Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces

DOI10.1215/S0012-7094-91-06227-7zbMath0742.44002OpenAlexW1979027120MaRDI QIDQ1814234

Enrico Casadio Tarabusi, Carlos. A. Berenstein

Publication date: 25 June 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06227-7

zbMATH Keywords

Radon transformharmonic analysishyperbolic spaceinversion formulasbackprojectionimpedance tomography

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Radon transform (44A12)

Related Items (18)

Hyperbolic geometry and local Dirichlet-Neumann map ⋮ Helgason-Marchaud inversion formulas for Radon transforms ⋮ The Abel, Fourier and Radon transforms on symmetric spaces ⋮ Reconstruction formulas for X-ray transforms in negative curvature ⋮ A geometric view on Radon transforms ⋮ Combining Radon transform and electrical capacitance tomography for a 2 d   +  1 imaging device ⋮ The range characterizations of the totally geodesic Radon transform on the real hyperbolic space ⋮ Explicit inversion formulas for the \(X\)-ray transform in \(\mathbb{Z}^n\) ⋮ X-ray transform and boundary rigidity for asymptotically hyperbolic manifolds ⋮ Radon transforms in hyperbolic spaces and their discrete counterparts ⋮ Radon transform on the torus ⋮ The \(\overline \delta\)-theory for inverse problems associated with Schödinger operators on hyperbolic spaces ⋮ Efficient inverse solvers for thermal tomography ⋮ Some constructions for the fractional Laplacian on noncompact manifolds ⋮ Inversion formulas of integral geometry in real hyperbolic space ⋮ Radon, cosine and sine transforms on real hyperbolic space ⋮ X-ray transform on a symmetric space ⋮ Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

Cites Work

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• The X-ray transform
• Differential operators on homogeneous spaces
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• Spherical Harmonics and Integral Geometry on Projective Spaces
• The inversion problem and applications of the generalized radon transform
• The Radon Transform on SL(2,R)/SO(2,R)
• The Radon Transform on a Family of Curves in the Plane
• A Radon Transform on Spheres Through the Origin in R n and Applications to the Darboux Equation
• Radon Inversion--Variations on a Theme
• The Radon Transform on a Family of Curves in the Plane. II
• Inversion ofk-Plane Transforms and Applications in Computer Tomog

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