An inverse problem of a simultaneous reconstruction of the dielectric constant and conductivity from experimental backscattering data

TL;DR

This paper advances a convexification method to simultaneously reconstruct dielectric constants, conductivities, and shapes of buried objects from experimental backscattering data, crucial for detecting land mines and explosive devices.

Contribution

It extends previous work by enabling the joint reconstruction of dielectric constants, conductivities, and shapes using experimental data, demonstrating improved imaging capabilities.

Findings

Accurate imaging of dielectric constants and shapes from experimental data.

Reliable distinction between conductive and non-conductive objects.

Verification of the convexification algorithm's performance on challenging targets.

Abstract

This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front surfaces of objects buried very closely under the ground. These objects mimic explosives, like, e.g., antipersonnel land mines and improvised explosive devices. We solve a coefficient inverse problem with the backscattering data generated by a moving source at a fixed frequency. This scenario has been studied so far by our newly developed convexification method that consists in a new derivation of a boundary value problem for a coupled quasilinear elliptic system. However, in our previous work only the unknown dielectric constants of objects and shapes of their front surfaces were calculated. Unlike this, in the current work performance of our numerical convexification algorithm is verified for the case when the dielectric constants, the electric conductivities and those shapes of objects are unknown. By running several tests with experimentally collected backscattering data, we find that we can accurately image both the dielectric constants and shapes of targets of interests including a challenging case of targets with voids. The computed electrical conductivity serves for reliably distinguishing conductive and non-conductive objects. The global convergence of our numerical procedure is shortly revisited.