On the range of the attenuated Radon transform in strictly convex sets

DOI10.1090/S0002-9947-2014-06307-1zbMath1317.30070arXiv1310.2501OpenAlexW1982840759MaRDI QIDQ5251600

Kamran Sadiq, Alexandru Tamasan

Publication date: 20 May 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.2501

zbMATH Keywords

Hilbert transformattenuated Radon transform

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Other generalizations of analytic functions (including abstract-valued functions) (30G30)

Related Items (12)

On the \(X\)-ray transform of planar symmetric 2-tensors ⋮ Efficient tensor tomography in Fan-beam coordinates ⋮ Efficient tensor tomography in fan-beam coordinates. II: Attenuated transforms ⋮ Numerical Reconstruction of Radiative Sources in an Absorbing and Nondiffusing Scattering Medium in Two Dimensions ⋮ Inversion formulas and range characterizations for the attenuated geodesic ray transform ⋮ Numerical Reconstruction of Radiative Sources from Partial Boundary Measurements ⋮ On the range of the \(X\)-ray transform of symmetric tensors compactly supported in the plane ⋮ Reconstruction of the Emission Coefficient in the Nonlinear Radiative Transfer Equation ⋮ Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces ⋮ A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium ⋮ Partial inversion of the 2D attenuated \(X\)-ray transform with data on an arc ⋮ On the Range Characterization of the Two-Dimensional Attenuated Doppler Transform

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The attenuated ray transform on simple surfaces
• The Radon transform.
• Novikov's inversion formula for the attenuated Radon transform -- a new approach
• Integral geometry for tensor fields. Transl. from the Russian
• An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces
• Inversion of the attenuated Radon transform
• Une formule d'inversion pour la transformation d'un rayonnement X atténué
• An inverse boundary value problem in two-dimensional transport
• On the range characterization for the two-dimensional attenuated x-ray transformation
• On the attenuated Radon transform with full and partial measurements
• On the Range of the Attenuated Ray Transform for Unitary Connections
• Uniform asymptotic expansions at a caustic
• Tomographic reconstruction of vector fields in variable background media

This page was built for publication: On the range of the attenuated Radon transform in strictly convex sets