Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
Direct Sampling for Recovering Sound Soft Scatterers from Point Source Measurements
复制标题
DOI：
10.3390/computation9110120
复制
发表时间：
2021-10
期刊：
影响因子：
--
通讯作者：
I. Harris
中科院分区：
文献类型：
--
作者：
I. Harris
本文考虑了从测量的散射场中恢复声软散射体的反问题。散射场假设是由已知曲线/曲面上的点源引起的。针对这一问题，我们提出并分析了新的直接抽样方法。我们考虑的第一种方法使用近场数据的远场变换，这允许我们在分辨率分析中导出直接采样法的成像泛函的显式界限。利用远场变换，研究了两种直接采样方法。对于这些成像泛函，我们使用Funk-Hecke恒等式来研究分辨率分析。对于给定柯西数据的情况，我们还研究了一种直接抽样方法。数值算例表明了新的成像泛函对全孔径和部分孔径数据恢复声软散射体的适用性。
In this paper, we consider the inverse problem of recovering a sound soft scatterer from the measured scattered field. The scattered field is assumed to be induced by a point source on a curve/surface that is known. Here, we propose and analyze new direct sampling methods for this problem. The first method we consider uses a far-field transformation of the near-field data, which allows us to derive explicit bounds in the resolution analysis for the direct sampling method’s imaging functional. Two direct sampling methods are studied, using the far-field transformation. For these imaging functionals, we use the Funk–Hecke identities to study the resolution analysis. We also study a direct sampling method for the case of the given Cauchy data. Numerical examples are given to show the applicability of the new imaging functionals for recovering a sound soft scatterer with full and partial aperture data.