An Elementary Proof of Local Invertibility for Generalized and Attenuated Radon Transforms

DOI10.1137/0516082zbMath0588.44005OpenAlexW2084527507MaRDI QIDQ3715617

Andrew Markoe, Eric Todd Quinto

Publication date: 1985

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0516082

zbMATH Keywords

injectivecounterexamplesgeneralized Radon transformattenuated Radon transformslimited angle tomographysingle photon emission tomography

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Integral equations with miscellaneous special kernels (45H05)

Related Items (14)

On the strength of streak artifacts in filtered back-projection reconstructions for limited angle weighted X-ray transform ⋮ Support theorems for real-analytic Radon transforms ⋮ An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions ⋮ An inversion formula for the attenuated \(X\)-ray transformation ⋮ The stability estimates of the inverse problem for the weighted Radon transform ⋮ Stability estimates for the Calderón problem with partial data ⋮ An example of non-uniqueness for Radon transforms with continuous positive rotation invariant weights ⋮ Paley-Wiener theorem for exponential Radon transform ⋮ On the Injectivity of the Attenuated Radon Transform ⋮ Inversion of exponential \(k\)-plane transforms ⋮ Variational regularization of the weighted conical Radon transform ⋮ Support Theorems for Radon Transforms on Real Analytic Line Complexes in Three-Space ⋮ Coherent Quantum Tomography ⋮ An example of non-uniqueness for generalized Radon transform

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