A model of spatial resolution uncertainty for Compton camera imaging

Abstract

Compton cameras use a pair of detectors to record the energy deposited during Compton scattering and photoabsorption of gamma ray photons. By inverting the forward model for these detection events, the 3D radioactive source distribution can be recovered computationally. However, existing methods of describing the forward model ignore the ambiguity in the Compton cone axis introduced by the detector pixel size. In this paper, we introduce approximations to the axis ambiguity that make the description of the source ambiguity computationally tractable and improve the accuracy of the detection forward model. Specifically, we model the pixel active areas as discs, so the intersection between all possible Compton cone axes and a plane parallel to the detectors is also a disc. Because of ambiguity in the Compton cone axis, the gamma source position is constrained to lie within a more complicated volume that we approximately bound by ellipses or hyperbolas at discrete depth slices. We perform simulations of single point gamma sources using the Geant4 software. Our forward model leads to improved source distribution recovery using both backprojection and iterative reconstruction methods, demonstrating that accurate localization can be performed from a smaller number of detected photons.