Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(6): 1773-1781

Online first article June 27, 2018      Printed November 30, 2018

https://doi.org/10.4134/BKMS.b171064

Copyright © The Korean Mathematical Society.

Inversion of the classical Radon transform on $\mathbb{Z}^n_p$

Yung Duk Cho, Jong Yoon Hyun, Sunghwan Moon

Dongguk University, Korea Institute for Advanced Study (KIAS), Kyungpook National University

Abstract

The Radon transform introduced by J. Radon in 1917 is the integral transform which is widely applicable to tomography. Here we study the discrete version of the Radon transform. More precisely, when $\mathcal{C}(\mathbb{Z}^n_p)$ is the set of complex-valued functions on $\mathbb{Z}^n_p$. We completely determine the subset of $\mathcal{C}(\mathbb{Z}^n_p)$ whose elements can be recovered from its Radon transform on $\mathbb{Z}^n_p$.

Keywords: classical Radon transform, tomography, inversion formula

MSC numbers: 44A12, 15A03

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