论文标题
降低的订单模型方法在有损分层介质中的反向散射
A reduced order model approach to inverse scattering in lossy layered media
论文作者
论文摘要
我们使用天线收集的数据引入了分层损耗介质中的逆电磁波散射的降低订单模型（ROM）方法，该数据由天线收集，该天线会产生探测波并测量时间分解的反射波。我们将波浪传播问题重新塑造为一个被动的无限维动力系统，其传递函数是根据天线的测量表达的。 ROM是一个近似此传输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，此外是：（1）数据驱动（即仅根据测量值构建），并且（2）它由具有特殊稀疏代数结构的矩阵组成，其条目包含有关层次介导的空间局部局部信息，这些信息涉及层次的介导性和电子电导率。在特殊有限差网格的间隔内局部平均值。本文的主要结果是通过分析和数值模拟显示这些未知数可以从ROM中有效提取。
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.
