Multistatic anisotropic travel-time as a tensor tomography problem

TL;DR

This paper formulates multistatic anisotropic travel-time imaging as a tensor tomography problem, relating it to Radon transforms of tensor fields, and discusses null-space implications for imaging anisotropic reflectivity.

Contribution

It introduces a tensor tomography framework for multistatic travel-time imaging, connecting it to known Radon transforms and analyzing null-space issues.

Findings

Relates travel-time imaging to tensor Radon transforms.

Identifies null-space implications for anisotropic reflectivity.

Provides a mathematical framework for anisotropic travel-time tomography.

Abstract

Travel-time imaging problems seek to reconstruct an image of reflectivity of a scene by measuring travel time (and amplitude, phase) of electromagnetic or acoustic signals, such as radar and sonar. Multistatic, in this context, means that the transmitters and receivers need not be co-located. The reflectivity is anisotropic if it depends on direction, and in the multistatic case this means incoming and outgoing direction. Travel-time problems can be formulated as generalized Radon transforms of integrals over isochrones, in the planar case ellipses with transmitter and receivers at foci. In a simplified case where transmitters and receivers are distant from the scene, isochrones can be approximated by straight lines. We relate this to tensor ray transforms, specifically the longitudinal ray transform of Sharafutdinov, and discuss the implication of its known null-space. In the volumetric case isochrones are spheroids and we relate the problem to the normal Radon transform of tensor fields.