Improved Line-of-Response Allocation for Inter-Crystal Compton Events in PET

In a PET detector, a gamma ray interacts through photoelectric absorption or Compton scattering. To locate the gamma ray direction for the line-of-response, the flood map of the detector was used. The flood map typically consists of the energy centroid of gamma ray events distributed in two-dimensional space. Based on the flood map, a crystal identification map was drawn and all gamma ray events around a crystal peak were allocated to the corresponding crystal. This has been done for both photoelectric and Compton events. However, this is mostly not correct for those inter-crystal Compton scatters. Since 511keV has higher probability in the forward scattering, it deposits more energy in the second interaction than the first. When the deposited energies were weighted to identify the direction of the gamma ray, the second interaction or second crystal gets more weight and so, assigned for the line-of-response, which is not correct. In short, the energy centroid method misallocates most of inter-crystal Compton scatters to wrong crystals. In this paper, we investigate the amount of misallocation on two different crystal geometries and propose an algorithm to improve its allocation.