Three-Dimensional Compton Imaging Using List-Mode Maximum Likelihood Expectation Maximization

Compton imaging is a gamma ray imaging technique that has many possible applications including homeland security and medical imaging. Using the Compton scattering formula the origin of a scattered $\gamma$-ray can be localized to a point on the surface of a cone using a minimum of two position and energy measurements. List-mode Maximum likelihood expectation maximization (MLEM) is an iterative statistical algorithm that makes successive approximations to the most probable source distribution that would have led to the observed data. Conventional MLEM is often performed in two dimensions, which still requires knowledge of the source-to-detector distance. We propose iteration over all three spatial dimensions in order to maximize the probability in three-dimensional space. This paper reports on the development of a three-dimensional MLEM (3DMLEM) algorithm to reconstruct images from a Compton imager in three dimensions for single, multiple and line sources. Several techniques for reducing convergence times are also discussed.