English

PSWF-Radon approach to reconstruction from band-limited Hankel transform

Classical Analysis and ODEs 2024-09-27 v1

Abstract

We give new formulas for reconstructions from band-limited Hankel transform of integer or half-integer order. Our formulas rely on the PSWF-Radon approach to super-resolution in multidimensional Fourier analysis. This approach consists of combining the theory of classical one-dimensional prolate spheroidal wave functions with the Radon transform theory. We also use the relation between Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.

Keywords

Cite

@article{arxiv.2409.17409,
  title  = {PSWF-Radon approach to reconstruction from band-limited Hankel transform},
  author = {Fedor Goncharov and Mikhail Isaev and Roman Novikov and Rodion Zaytsev},
  journal= {arXiv preprint arXiv:2409.17409},
  year   = {2024}
}