Characterization and correction for scatter in 3D PET using rebinned plane integrals

The scatter characteristics of three-dimensional (3D) positron emission tomography (PET) in terms of the plane-integral scatter response function (SRF) are studied. To obtain the plane-integral SRF and study its properties, Monte Carlo simulations, were carried out which generated coincidence events from point sources located at different positions in water-filled spheres of various sizes. In each simulation, the plane-integral SRF is obtained by rebinning the detected true and scatter events into two separate sets of plane integrals and then dividing the plane integrals of scatter events by the plane integral of true events of the plane in which the point source is located. A spherical PET scanner was assumed for these simulations. Examination of the SRF shows that the SRF in 3D PET can be modeled not by an exponential function as in the case of 2D PET, but by a Gaussian with its peak shifted away from the primary peak. Using this plane-integral SRF a scatter correction method was developed for 3D PET that first converts an attenuation-corrected 3D PET data set into plane integrals, then obtains the scatter components in the rebinned plane integrals by integral transformation of the rebinned plane integrals with the SRF, and finally subtracts the scatter components from the rebinned plane integrals to yield the scatter-corrected plane integrals, From the scatter-corrected plane integrals, a 3D image was reconstructed by using a 3D filtered-backprojection algorithm. To test the method, a cylindrical PET scanner imaging an ellipsoid phantom with a 3-cm cold bar at the center was simulated, and 3D images of the phantom with and without scatter correction were reconstructed. Comparison of the two images shows that this method compensates reasonably well for scatter events. The advantages of the proposed method are that it treats the scatter in 3D PET in a truly 3D manner and that it is computationally efficient.<>