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

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-dimens...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Borcea, Liliana, Druskin, Vladimir, Zimmerling, Jörn
Format: Article
Language:English
Subjects:
Antennas
Dynamical systems
Electrical resistivity
Electromagnetic radiation
Finite difference method
Inverse scattering
Lossy media
Mathematical models
Reduced order models
Reflected waves
Transfer functions
Wave propagation
Wave scattering
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Summary: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.
ISSN:2331-8422