The Radon Transform on a Family of Curves in the Plane. II

DOI10.2307/2043399zbMath0501.44002OpenAlexW4241999508MaRDI QIDQ3966591

Allan McLeod Cormack

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/2043399

zbMATH Keywords

computed tomographyRadon transformorthogonal expansionsFourier componentscurves in the plane

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Harmonic analysis on homogeneous spaces (43A85) Integral equations with miscellaneous special kernels (45H05)

Related Items (12)

Support theorems for real-analytic Radon transforms ⋮ On the inversion of a generalized Radon transform of seismic type ⋮ Approximate reconstruction from ray integrals of a function on a domain with low refraction ⋮ Uniqueness and stability for a seismic-type generalized Radon transform ⋮ Radon transform on algebraic Cormack α-curves inversion formula ⋮ Inversion of higher dimensional Radon transforms of seismic-type ⋮ Inversion formulas for the \(k\)-dimensional Radon transform in real hyperbolic spaces ⋮ Inversion of seismic-type Radon transforms on the plane ⋮ Range characterizations and singular value decomposition of the geodesic X-ray transform on disks of constant curvature ⋮ The invertibility of rotation invariant Radon transforms ⋮ On a three-dimensional Compton scattering tomography system with fixed source ⋮ Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform

Cites Work

• The Radon transform
• On reconstructing a function on the exterior of a disk from its Radon transform
• On the reconstruction of a function on a circular domain from a sampling of its line integrals
• 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
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