Explicit inversion formulas for the \(X\)-ray transform in \(\mathbb{Z}^n\)
type: Item
instance of: scholarly article
title: Explicit inversion formulas for the \(X\)-ray transform in \(\mathbb{Z}^n\)
zbMATH Open document ID: 1209.44002
author: A. Abouelaz
published in: Mediterranean Journal of Mathematics
publication date: 2011-01-25T00:00:00Z
review text: The author reconstructs a function \(f\) defined on the lattice \({\mathbb{Z}^n}\) with finite support from its \(d\)-plane Radon transform. He establishes also a Plancherel formula relatively at discrete Radon transform for the functions \(f\) on \({\mathbb{Z}^n}\). Finally, the author states and proves explicit inversion formulas for the \(X\)-ray transform in the lattice \({\mathbb{Z}^n}\) by using certain arithmetical geometrical techniques. Also, another inversion formula for the discrete \(d\)-plane Radon transform is given.
reviewed by: Kun Soo Chang
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 5841053
zbMATH Keywords: \(d\)-plane Radon transform
zbMATH Keywords: inversion formulas
zbMATH Keywords: dilatation of the \(d\)-planes
zbMATH Keywords: Smith normal form
zbMATH Keywords: Möbius function
zbMATH Keywords: Plancherel's formula
MaRDI profile type: Publication
full work available at URL: s00009-010-0032-5
OpenAlex ID: W1977693693
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DOI: 10.1007/S00009-010-0032-5
description: scientific article; zbMATH DE number 5841053