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arXiv · 2409.17409

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

Fedor Goncharov·Mikhail Isaev·Roman Novikov·Rodion Zaytsev
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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.

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Fedor Goncharov, Mikhail Isaev, Roman Novikov, Rodion Zaytsev. 2024-09-25. PSWF-Radon approach to reconstruction from band-limited Hankel transform. https://arxiv.org/abs/2409.17409

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