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arXiv · 2502.02058

Inversion of generalized Radon transform over symmetric $m$-tensor fields in $\mathbb{R}^n$

Anuj Abhishek·Rohit Kumar Mishra·Chandni Thakkar
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Abstract

In this work, we study a set of generalized Radon transforms over symmetric $m$-tensor fields in $\mathbb{R}^n$. The longitudinal/transversal Radon transform and corresponding weighted integral transforms for symmetric $m$-tensor field are introduced. We give the kernel descriptions for the longitudinal and transversal Radon transform. Further, we also prove that a symmetric $m$-tensor field can be recovered uniquely from certain combinations of these integral transforms of the unknown tensor field. This generalizes a recent study done for the recovery of vector fields from its weighted Radon transform data to recovery of a symmetric $m$-tensor field from analogously defined weighted Radon transforms.

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Anuj Abhishek, Rohit Kumar Mishra, Chandni Thakkar. 2025-02-04. Inversion of generalized Radon transform over symmetric $m$-tensor fields in $\mathbb{R}^n$. https://arxiv.org/abs/2502.02058

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