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

• Published in: IEEE transactions on nuclear science Vol. 62; no. 4; pp. 1911 - 1917
• Main Authors: Haefner, Andrew, Gunter, Donald, Barnowski, Ross, Vetter, Kai
• Format: Journal Article
• Language: English
• Published: IEEE 01.08.2015
• Subjects: Cameras; Compton imaging; Compton telescope; Detectors; filtered back-projection; Geometry; Image reconstruction; Image resolution; radon transform; Scattering
• ISSN: 0018-9499; 1558-1578
• DOI: 10.1109/TNS.2015.2457436

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 S 2 into R 3 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.