Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$

Rahul Bhardwaj; Rohit Kumar Mishra; Manmohan Vashisth

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arXiv · 2404.12479

Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$

Rahul Bhardwaj·Rohit Kumar Mishra·Manmohan Vashisth

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Abstract

This article studies the inverse problem of recovering a vector field supported in $\mathbb{D}_R$, 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 $\mathbb{R}^2$ from the knowledge of its longitudinal and transverse V-line transforms over two different subsets of aforementioned broken lines in $\mathbb{R}^2$.

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Rahul Bhardwaj, Rohit Kumar Mishra, Manmohan Vashisth. 2024-04-18. Inversion of generalized V-line transforms of vector fields in $\mathbb{R}^2$. https://arxiv.org/abs/2404.12479

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