Two direct factorization methods for inverse scattering problems
Two direct factorization methods for inverse scattering problems
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DOI：
10.1088/1361-6420/aae15e
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发表时间：
2018-10
期刊：
影响因子：
2.1
通讯作者：
Koung Hee Leem;Jun Liu;G. Pelekanos
中科院分区：
文献类型：
--
作者：
Koung Hee Leem;Jun Liu;G. Pelekanos
在本文中，我们提出并分析了两种新的直接因式分解方法来解决逆散射问题。两种直接因式分解方法均建立在 Kirsch 开发的数学上合理的因式分解方法的基础上。第一个自然是从最近的直接采样方法中导出的，通过将指示函数中相应的远场算子 F 替换为因式分解的远场算子 。第二个基于适当缩放的分解远场算子的逆的截断诺依曼级数近似。两种直接因式分解方法对于噪声来说都是稳定的并且在数学上是等效的。给出了合成和真实实验数据的数值结果，以说明我们提出的直接因式分解方法与基尔希因式分解方法和直接采样方法相比的有希望的准确性。
In this paper, we propose and analyze two new direct factorization methods for solving inverse scattering problems. Both direct factorization methods are built upon the mathematically justified factorization method developed by Kirsch. The first one is naturally derived from a recent direct sampling method by replacing the corresponding far-field operator F in the indicator function by the factorized far-field operator . The second one is based on a truncated Neumann series approximation of the inverse of an appropriately scaled factorized far-field operator. Both direct factorization methods are shown to be stable with respect to noise and mathematically equivalent. Numerical results with both synthetic and real experimental data are presented to illustrate the promising accuracy of our proposed direct factorization methods in comparison to Kirsch’s factorization method and the direct sampling method.