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.

翻译：本文针对作用于平面内对称二阶张量场的V线变换，提出了多种反演算法的数值验证与确认。这些变换的分析及其反演方法的理论基础已在近期研究[G. Ambartsoumian, R. K. Mishra, and I. Zamindar, Inverse Problems, 40 (2024), 035003]中完成。我们展示了如何从纵向、横向及混合V线变换、其对应的一阶矩以及星型V线变换的不同组合中，有效重建未知的对称二阶张量场。本文检验了所提算法在不同设置下的性能，并通过光滑与非光滑体模的数值模拟对结果进行了可视化说明。