A globally convergent numerical method for a 1-d inverse medium problem with experimental data
A globally convergent numerical method for a 1-d inverse medium problem with experimental data
复制标题
DOI：
10.3934/ipi.2016032
复制
发表时间：
2016-02
期刊：
影响因子：
--
通讯作者：
M. Klibanov;L. Nguyen;A. Sullivan;Lam Nguyen
中科院分区：
文献类型：
--
作者：
M. Klibanov;L. Nguyen;A. Sullivan;Lam Nguyen
本文研究了由后向散射波场在频域中重建介质介电常数空间分布的方法。我们的方法是提出一个全局收敛的算法，它不需要任何知识的一个小邻域的解的反问题。算法中采用了拟可逆方法。通过Carleman估计证明了QRM的收敛性。计算模拟和实验数据的方法进行了测试。
In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm, which does not require any knowledge of a small neighborhood of the solution of the inverse problem in advance. The Quasi-Reversibility Method (QRM) is used in the algorithm. The convergence of the QRM is proved via a Carleman estimate. The method is tested on both computationally simulated and experimental data.