A Filtered Back-Projection Algorithm for 4π Compton Camera Data

Compton imaging is a gamma-ray imaging technique useful for photons with energies in the range of a hundred keV to several MeV. Measuring gamma rays with a Compton camera results in cone data that needs to be mathematically inverted to determine the incident flux distribution. In the past, filtered back-projection solutions for Compton telescope data required sums of spherical harmonics or stereographically mapping the back-projection, which can result in imaging artifacts. We present a solution to this inversion problem that removes these complexities by embedding the 2-D directional image on the surface of a sphere S² into R³ where it is easily solvable. In this manner we relate 2-D Compton 4π imaging to the 3-D Radon transform, which has known solutions. To accomplish this, the cone data is converted to planar data. Additionally we show how the planar geometry can be used to produce a computationally efficient implementation. This reconstruction is demonstrated with a two-plane, double-sided strip, HPGe Compton camera.