The no-response approach and its relation to non-iterative methods for the inverse scattering
The no-response approach and its relation to non-iterative methods for the inverse scattering
复制标题
DOI：
10.1007/s10231-006-0030-1
复制
发表时间：
2005-10
影响因子：
1
通讯作者：
N. Honda;G. Nakamura;R. Potthast;M. Sini
中科院分区：
文献类型：
--
作者：
N. Honda;G. Nakamura;R. Potthast;M. Sini
本文解决了逆障碍物散射问题。近年来，人们提出了几种非迭代方法来根据近场或远场测量重建障碍物（可穿透或不可穿透）。按照时间顺序，我们列举了线性抽样法、因式分解法、探测法和奇异源法等。这些方法使用不同的测量来检测未知障碍物，并且它们需要使用许多入射场（即远场图的全部或部分）。最近，添加了另外两种方法。它们是无响应测试和范围测试。两者都使用很少的入射场来检测有关散射体的一些信息。所有提到的方法都是基于根据某些参数构建函数。这些函数都有一个共同的特性，即它们的行为相对于参数会发生巨大的变化。障碍物的表面最多位于这些函数变大的界面中。这项工作的目标是研究一些关于收敛问题的非迭代重建方案之间的关系。如果给定方法分别使用少量或大量入射场重建部分或整个障碍物，则称该方法是收敛的。为了简单起见，我们考虑亥姆霍兹方程的远场数据的障碍物重建问题。
This paper addresses the inverse obstacle scattering problem. In the recent years several non-iterative methods have been proposed to reconstruct obstacles (penetrable or impenetrable) from near or far field measurements. In the chronological order, we cite among others the linear sampling method, the factorization method, the probe method and the singular sources method. These methods use differently the measurements to detect the unknown obstacle and they require the use of many incident fields (i.e. the full or a part of the far field map). More recently, two other approaches have been added. They are the no-response test and the range test. Both of them use few incident fields to detect some informations about the scatterer. All the mentioned methods are based on building functions depending on some parameter. These functions share the property that their behaviors with respect to the parameter change drastically. The surface of the obstacle is located at most in the interface where these functions become large. The goal of this work is to investigate the relation between some of the non-iterative reconstruction schemes regarding the convergence issue. A given method is said to be convergent if it reconstructs a part or the entire obstacle by using few or many incident fields respectively. For simplicity we consider the obstacle reconstruction problem from far field data for the Helmholtz equation.