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：本文对作用于平面内对称二阶张量场的V线变换的几种反演算法进行了数值验证与确认。这些变换的分析及其反演方法的理论基础已在近期工作[G. Ambartsoumian, R. K. Mishra, and I. Zamindar, Inverse Problems, 40 (2024), 035003]中进行了研究。我们展示了如何从纵向、横向、混合V线变换及其对应的一阶矩以及星形V线变换的各种组合中，高效恢复未知的对称二阶张量场。本文考察了所提算法在不同场景下的性能，并通过光滑与非光滑模体上的数值模拟结果进行了说明。