An explicit inversion formula for the exponential Radon transform using data from \(180^\circ\)
type: Item
instance of: scholarly article
title: An explicit inversion formula for the exponential Radon transform using data from \(180^\circ\)
zbMATH Open document ID: 1056.44004
DOI: 10.1007/BF02385485
author: Hans Rullgård
published in: Arkiv för Matematik
publication date: 2004-09-28T00:00:00Z
review text: The exponential Radon transform on the plane is defined by \[ R\mu f(\theta,s)=\int_{-\infty}^{\infty} f (s \theta +t\theta^{\perp}) e^{\mu t} \,dt, \quad (\theta,s) \in S^1 \times {\mathbb R}, \tag{1} \] \(\mu\) being a real number. The author obtains an explicit inversion formula provided that \(R\mu f(\theta,s)\) is known only for \(\theta\) belonging to the right half of the unit circle. Comment: Explicit inversion formulas for the more general exponential transform associated to \(k\)-dimensional planes in \( {\mathbb R}^n\) and \(\mu \in {\mathbb C}^k\), where obtained by \textit{B. Rubin} [J. Fourier Anal. Appl. 6, No. 2, 185--205 (2000; Zbl 0973.44001)].
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 44A12
Mathematics Subject Classification ID: 92C55
zbMATH DE Number: 2103854
zbMATH Keywords: exponential Radon transform
zbMATH Keywords: inversion formula
MaRDI profile type: Publication
cites work: Some inversion formulas in the single photon emission computed tomography
cites work: Q3754464
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full work available at URL: https://doi.org/10.1007/bf02385485
OpenAlex ID: W2094986448
description: scientific article; zbMATH DE number 2103854