Exact reconstruction formulas for a Radon transform over cones

Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper, we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account. This transform integrates a function in R-d over all conical surfaces having vertices on a hyperplane and symmetry axis orthogonal to this plane. As the main result, we derive exact reconstruction formulas of the filtered back-projection type for inverting this transform. Further, a Fourier slice identity is established.