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

Abstract

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 θ₀, as it is determined by the deposited energy on the absorber, and any other potential scattering angle θ_J, 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.

Keywords: Compton Camera; Compton kinematics; Dopamine Transporter scan; GEANT4/GATE Monte-Carlo simulation; Iterative reconstruction algorithms; List-Mode MLEM; Log-likelihood; Maximum Likelihood Expectation-Maximization (MLEM).