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

2024/02/27 by Mishra, Rohit Kumar, Thakkar, Chandni · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.17683

Abstract

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 ℝ³ and vector fields in ℝⁿ. 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.

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