On the range of the Radon transform and its dual

DOI10.1007/BF01458472zbMath0554.46016OpenAlexW2082671299MaRDI QIDQ759964

Alexander Hertle

Publication date: 1984

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163882

zbMATH Keywords

Radon transform

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15)

Related Items (17)

New range theorems for the dual Radon transform ⋮ Characterizations of function spaces by the discrete Radon transform ⋮ Range characterization of Radon transforms on quaternionic projective spaces ⋮ The Radon transform is an isomorphism between \(L^ 2(B_ a)\) and \(H_ e(Z_ a)\) ⋮ Radon transforms on affine Grassmannians ⋮ Radon transform on distributions ⋮ Radon transforms on Grassmann manifolds ⋮ Invariant differential operators and the range of the Radon d-plane transform ⋮ Integral geometry on Grassmann manifolds and calculus of invariant differential operators ⋮ Inversion formula and singularities of the solution for the backprojection operator in tomography ⋮ The flat horocycle transform for a symmetric space ⋮ The Ridgelet transform of distributions ⋮ Surjectivity of mean value operators on noncompact symmetric spaces ⋮ A Functional From Geometry with Applications to Discrepancy Estimates and the Radon Transform ⋮ Variational methods for tomographic reconstruction with few views ⋮ A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images ⋮ Understanding neural networks with reproducing kernel Banach spaces

Cites Work

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• Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform
• The Radon transform
• Null spaces and ranges for the classical and spherical Radon transforms
• 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 Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Distances between measures from 1-dimensional projections as implied by continuity of the inverse radon transform
• Computerized Tomography with Unknown Sources
• Picture reconstruction from projections in restricted range
• Uniform asymptotic expansions at a caustic

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