Reconstruction of scattered and unscattered PET coincidences using TOF and energy information

In positron emission tomography (PET), a typical reconstruction algorithm relies on a method to estimate and subtract the scatter from the net trues coincidences. The remaining unscattered coincidences are then used to reconstruct an image of the original activity distribution. The introduction of time-of-flight (TOF) PET opens the possibility to change this scheme, and use the spatial information carried by the scattered events for the reconstruction. The combined knowledge of TOF difference and detected photon energy provides spatial information on the position of the source even after single scattering, and can be used for the reconstruction of scattered photons, using a 'scatter back projector' in addition to the conventional 'trues back projector'. In the scatter back projector, the scattering angle is derived from the energy of the scattered photon through Compton kinematics, and this identifies a set of possible scattering trajectories, or 'broken' line of response (LOR). The TOF information localizes the position of the source along the set of broken LOR. The advantages of this proposed method are twofold: including the spatial information about the origin of the scattered pairs could improve the image quality particularly in low count datasets; and the threshold of the energy window can be lowered to include more scatter, thus increasing sensitivity. In this work, this novel approach to scatter in PET is introduced, different implementations are discussed, and the performance of a preliminary version of the 'scatter back projector' is presented.