Tensor tomography using V-line transforms with vertices restricted to a circle

In this article, we study the problem of recovering symmetric \(m\)-tensor fields (including vector fields) supported in a unit disk \(\mathbb{D}\) from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circ...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Mishra, Rohit Kumar, Purohit, Anamika, Zamindar, Indrani
Format: Article
Language:English
Subjects:
Algorithms
Apexes
Fields (mathematics)
Symmetry
Tensors
Online Access:Get full text
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Summary:In this article, we study the problem of recovering symmetric \(m\)-tensor fields (including vector fields) supported in a unit disk \(\mathbb{D}\) from a set of generalized V-line transforms, namely longitudinal, transverse, and mixed V-line transforms, and their integral moments. We work in a circular geometric setup, where the V-lines have vertices on a circle, and the axis of symmetry is orthogonal to the circle. We present two approaches to recover a symmetric \(m\)-tensor field from the combination of longitudinal, transverse, and mixed V-line transforms. With the help of these inversion results, we are able to give an explicit kernel description for these transforms. We also derive inversion algorithms to reconstruct a symmetric \(m\)-tensor field from its first \((m+1)\) moment longitudinal/transverse V-line transforms.
ISSN:2331-8422