On Radon transforms between lines and hyperplanes
Document Type
Article
Publication Date
12-1-2017
Abstract
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in Rn. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions that are constant on symmetric clusters of lines. For the corresponding dual transform, which is injective, explicit inversion formulas are obtained both in the symmetric case and in full generality. The main tools are the Funk transform on the sphere, the Radon-John d-plane transform in Rn, the Grassmannian modification of the Kelvin transform, and the Erdélyi-Kober fractional integrals.
Publication Source (Journal or Book title)
International Journal of Mathematics
Recommended Citation
Rubin, B., & Wang, Y. (2017). On Radon transforms between lines and hyperplanes. International Journal of Mathematics, 28 (13) https://doi.org/10.1142/S0129167X17500938