有耗分层介质逆散射的降阶模型方法
A reduced order model approach to inverse scattering in lossy layered media
摘要：
我们介绍了一种降阶模型（ROM）的方法，在分层有耗介质中的逆电磁波散射，使用由天线产生的探测波和测量的时间分辨反射波收集的数据。我们重铸的波传播问题作为一个被动的无限维动力系统，其传递函数表示在天线的测量。ROM是一个低维的动力系统，近似这个传递函数。虽然有许多可能的ROM实现，但我们感兴趣的是保持被动性的一种，此外还有：（1）数据驱动（即，仅根据测量值构造）和（2）它由具有特殊稀疏代数结构的矩阵组成，其条目包含关于分层介质的未知介电常数和电导率的空间局部化信息。局部化的意思是在一个特殊的有限差分网格的间隔。本文的主要结果是通过分析和数值模拟表明，这些未知量可以有效地从ROM中提取。
英文摘要：
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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