Exact inversion of Funk-Radon transforms with non-algebraic geometries
Functional Analysis
2017-11-29 v1
Abstract
Any even function defined on 2-sphere is reconstructed from its integrals over big circles by means of the classical Funk formula. For the non-geodesic Funk transform on the sphere of arbitrary dimension, there is the explicit inversion formula similar to that for the geodesic transform. A function defined on the sphere of radius one is integrated over traces of hyperplanes tangent to a sphere contained in the unit ball. This reconstruction is generalized in the paper for Riemannian hypersurfaces in an affine space.
Keywords
Cite
@article{arxiv.1711.10392,
title = {Exact inversion of Funk-Radon transforms with non-algebraic geometries},
author = {Victor Palamodov},
journal= {arXiv preprint arXiv:1711.10392},
year = {2017}
}