A unified radon inversion formula

DOI10.1063/1.523592zbMath0439.44002OpenAlexW1990313830MaRDI QIDQ3881320

Stanley R. Deans

Publication date: 1978

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://escholarship.org/uc/item/7833j3w8

zbMATH Keywords

inversion formulaRadon transformsinverse transformLegendre transformsGegenbauer transformsTchebycheff transforms

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spherical harmonics (33C55)

Related Items (10)

Positive definite symmetric functions on finite dimensional spaces. I: Applications of the Radon transform ⋮ Convolution integral equations with Gegenbauer function kernel ⋮ Representation of Euclidean Random Field ⋮ Relation-based variations of the discrete Radon transform ⋮ Exterior reconstruction of a three dimensional scatterer ⋮ The totally geodesic Radon transform on the Lorentz space of curvarture \(-1\) ⋮ New unified Radon inversion formulas ⋮ Evaluation of integrals and the Mellin transform ⋮ The invertibility of rotation invariant Radon transforms ⋮ Singular value decompositions and inversion methods for the exterior Radon transform and a spherical transform

Cites Work

• Bestimmung einer Funktion aus ihren Integralen über gewisse Mannigfaltigkeiten
• The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds
• Practical and mathematical aspects of the problem of reconstructing objects from radiographs
• Expansion formulas and addition theorems for Gegenbauer functions
• An Inversion Integral for a Gegenbauer Transformation
• A procedure for deriving inversion formulae for integral transform pairs of a general kind
• An Integral Equation Involving Legendre Functions
• A Hypergeometric Function Transform

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