Including pair-production events in the system response function for energy-imaging integrated deconvolution algorithm

In previous research, our group developed a gamma-ray image reconstruction method using Compton events from a 3-D position-sensitive CdZnTe detector, which is capable of deconvolving the source image at any specific energy, as well as the incident spectrum at any specific direction. This gamma-ray energy-imaging integrated deconvolution method takes place in integrated spatial and energy space using the maximum-likelihood expectation maximization (MLEM) algorithm. By including Compton scattering events in the system model, the MLEM solution estimates the incident gamma-ray spectrum in the source direction free of the Compton continuum for source energies lower than 1.02 MeV. In order to correctly reconstruct images for higher energy events, pair-production effect needs to be included in the system model. Since it is impossible to pre-calculate the system response function due to the huge number of possible recorded events, analytic formulas are derived to allow the calculation of the system response function during the reconstruction. After including pair-production events in the system response function, the deconvolved spectrum reflects the incident spectrum and is free of single and double escape peaks.