Novikov's inversion formula for the attenuated Radon transform -- a new approach
type: Item
instance of: scholarly article
title: Novikov's inversion formula for the attenuated Radon transform -- a new approach
zbMATH Open document ID: 1072.44002
DOI: 10.1007/BF02922067
author: Jan Boman
author: Jan-Olov Strömberg
published in: The Journal of Geometric Analysis
publication date: 2005-03-18T00:00:00Z
review text: Let \(L\) be a line on the 2-dimensional plane, and let \(R_\rho f(L)=\int_L f (\cdot) \rho(L, \cdot) ds\) be the weighted (attenuated) Radon transform of \(f\) where the weight function \(\rho\) has a special form. Explicit inversion formula for \(R_\rho\) was obtained in the famous paper by \textit{R. G. Novikov} [Ark. Mat. 40, No. 1, 145--167 (2002; Zbl 1036.53056)]. The authors obtain similar results for a larger class of weight functions using completely different and quite elementary methods.
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 92C55
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 2147096
zbMATH Keywords: attenuated Radon transform
zbMATH Keywords: generalized Radon transform
zbMATH Keywords: inversion formula
MaRDI profile type: Publication
cites work: Two-dimensional tomography problems and the theory of \(A\)-analytic functions
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cites work: Q5702458
cites work: Inversion of the attenuated Radon transform
cites work: An inversion formula for the attenuated \(X\)-ray transformation
full work available at URL: https://doi.org/10.1007/bf02922067
OpenAlex ID: W2078084833
description: scientific article; zbMATH DE number 2147096