标题： 一种使用内部共振模式的新型定量反散射方案 显示英文标题

标题： A novel quantitative inverse scattering scheme using interior resonant modes

摘要： 本文致力于一种新的定量成像方案，用于从相关的远场数据中识别时谐声散射中的不可穿透障碍物。 所提出的方法包括两个阶段。 在第一阶段，我们通过线性采样方法的指示行为，从远场数据中确定底层未知障碍物的内部特征值。 然后，我们通过求解一个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，我们提出了一种新型的牛顿型迭代方案来识别障碍物的边界表面。 通过使用第一阶段确定的内部特征函数，我们可以避免在每次牛顿迭代中计算任何直接散射问题。 该方法对于恢复硬声障碍物特别有价值，其中牛顿公式以自然的方式涉及未知边界表面的几何量。 我们提供了所提出方法的严格理论依据。 进行了二维和三维的数值实验，这些实验证实了所提出成像方案的有希望的特性。 特别是，它能够以非常高效的方式产生高精度的定量重建。 显示英文摘要

摘要： 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.