Inversion of exponential \(k\)-plane transforms

DOI10.1007/BF02510660zbMath0973.44001MaRDI QIDQ1976481

Boris Rubin

Publication date: 22 November 2001

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59639

zbMATH Keywords

Radon transformmagnetic resonance imagingmedical diagnosisfractional integralsX-ray computerized tomographyexplicit inversion formulaewavelet measureexponential \(k\)-plane transformsexpontial X-ray transformsingle photon emission tomographywindowed Radon transform

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Biomedical imaging and signal processing (92C55) Radon transform (44A12)

Related Items (1)

Spherical Radon transform and related wavelet transforms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The invertibility of rotation invariant Radon transforms
• On the inversion of the attenuated Radon transform
• On some Bessel-function integral equations
• Inversion of \(k\)-plane transforms via continuous wavelet transforms
• The Calderón reproducing formula, windowed \(X\)-ray transforms, and Radon transforms in \(L^p\)-spaces
• Fractional integrals and weakly singular integral equations of the first kind in the \(n\)-dimensional ball
• Filtered-backprojection and the exponential Radon transform
• Computerized Tomography with Unknown Sources
• On the Injectivity of the Attenuated Radon Transform
• Fourier Inversion of the Attenuated X-Ray Transform
• An Elementary Proof of Local Invertibility for Generalized and Attenuated Radon Transforms
• Single-photon emission computed tomography by inverting the attenuated Radon transform with least-squares collocation
• Inversion of the exponential X-ray transform. I: Analysis
• The Exponential Radon Transform
• Inverse Radon transforms through inverse wavelet transforms
• Continuity and invertibility of distributional multidimensional fractional integrals
• An inversion method for an attenuated x-ray transform
• Inversion ofk-Plane Transforms and Applications in Computer Tomog
• Some inversion formulas in the single photon emission computed tomography
• Inversion of the exponential X‐ray transform. II: Numerics
• A generalisation of the Erdélyi-Kober operators

This page was built for publication: Inversion of exponential \(k\)-plane transforms