Reconstruction of the singular support of a tensor field given in a refracting medium by its ray transform

DOI10.1134/S1990478915040018zbMath1349.53107MaRDI QIDQ3186885

E. Yu. Derevtsov, Svetlana Vasilevna Maltseva

Publication date: 12 August 2016

Published in: Journal of Applied and Industrial Mathematics (Search for Journal in Brave)

zbMATH Keywords

refractionray transformtomographytensor analysistensor fieldsingular supportback-projection operatorfunction discontinuity

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Inverse problems for PDEs (35R30) Integral geometry (53C65)

Related Items (5)

On the angular moment operators of attenuated ray transforms of scalar 3D-fields ⋮ Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields ⋮ Generalized attenuated ray transforms and their integral angular moments ⋮ Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform ⋮ On solenoidal-injective and injective ray transforms of tensor fields on surfaces

Cites Work

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• A special problem of integral geometry
• Some approaches to the reconstruction of a singular support of scalar, vector and tensor fields by their known tomographic data
• The method of orthogonal projection in potential theory
• Local Tomography
• Local Tomography II
• On reconstruction formulas for the ray transform acting on symmetric differentials on surfaces
• Reconstruction of vector fields and their singularities from ray transforms

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