PSWF-Radon approach to reconstruction from band-limited Hankel transform
Abstract
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 the Fourier and Hankel transforms and Cormack-type inversion of the Radon transform. As a result, we also establish new connections among the Fourier, Hankel, and Abel-type transforms. Finally, we investigate numerically the capabilities of our approach to super-resolution for band-limited Hankel inversion in relation to varying levels of noise.
Fields of Study & Subjects
Seismic Imaging and Inversion Techniques
Medical Imaging Techniques and Applications
Image and Signal Denoising Methods
Publication details
- Journal / source
- Journal of Inverse and Ill-Posed Problems
- Publisher
- Walter de Gruyter GmbH
- Volume
- 34
- Issue
- 5
- Pages
- 775-789
- Publication date
- 20 April 2026
- Language
- EN