Exact reconstruction formulas for a Radon transform over cones
arXiv:1310.0239 · doi:10.1088/0266-5611/30/3/035001
Abstract
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. The conical Radon transform we study integrates a function in 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.
8 pages, 1 figure