On the inversion of the attenuated Radon transform

DOI10.1007/BF01401046zbMath0427.65082MaRDI QIDQ1136491

Frank Natterer

Publication date: 1979

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132621

zbMATH Keywords

numerical examplesinversion formulaintegral equation of the second kindattenuated Radon transformgeneralized filtered backprojection algorithm

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Theoretical approximation of solutions to integral equations (45L05) Linear integral equations (45A05)

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On the strength of streak artifacts in filtered back-projection reconstructions for limited angle weighted X-ray transform ⋮ The identification problem for the constantly attenuated Radon transform ⋮ Inversion of the attenuated X-ray transforms: method of Riesz potentials ⋮ Range conditions for the exponential Radon transform ⋮ Adaptive estimation of a function from its exponential Radon transform in presence of noise ⋮ Minimax optimal estimator in a stochastic inverse problem for exponential Radon transform ⋮ On the Injectivity of the Attenuated Radon Transform ⋮ Inversion of exponential \(k\)-plane transforms ⋮ Fast Laplace transforms for the exponential Radon transform ⋮ Inversion of the attenuated X-ray transforms -- method of convolution-backprojection

Cites Work

• Uniform asymptotic expansions at a caustic
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