Injectivity of rotation invariant windowed Radon transforms
type: Item
instance of: scholarly article
title: Injectivity of rotation invariant windowed Radon transforms
zbMATH Open document ID: 1096.44001
author: Hermine Biermé
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-03-29T00:00:00Z
review text: The author considers rotation invariant windowed Radon transforms that integrate a function over hyperplanes by using a radial weight (called window). \textit{E. T. Quinto} [J. Math. Anal. Appl. 91, 510--522 (1983; Zbl 0517.44009)] proved an injectivity result for square integrable functions with compact support. However this can not be extended in general. In fact, when the Laplace transform of the window has a zero with positive real part \(\delta\) the windowed Radon transform is not injective on functions with a Gaussian decay at infinity, depending on \(\delta\). Here the author obtains conditions on the window that imply injectivity of the windowed Radon transform on functions with a more rapid decay than any Gaussian function.
Mathematics Subject Classification ID: 44A12
zbMATH DE Number: 5016188
zbMATH Keywords: rotation invariant windowed Randon transforms
zbMATH Keywords: injective
Wikidata QID: Q123219290
reviewed by: Som Prakash Goyal
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.04.062
OpenAlex ID: W2170837808
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DOI: 10.1016/J.JMAA.2005.04.062
description: scientific article; zbMATH DE number 5016188