PET projection data supersets for reconstruction with acquisition motion

Motion during PET data acquisition is either introduced by design (e.g. couch wobble, detector rotation, bed translations) or through motion of the subject (e.g. rigid body motion of the head, respiratory motion). At present such effects are generally considered very differently in PET imaging, with intentional motion regarded as beneficial for enriching data sampling whilst subject motion is regarded as a detrimental effect to be eliminated. In this paper we propose the framework of PET projection data supersets leading to a generalisation of PET image reconstruction in the presence of any type of known acquisition motion. This could open the way to optimal and unified exploitation of all sources of motion in image reconstruction. Our work includes rigid body and elastic object motion. As such, conventional motion-compensation techniques are special cases of our proposed method. We propose different approaches for the practical implementation of the PET data superset and reveal both the connections and differences between them. Using simulated data, we demonstrate the PET data superset framework and its potential to exploit known object motion to the benefit of reconstruction.