Scatter correction for 3-D PET by convolution of plane-integral projections

The authors have studied the scatter characteristics of three-dimensional (3D) positron emission tomography (PET) in terms of the plane-integral scatter response function (SRF). To obtain the plane-integral SRF and study its properties, the authors carried out Monte Carlo simulations to generate coincidence events of a point source located at different positions in water-filled spheres of various sizes. 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 true-event plane integral of the plane in which the point source is located. For these simulations, the authors assumed a spherical PET scanner. The examination of the SRF shows that the SRF in 3D PET can be modeled not by an exponential as in the case of 2D PET, but by a Gaussian with its peak shifted away from the center of the scatter media. Using this plane-integral SRF, the authors have developed a scatter correction method for 3D PET that first converts an attenuation-corrected 3D PET data set into plane integrals, and then obtains the scatter components in the rebinned plane integrals by convolving 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, the authors reconstructed a 3D image using a 3D filtered-backprojection algorithm. To test the method, the authors simulated a cylindrical PET scanner imaging an ellipsoid phantom with a 3-cm cold bar at the center, and reconstructed 3D images of the phantom with and without scatter correction. By comparing the two images, the authors found 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