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

We present a scatter correction for singles-mode transmission data and its implementation as part of an iterative image reconstruction algorithm (OSTR). We compared our scatter calculation data with previously validated simulation data for three uniform water cylinders (radii of 25, 30 and 45 mm) using ⁶⁸Ge (a positron emitter) and ⁵⁷Co (122 keV photon emitter) transmission sources. Our scatter correction correctly predicts the contribution from single-scattered (one Compton interaction) photons to the sinogram data. Our correction also provides good agreement for the percent scatter fraction (SF) per sinogram for all phantom sizes and both transmission sources. We applied our scatter correction to experimental data from the microPET Focus 120 small animal scanner for three different sized uniform water cylinders and for a non-uniform phantom consisting of water, Teflon and air. The reconstructed linear attenuation coefficients (mu-values) agreed with expected values to within 4% for both the ⁶⁸Ge and ⁵⁷Co transmission sources and all phantoms. Using a 2.2 GHz processor our scatter correction requires between 7 to 20 minutes of CPU time 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 28 to 40% depending on the phantom size and transmission source used. Simple rescaling or segmentation of uncorrected mu-map images does not provide an adequate alternative to scatter correction, since these errors depend on the radial position within an image slice and can be on the order of the difference between the mu-values for water and bone.