arXiv subjects

Chandni Thakkar

Publications and source records attributed to Chandni Thakkar.

5 recordsLinked to original sources

arXiv2026

Radon Transform over Tensor Fields: Injectivity, Range, and Unique Continuation Principle

A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms. In this paper, we study all these aspects for Radon transforms acting on symmetric $m$-tensor fields in $\mathbb{R}^n$. Our results show that these transforms admit a coherent analytic structure, extending several key features of the classical Radon transform and tensor ray transforms to a broader geometric setting.

math.AP↗

arXiv2025

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

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.

math.AP↗

arXiv2024

Microlocal inversion of a restricted mixed ray transform for second-order tensor fields in $\mathbb{R}^3$

In this article, we study a restricted mixed ray transform acting on second-order tensor fields in 3-dimensional Euclidean space and prove the invertibility of this integral transform using microlocal techniques. Here, the mixed ray transform is restricted over lines passing through a fixed curve $γ$ in $\mathbb{R}^3$ satisfying certain geometric conditions. The main theorem of the article shows that a second-order tensor field can be recovered from its restricted mixed-ray transform up to the kernel of the transform, a smoothing term, and a known singular term.

math.AP↗

arXiv2024

Inversion formula, Unique continuation property, and range characterization of the mixed ray transform in $\mathbb{R}^2$

In this article, we study various aspects of the mixed ray transform of $(k + \ell)$-tensor fields that are symmetric in its first $k$ and last $\ell$ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result.

math.AP↗

arXiv2024

Inversion of a restricted transverse ray transform with sources on a curve

In this paper, a restricted transverse ray transform acting on vector and symmetric $m$-tensor fields is studied. We developed inversion algorithms using restricted transverse ray transform data to recover symmetric $m$-tensor fields in $\mathbb{R}^3$ and vector fields in $\mathbb{R}^n$. We restrict the transverse ray transform to all lines going through a fixed curve $γ$ that satisfies the Kirillov-Tuy condition. We show that the known restricted data can be used to reconstruct a specific weighted Radon transform of the unknown vector/tensor field's components, which we then use to explicitly recover the unknown field.

math.CA↗