Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems
复制标题
用于逆散射问题的 Lippmann-Schwinger-Lanczos 算法
DOI：
10.1088/1361-6420/abfca4
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Druskin, Zaslavsky
中科院分区：
文献类型：
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作者：
Druskin, Zaslavsky
数据驱动的降阶模型（ROM）与Lippmann-Schwinger积分方程相结合，产生一个直接的非线性反演方法。ROM被视为Galerkin投影，由于Lanczos正交化而稀疏。嵌入到连续问题中，产生了数据驱动的内部解决方案。这个内部解然后被用于李普曼-施温格方程中，从而使进一步的迭代更新变得不必要。我们的反演是远远上级玻恩反演和工程，以及当真正的内部解决方案是已知的谱域域数据的数值实验。
Data-driven reduced order models (ROMs) are combined with the Lippmann–Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization. Embedding into the continuous problem, a data-driven internal solution is produced. This internal solution is then used in the Lippmann–Schwinger equation, thus making further iterative updates unnecessary. We show numerical experiments for spectral domain domain data for which our inversion is far superior to the Born inversion and works as well as when the true internal solution is known.