An inversion formula for the attenuated \(X\)-ray transformation
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Publication:1397593
DOI10.1007/BF02384507zbMath1036.53056OpenAlexW2030727075MaRDI QIDQ1397593
Publication date: 6 August 2003
Published in: Arkiv för Matematik (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02384507
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Cites Work
- Unnamed Item
- Unnamed Item
- Support theorems for real-analytic Radon transforms
- An example of non-uniqueness for generalized Radon transform
- Small angle scattering and \(X\)-ray transform in classical mechanics
- Une formule d'inversion pour la transformation d'un rayonnement X atténué
- An Elementary Proof of Local Invertibility for Generalized and Attenuated Radon Transforms
- The Exponential Radon Transform
- ON DETERMINATION OF A GAUGE FIELD ON ℝd FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES
- An inversion method for an attenuated x-ray transform
- On local tomography
- Range conditions for the multidimensional exponential X-ray transform
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