Untangling the nonlinearity in inverse scattering with data-driven reduced order models
Untangling the nonlinearity in inverse scattering with data-driven reduced order models
复制标题
通过数据驱动的降阶模型理清逆散射中的非线性
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Zaslavsky
中科院分区：
文献类型：
--
作者：
L. Borcea;V. Druskin;A. Mamonov;M. Zaslavsky
这项工作的动机是声波方程的逆问题，其中传感器阵列用脉冲探测未知介质并测量散射波。反演的目标是从这些测量中确定散射介质的结构，由空间变化的声阻抗函数建模。许多反演算法假设从未知阻抗到散射波的映射近似为线性。线性化，即玻恩近似，在强散射介质中是不准确的，在强散射介质中，波在到达阵列中的传感器之前经历多次反射。因此，阻抗的重建具有许多伪影。本文的主要结果是一种新的，线性代数算法，使用降阶模型（ROM）映射的数据对应的单散射（玻恩）模型。ROM构造仅基于阵列中的传感器处的测量。ROM是波传播算子的代理，其在时间采样间隔的持续时间内在未知介质中传播波。该算法的输出可以输入到任何现成的反演软件中，该软件结合了最先进的线性反演算法来重建未知的声阻抗。
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these measurements the structure of the scattering medium, modeled by a spatially varying acoustic impedance function. Many inversion algorithms assume that the mapping from the unknown impedance to the scattered waves is approximately linear. The linearization, known as the Born approximation, is not accurate in strongly scattering media, where the waves undergo multiple reflections before they reach the sensors in the array. Thus, the reconstructions of the impedance have numerous artifacts. The main result of the paper is a novel, linear-algebraic algorithm that uses a reduced order model (ROM) to map the data to those corresponding to the single scattering (Born) model. The ROM construction is based only on the measurements at the sensors in the array. The ROM is a proxy for the wave propagator operator, that propagates the wave in the unknown medium over the duration of the time sampling interval. The output of the algorithm can be input into any off-the-shelf inversion software that incorporates state of the art linear inversion algorithms to reconstruct the unknown acoustic impedance.
DOI：
10.1145/3323679.3326516
发表时间：
2019-07
期刊：
Proceedings of the Twentieth ACM International Symposium on Mobile Ad Hoc Networking and Computing
影响因子：
--
作者：
Qiang Liu;Tao Han
通讯作者：
Qiang Liu;Tao Han