Reconstruction from blind experimental data for an inverse problem for a hyperbolic equation

TL;DR

This paper presents a globally convergent numerical method for reconstructing the dielectric constant in a hyperbolic PDE from blind backscattered experimental data collected by a specialized device.

Contribution

It introduces a novel approach for reconstructing dielectric properties from blind experimental data using a globally convergent numerical method.

Findings

Successfully reconstructed dielectric constant from experimental data

Demonstrated effectiveness of the method on real-world backscattered data

Achieved accurate reconstructions in blind data scenarios

Abstract

We consider the problem of reconstruction of dielectrics from blind backscattered experimental data. Experimental data were collected by a device, which was built at University of North Carolina at Charlotte. This device sends electrical pulses into the medium and collects the time resolved backscattered data on a part of a plane. The spatially distributed dielectric constant $\varepsilon_{r}(\mathbf{x}),\mathbf{x}\in \mathbb{R}^{3}$ is the unknown coefficient of a wave-like PDE. This coefficient is reconstructed from those data in blind cases. To do this, a globally convergent numerical method is used.