Sampling the Xray transform on simple surfaces
Abstract
We study the problem of proper discretizing and sampling issues related to geodesic Xray transforms on simple surfaces, and illustrate the theory on simple geodesic disks of constant curvature. Given a notion of band limit on a function, we provide the minimal sampling rates of its Xray transform for a faithful reconstruction. In Cartesian sampling, we quantify the quality of a sampling scheme depending on geometric parameters of the surface (e.g. curvature and boundary curvature), and the coordinate system used to represent the space of geodesics. When aliasing happens, we explain how to predict the location, orientation and frequency of the artifacts
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05761
 Bibcode:
 2021arXiv211005761M
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Differential Geometry
 EPrint:
 28 pages, 14 figures