Motion Compensation for Dynamic PET with Continuous Motion Blur

Dynamic positron emission tomography reconstructs the space-time dependence of radiotracer concentration in a human or animal body. The self-motion of the examined subject often cannot be avoided. Therefore, the motion should be measured and this information should be incorporated into the reconstruction process. The ML-EM reconstruction procedure [1] can be generalized to consider subject movement by concatenating a geometric transformation to the system matrix multiplication. However, a transformation is valid only for a single point in time, thus time frames should be short enough to allow the assumption that motion is constant within them. Fast movements, which occur in the study of neurological disorders, would require a very high number of frames, leading to unacceptable reconstruction times. To attack this problem, we re-formulate the ML-EM scheme to incorporate continuous motion during frames. Instead of a geometric transformation, we apply 3D motion blur. For efficient implementation, the paths of object-space voxels are approximated by polylines and antialiasing line drawing methods are adapted to calculate the blurred result. Having executed motion blur on the voxel array before forward projection and twice during back projection, all other components of the simulation can be reused from the dynamic reconstruction system developed without motion compensation.