V-line tensor tomography: numerical results

This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation of their inversion methods were studied in a recent work [G....

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Bibliographic Details
Published in:arXiv.org 2024-07
Main Authors: Ambartsoumian, Gaik, Mishra, Rohit Kumar, Zamindar, Indrani
Format: Article
Language:English
Subjects:
Algorithms
Inverse problems
Mathematical analysis
Tensors
Online Access:Get full text
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Summary:This article presents the numerical verification and validation of several inversion algorithms for V-line transforms (VLTs) acting on symmetric 2-tensor fields in the plane. The analysis of these transforms and the theoretical foundation of their inversion methods were studied in a recent work [G. Ambartsoumian, R. K. Mishra, and I. Zamindar, Inverse Problems, 40 (2024), 035003]. We demonstrate the efficient recovery of an unknown symmetric 2-tensor field from various combinations of the longitudinal, transverse, and mixed VLTs, their corresponding first moments, and the star VLT. The paper examines the performance of the proposed algorithms in different settings and illustrates the results with numerical simulations on smooth and non-smooth phantoms.
ISSN:2331-8422