On Radon transforms between lines and hyperplanes

Boris Rubin, Yingzhan Wang

Published 2016-01-15Version 1

We derive new inversion formulas for the Radon transform between lines and hyperplanes in Rn and the corresponding dual transform. In this setting, the Radon transform is noninjective and the consideration is restricted to the so-called quasiradial functions that are constant on symmetric clusters of lines. For the dual transform, which is injective, explicit inversion formulas are obtained in full generality. The main tools are the Funk transform on the sphere and the Erdelyi-Kober fractional integrals.