The cone-beam transform and spherical convolution operators
Numerical Analysis
2021-08-13 v2 Numerical Analysis
Abstract
The cone-beam transform consists of integrating a function defined on the three-dimensional space along every ray that starts on a certain scanning set. Based on Grangeat's formula, Louis [2016, Inverse Problems 32 115005] states reconstruction formulas based on a new generalized Funk-Radon transform on the sphere. In this article, we give a singular value decomposition of this generalized Funk-Radon transform. We use this result to derive a singular value decomposition of the cone-beam transform with sources on the sphere thus generalizing a result of Kazantsev [2015, J. Inverse Ill-Posed Probl. 23(2):173-185].
Keywords
Cite
@article{arxiv.1803.10515,
title = {The cone-beam transform and spherical convolution operators},
author = {Michael Quellmalz and Ralf Hielscher and Alfred K. Louis},
journal= {arXiv preprint arXiv:1803.10515},
year = {2021}
}