An analytical scatter correction for singles-mode transmission data in PET

We present an analytical scatter correction, based upon the Klein-Nishina formula, for singles-mode transmission data in positron emission tomography (PET) and its implementation as part of an iterative image reconstruction algorithm. We compared our analytically-calculated scatter sinogram data with previously validated simulation data for a small animal PET scanner with 68 Ge (a positron emitter) and 57 Co (approximately 122-keV photon emitter) transmission sources using four different phantom configurations (three uniform water cylinders with radii of 25, 30, and 45 mm and a nonuniform phantom consisting of water, Teflon, and air). Our scatter calculation correctly predicts the contribution from single-scattered (one incoherent scatter interaction) photons to the simulated sinogram data and provides good agreement for the percent scatter fraction (SF) per sinogram for all phantoms and both transmission sources. We then applied our scatter correction as part of an iterative reconstruction algorithm for PET transmission data for simulated and experimental data using uniform and nonuniform phantoms. For both simulated and experimental data, the reconstructed linear attenuation coefficients (mu-values-values) agreed with expected values to within 4% when scatter corrections were applied, for both the 68 Ge and 57 Co transmission sources. We also tested our reconstruction and scatter correction procedure for two experimental rodent studies (a mouse and rat). For the rodent studies, we found that the average mu-values for soft-tissue regions of interest agreed with expected values to within 4%. Using a 2.2-GHz processor, each scatter correction iteration required between 6-27 min of CPU time (without any code optimization) depending on the phantom size and source used. This extra calculation time does not seem unreasonable considering that, without scatter corrections, errors in the reconstructed mu-values were between 18%-45% depending on the phantom size and transmission source used.