论文标题
在逆介质问题的数值解决方案上
On the numerical solution to an inverse medium problem
论文作者
论文摘要
本文涉及从散射场测量值确定可渗透散射对象的位置和形状的逆问题。我们研究以快速稳固的方式恢复散射对象的采样指标函数。该指标函数的灵活性是它适用于在近场政权或远场制度中测量的数据。该功能的实现很简单，并且不涉及解决任何不适的问题。使用Funk-Hecke公式的分数分析研究了指标函数的分辨率分析和稳定性估计。该方法的性能在模拟和实验数据上均得到验证。
This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data.
