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

2024/11/05 by Rohit Kumar Mishra, Mishra, Rohit Kumar, A. K. Purohit +3 · 3 citations
Computer Science · Earth and Planetary Sciences · #Classical Analysis and ODEs (math.CA) #Computational Physics and Python Applications #FOS: Mathematics #Geophysics and Gravity Measurements #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.2411.04145

openalex publication_date 2024/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the problem of recovering symmetric m-tensor fields (including vector fields) supported in a unit disk \mathbbD 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.

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• The head-wave transform
• Reconstruction of scalar functions and vector fields from weighted V-line transforms with swinging branches
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