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arXiv · 2012.00861

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

Liliana Borcea·Vladimir Druskin·Jörn Zimmerling
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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.

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Liliana Borcea, Vladimir Druskin, Jörn Zimmerling. 2021-08-03. A reduced order model approach to inverse scattering in lossy layered media. https://arxiv.org/abs/2012.00861

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