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.

我们介绍了一种降阶模型 (ROM) 方法，用于分层有损介质中的逆电磁波散射，使用由天线收集的数据，该天线生成探测波并测量时间分辨反射波。我们将波传播问题重新定义为无源无限维动力系统，其传递函数以天线测量值表示。ROM 是一个近似这个传递函数的低维动力系统。虽然有许多可能的 ROM 实现，但我们对保留被动性的一种感兴趣，此外还有：（1）数据驱动（即，仅从测量值构建）和（2）它由具有特殊稀疏代数结构的矩阵组成, 其条目包含关于层状介质的未知介电常数和电导率的空间局部信息。局部化意味着在一个特殊的有限差分网格的区间内。本文的主要结果是通过分析和数值模拟表明可以从 ROM 中有效地提取这些未知数。