论文标题
分析非线性逆散射问题散射场中的自由度
Analysis of Degrees of Freedom in Scattered Fields for Nonlinear Inverse Scattering Problems
论文作者
论文摘要
在非线性逆散射问题（ISP）的研究中，估计散射场的自由度（NDOF）数量的传统方法不考虑散射器对比的效果。在这项工作中，我们通过修改辐射基质来研究NDOF与散射器对比度之间的关系。具体而言，提出了用于计算NDOF的三种数值方法。第一个NDOF定义为外部辐射矩阵的主要奇异值的数量，该值用作基准。第二个NDOF是根据修饰的辐射基质定义的，该辐射矩阵将研究域（DOI）与外部辐射基质的对比度结合在一起。通过探索第二个NDOF和对比之间的关系，获得了第二个NDOF的近似上限，即第三个NDOF。通过使用频率域零盖方法对综合和实验数据的插值实验验证了所提出的NDOF的准确性。结果表明，对于高对比度散射器而言，第二个NDOF比传统NDOF更准确，并且第三个NDOF可以通过传统NDOF加上正常常数轻松估算，这提供了一种简单的方法来估计NDOF的上限。
In the study of nonlinear inverse scattering problems (ISPs), the traditional method for estimating the number of degrees of freedom (NDoF) of the scattered field does not consider the effect of the scatterer contrast. In this work, we study the relationship between NDoF and scatterer contrast by modifying the radiation matrix. Specifically, three numerical methods for calculating the NDoF are presented. The first NDoF is defined as the number of principle singular values of the external radiation matrix, which is used as a benchmark. The second NDoF is defined based on the modified radiation matrix that incorporates the contrast of domain of investigation (DoI) with the external radiation matrix. By exploring the relationship between the second NDoF and contrast, an approximate upper bound of the second NDoF is obtained, that is, the third NDoF. The accuracy of the proposed NDoF is verified by interpolation experiments on both synthetic and experimental data using frequency-domain zero-padding method. Results show that the second NDoF is more accurate than traditional NDoF for high-contrast scatterers, and the third NDoF can be easily estimated by the traditional NDoF plus a positive constant, which provides a simple way to estimate the upper bound of NDoF.
