Inversion of the classical Radon transform on $\mathbb{Z}^n_p$
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1773-1781
Published online June 27, 2018
Printed November 30, 2018
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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