On range condition of the tensor x-ray transform in \(\mathbb R^n\)

DOI10.3934/IPI.2020020zbMath1451.44003OpenAlexW3013055509MaRDI QIDQ2188145

Aleksander Denisiuk

Publication date: 4 June 2020

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2020020

zbMATH Keywords

Radon transformtensor fieldrange conditionsx-ray transformJohn differential operator

Mathematics Subject Classification ID

Differential geometric aspects in vector and tensor analysis (53A45) Radon transform (44A12)

Related Items (2)

An extension of Asgeirsson's mean value theorem for solutions of the ultra-hyperbolic equation in dimension four ⋮ Iterative inversion of the tensor momentum x-ray transform

Cites Work

• Unnamed Item
• Integral geometry in affine and projective spaces
• Integral geometry for tensor fields. Transl. from the Russian
• Integral geometry on k-dimensional planes
• Inversion of the x-ray transform for complexes of lines in ${{\mathbb{R}}}^{n}$
• The John equation for tensor tomography in three-dimensions
• The x-ray transform: singular value decomposition and resolution
• An example of non-uniqueness for the weighted Radon transforms along hyperplanes in multidimensions
• Reconstruction in the cone-beam vector tomography with two sources
• Inversion of the x-ray transform for 3D symmetric tensor fields with sources on a curve

This page was built for publication: On range condition of the tensor x-ray transform in \(\mathbb R^n\)