Numerical Solution of a Coefficient Inverse Problem with Multi-Frequency Experimental Raw Data by a Globally Convergent Algorithm

TL;DR

This paper demonstrates a globally convergent numerical method that effectively reconstructs dielectric properties and locations of objects from noisy, minimal multi-frequency experimental backscatter data, relevant for explosive detection.

Contribution

The paper introduces a new globally convergent algorithm capable of handling high nonlinearity and noise in multi-frequency experimental data for inverse problems.

Findings

Successfully reconstructed dielectric constants and object locations

Handled high noise levels without prior object knowledge

Achieved accurate results with minimal and raw data

Abstract

We analyze in this paper the performance of a newly developed globally convergent numerical method for a coefficient inverse problem for the case of multi-frequency experimental backscatter data associated to a single incident wave. These data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. The challenges for the inverse problem under the consideration are not only from its high nonlinearity and severe ill-posedness but also from the facts that the amount of the measured data is minimal and that these raw data are contaminated by a significant amount of noise, due to a non-ideal experimental setup. This setup is motivated by our target application in detecting and identifying explosives. We show in this paper how the raw data can be preprocessed and successfully inverted using our inversion method. More precisely, we are able to reconstruct the dielectric constants and the locations of the scattering objects with a good accuracy, without using any advanced \emph{a priori} knowledge of their physical and geometrical properties.