The ray transform of symmetric tensor fields with incomplete projection data. I: The kernel of the ray transform

DOI10.33048/semi.2021.18.093zbMath1490.44003OpenAlexW4205469554MaRDI QIDQ2058326

Vladimir Altafovich Sharafutdinov

Publication date: 8 December 2021

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.33048/semi.2021.18.093

zbMATH Keywords

ray transformtensor analysistomography with incomplete data

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Radon transform (44A12) Numerical methods for inverse problems for integral equations (65R32)

Cites Work

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• Nonlocal inversion formulas for the X-ray transform
• The Radon transform.
• Inverting the local geodesic X-ray transform on tensors
• Microlocal analaysis of the Doppler transform on \(\mathbb{R}^3\)
• Integral geometry for tensor fields. Transl. from the Russian
• A support theorem for the geodesic ray transform of symmetric tensor fields
• The 3D Doppler transform: elementary properties and computation of reconstruction kernels
• Integral geometry problems for symmetric tensor fields with incomplete data
• An Inversion Formula for Cone-Beam Reconstruction
• Inversion of the x-ray transform for 3D symmetric tensor fields with sources on a curve
• Slice-by-slice reconstruction algorithm for vector tomography with incomplete data

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