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

TL;DR

This paper introduces a novel reconstruction method for band-limited Hankel transforms using PSWF-Radon techniques, combining classical wave functions with Radon transform theory to achieve super-resolution, supported by numerical analysis.

Contribution

It develops new formulas for Hankel transform inversion based on PSWF-Radon approach, integrating Fourier, Radon, and Cormack inversion methods for improved super-resolution.

Findings

Effective super-resolution demonstrated numerically.

Method handles noise levels in Hankel inversion.

Integrates classical wave functions with Radon transform theory.

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.