the annihilation radiation, contribute uniformly to the resolution degradation, the lack of DOI leads to radial resolution loss.