A reduced order model approach to inverse scattering in lossy layered media

TL;DR

This paper develops a data-driven reduced order model for inverse electromagnetic scattering in layered lossy media, enabling efficient extraction of unknown dielectric and conductivity parameters from measurements.

Contribution

It introduces a passivity-preserving, sparse-structured ROM constructed solely from measurement data for inverse scattering in layered media.

Findings

ROM accurately approximates the transfer function

Unknown parameters can be efficiently extracted from the ROM

Numerical simulations validate the method's effectiveness

Abstract

We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an antenna which generates a probing wave and measures the time resolved reflected wave. We recast the wave propagation problem as a passive infinite-dimensional dynamical system, whose transfer function is expressed in terms of the measurements at the antenna. The ROM is a low-dimensional dynamical system that approximates this transfer function. While there are many possible ROM realizations, we are interested in one that preserves passivity and in addition is: (1) data driven (i.e., is constructed only from the measurements) and (2) it consists of a matrix with special sparse algebraic structure, whose entries contain spatially localized information about the unknown dielectric permittivity and electrical conductivity of the layered medium. Localized means in the intervals of a special finite difference grid. The main result of the paper is to show with analysis and numerical simulations that these unknowns can be extracted efficiently from the ROM.