Compton scattering tomography in translational geometries

Here we present new L2 injectivity results for 2D and 3D Compton scattering tomography (CST) problems in translational geometries. The results are proven through the explicit inversion of a new toric section and apple Radon transform, which describe novel 2D and 3D acquisition geometries in CST. The geometry considered has potential applications in airport baggage screening and threat detection. We also present a generalization of our injectivity results in 3D to Radon transforms which describe the integrals of the charge density over the surfaces of revolution of a class of C1 curves.