V-line tensor tomography: numerical results

TL;DR

This paper numerically verifies and validates algorithms for inverting V-line transforms on symmetric 2-tensor fields, demonstrating efficient recovery from various data types through simulations on different phantoms.

Contribution

It provides the first comprehensive numerical validation of inversion algorithms for V-line transforms on tensor fields, extending theoretical foundations to practical algorithms.

Findings

Successful numerical recovery of tensor fields from multiple VLT data types

Algorithms perform well on both smooth and non-smooth phantoms

Demonstrates the effectiveness of the proposed inversion methods

Abstract

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.