Inversion of generalized V-line transforms of vector fields in ℝ²

2024/04/18 by Rahul Bhardwaj, Rohit Kumar Mishra, Bhardwaj, Rahul +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2404.12479

openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article studies the inverse problem of recovering a vector field supported in \mathbbD_R, the disk of radius R centered at the origin, through a set of generalized broken ray/V-line transforms, namely longitudinal and transverse V-line transforms. Geometrically, we work with broken lines that start from the boundary of a disk and break at a fixed angle after traveling a distance along the diameter. We derive two inversion algorithms to recover a vector field in ℝ² from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in ℝ².

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