On the Range Characterization of the Two-Dimensional Attenuated Doppler Transform

DOI10.1137/140984282zbMath1317.30071arXiv1411.4923OpenAlexW2962993693MaRDI QIDQ5254875

Alexandru Tamasan, Kamran Sadiq

Publication date: 10 June 2015

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4923

zbMATH Keywords

Radon transformHilbert 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 (11)

On the \(X\)-ray transform of planar symmetric 2-tensors ⋮ Efficient tensor tomography in Fan-beam coordinates ⋮ The attenuated geodesic x-ray transform ⋮ 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 ⋮ On the range of the \(X\)-ray transform of symmetric tensors compactly supported in the plane ⋮ Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Tensor tomography on surfaces
• The attenuated ray transform on simple surfaces
• The weighted Doppler transform
• Two-dimensional tomography problems and the theory of \(A\)-analytic functions
• The Radon transform.
• Novikov's inversion formula for the attenuated Radon transform -- a new approach
• Integral geometry for tensor fields. Transl. from the Russian
• Range conditions for the exponential Radon transform
• The attenuated ray transform for connections and Higgs fields
• An analogue of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces
• Inversion of the attenuated Radon transform
• Mathematical Methods in Image Reconstruction
• Une formule d'inversion pour la transformation d'un rayonnement X atténué
• Tomographic Reconstruction of the Curl and Divergence of 2D Vector Fields Taking Refractions into Account
• The Chebyshev ridge polynomials in 2D tensor tomography
• On the range characterization for the two-dimensional attenuated x-ray transformation
• On the attenuated Radon transform with full and partial measurements
• Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
• Range conditions for the multidimensional exponential X-ray transform
• Finiteness theorem for the ray transform on a Riemannian manifold
• Doppler tomography for vector fields
• On the Range of the Attenuated Ray Transform for Unitary Connections
• On the range of the attenuated Radon transform in strictly convex sets
• Uniform asymptotic expansions at a caustic
• Tomographic reconstruction of vector fields in variable background media
• Inverse Source Problems in Transport Equations

This page was built for publication: On the Range Characterization of the Two-Dimensional Attenuated Doppler Transform