论文标题
使用内部谐振模式的新型定量逆散射方案
A novel quantitative inverse scattering scheme using interior resonant modes
论文作者
论文摘要
本文专门针对一种新型的定量成像方案，该方案从相关的远场数据中鉴定出时间谐波声音散射的不可穿透障碍。提出的方法由两个阶段组成。在第一阶段，我们通过指示线性采样方法的表明行为来确定远场数据的基本未知障碍物的内部特征值。然后，我们通过解决约束优化问题，进一步确定相关的内部特征函数，再次仅涉及远场数据。在第二阶段，我们提出了牛顿类型的新型迭代方案，以识别障碍物的边界表面。通过使用在第一阶段确定的内部本征函数，我们可以避免在每个牛顿的迭代中计算任何直接散射问题。所提出的方法对于恢复声音障碍的障碍物特别有价值，其中牛顿的公式涉及以自然方式的未知边界表面的几何量。我们提供了对拟议方法的严格理论理由。进行了2D和3D的数值实验，这证实了提出的成像方案的有希望的特征。特别是，它可以以非常有效的方式产生高精度的定量重建。
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we determine the interior eigenvalues of the underlying unknown obstacle from the far-field data via the indicating behaviour of the linear sampling method. Then we further determine the associated interior eigenfunctions by solving a constrained optimization problem, again only involving the far-field data. In the second phase, we propose a novel iteration scheme of Newton's type to identify the boundary surface of the obstacle. By using the interior eigenfunctions determined in the first phase, we can avoid computing any direct scattering problem at each Newton's iteration. The proposed method is particularly valuable for recovering a sound-hard obstacle, where the Newton's formula involves the geometric quantities of the unknown boundary surface in a natural way. We provide rigorous theoretical justifications of the proposed method. Numerical experiments in both 2D and 3D are conducted, which confirm the promising features of the proposed imaging scheme. In particular, it can produce quantitative reconstructions of high accuracy in a very efficient manner.
