MLEM-based Reconstruction with a New Stochastic Enhancement for Compton Imaging

Considering the lack of algorithmic schemes to depict objects of interest in Compton imaging in a realistic and efficient way, a new List Mode MLEM-based approach is presented in this work. The developed algorithm is based on the standard LM-MLEM enhanced with a new probabilistic formula of the well-known system matrix based on the angular information of the incident photons. An accumulated probability, involving the Compton scattering angle, allows all detected events to originate from any pixel of the image giving a different weight. Hence, the proposed technique is free of any other conical section calculations normally introduced in a geometrical approach or any complicated mathematical expressions based on deterministic models. For a given focal plane, any point of the image to be reconstructed constitutes a potential solution assigned to a probability, which can be estimated for all events. Based on maximizing likelihood principles, the proposed model calculates the difference of the scatterer-to-source angle θ
0
, as it is determined by the deposited energy on the absorber, and any potential scattering angle θ
J
, specified by the position coordinates on the reconstruction matrix. The variation of the angular acceptance and the overall efficiency of the system for different source depths are used to perform volume corrections and further image optimization. Quantitative results of the proposed method tested with a plethora of source geometries for a simple two-stage scatterer-absorber Compton prototype simulated in the GEANT4/GATE environment are presented and discussed.