The Funk-Radon transform for hyperplane sections through a common point
Numerical Analysis
2021-03-30 v1
Abstract
The Funk-Radon transform, also known as the spherical Radon transform, assigns to a function on the sphere its mean values along all great circles. Since its invention by Paul Funk in 1911, the Funk-Radon transform has been generalized to other families of circles as well as to higher dimensions. We are particularly interested in the following generalization: we consider the intersections of the sphere with hyperplanes containing a common point inside the sphere. If this point is the origin, this is the same as the aforementioned Funk--Radon transform. We give an injectivity result and a range characterization of this generalized Radon transform by finding a relation with the classical Funk--Radon transform.
Keywords
Cite
@article{arxiv.1810.08105,
title = {The Funk-Radon transform for hyperplane sections through a common point},
author = {Michael Quellmalz},
journal= {arXiv preprint arXiv:1810.08105},
year = {2021}
}