Carleman contraction mapping for a 1D inverse scattering problem with experimental time-dependent data

TL;DR

This paper demonstrates a Carleman contraction mapping approach for solving a 1D inverse scattering problem, establishing global convergence and validating with both simulated and experimental data, including dielectric constant estimation of targets.

Contribution

Introduces a novel Carleman-based contraction mapping method with proven global convergence for a 1D inverse hyperbolic problem, validated on real experimental data.

Findings

Global convergence of the numerical method is proven.

Successful computation of dielectric constants from experimental data.

Method effective for severely underdetermined data.

Abstract

It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data.