论文标题
逆电磁障碍物散射问题与多频稀疏反向散射远处数据
Inverse electromagnetic obstacle scattering problems with multi-frequency sparse backscattering far field data
论文作者
论文摘要
本文致力于设计一种逆电磁散射问题的直接采样方法，该方法使用多频率稀疏的反向散射远距离数据来重建完美导致障碍的边界。我们表明，包含未知物体的最小条可以通过两个相反的观察方向的多频反向范围数据来近似确定。证明基于Kirchhoff近似和傅立叶变换。然后，通过指示器重建这样的条带，这是数据乘积积分的绝对值，并且在频率间隔内正确选择了一些函数。随着反向散射数据的数量的增加，可以重建基础对象的位置和形状。进行数值示例以显示所提出的抽样方法的有效性和鲁棒性。数值示例还表明，基础对象的凹点可以很好地重建，并且可以很好地分开基础对象的不同连接组件。
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We show that a smallest strip containing the unknown object can be approximately determined by the multi-frequency backscattering far field data at two opposite observation directions. The proof is based on the Kirchhoff approximation and Fourier transform. Such a strip is then reconstructed by an indicator, which is the absolute value of an integral of the product of the data and some properly chosen function over the frequency interval. With the increase of the number of the backscattering data, the location and shape of the underlying object can be reconstructed. Numerical examples are conducted to show the validity and robustness of the proposed sampling method. The numerical examples also show that the concave part of the underlying object can be well reconstructed, and the different connected components of the underlying object can be well separated.
