A stochastic alternative technique for Compton Maximum Likelihood Expectation-Maximization (MLEM) reconstruction.

Even though iterative methods and particularly Maximum Likelihood Expectation-Maximization (MLEM) algorithms have been established in reconstruction with Compton data, their detailed design with respect to physical rules and processes dominate their plain implementation in the form of a system matrix. A new elementary but efficient alternative for the well-known system matrix with respect to Compton Camera image reconstruction is presented in this work. For each detected event there is a weighting factor inserted as an accumulated probability which carries all the necessary information. This probability which involves only the Compton scattering angle of the incident photon corresponds to a map that correlates all events within all possible source origins. Based on maximizing likelihood principles, the proposed model weights in a stochastic way the difference of the scatterer-to-source angle θ, as it is determined by the deposited energy on the absorber, and any other potential scattering angle θ, specified by the position coordinates on the reconstruction matrix. Obtained image spatial resolution, angular distortions and response to focal length determination are a few of the studied cases for the algorithms' evaluation via simulations in GEANT4/GATE with a set of radioactive sources and phantoms with in- and out-of-plane arrangement.