三维稀疏目标探测的电磁逆散射问题高效求解方法研究

Technique of object detection and reconstruction is one of the important techniques in modern information science. The nonlinear inverse scattering method considering the multiple scattering effect, can accurately obtain the geometry and physical properties of target objects. The computational efficiency and ill-posed property of the nonlinear inverse scattering method are the bottlenecks and main research focuses. The applicant has developed the conformal Fourier transform for 1D and 2D cases, whose computational efficiency is tens to tens of thousands times better than FFT; and designed a novel method for solving the volume integral equation in 1D, who can get 2 to 6 magnitudes better performance in accuracy than BCGS-FFT. Based on these works, this proposal takes the nonlinear inverse scattering problem for sparse 3D object reconstruction as the research background; takes the efficient method of computing the convolution in the forward problem of the electromagnetic volume integral equation, and the reliable method of solving the ill-posed equation that updates parameters when using variational Born iteration method in the backward problem, as the research core. The research mainly focuses on three aspects: (1) the 3D conformal Fourier transform method; (2) the fast and high accurate half-analytical method of solving the forward problem; (3) the configuration of the measurement matrix based on compressive sensing in the equation that updating the parameters, when using variational Born iteration method. This research will propose a fast and high accurate method for solving the nonlinear electromagnetic inverse scattering problem, and develop a reliable technique in sparse 3D object reconstruction based on electromagnetic inverse scattering problem. This research will play a positive role to promote the development of the object detection and reconstruction technique, especially for the large scale cases in 3D.

探测目标重建技术是现代信息科学的重要技术之一。非线性逆散射方法考虑多次散射效应，可精确得到目标的几何和物理性质。求解效率的提高和不适定性的处理方法是非线性逆散射问题的发展瓶颈和研究热点。申请者前期提出的一维和二维共形傅立叶变换方法计算效率比FFT高几十到上万倍，提出的一维电磁散射非线性体积分方程解法求解精度比BCGS-FFT高2到6个数量级。在此基础上，本项目以三维稀疏目标重建的非线性电磁逆散射问题为背景；以电磁体积分方程正演问题中卷积的高效计算方法与反演问题迭代中参数的可靠更新方法为核心。研究1）三维共形傅立叶变换方法；2）正演问题半解析卷积快速高精度计算方法；3）压缩感知理论指导下，反演迭代中欠定参数更新方程测量矩阵的构造方式。最终形成系统的非线性电磁逆散射问题快速高精度解法，实现高效可靠的电磁逆散射稀疏目标重建技术，积极的推动电磁逆散射目标探测技术，尤其是大规模三维探测技术的发展。

探测目标重建技术是现代信息科学的重要技术之一。非线性逆散射方法考虑多次散射效应，可精确得到目标的几何和物理性质。求解效率的提高和不适定性的处理方法是非线性逆散射问题的发展瓶颈和研究热点。为了提高三维正演方法的效率，本项目研究了三维共形Fourier变换算法，建立了基于混合谱元法的三维电磁体积分方程正演问题的快速高精度求解方法，结合压缩感知和波恩迭代技术实现了高效可靠的电磁场逆散射反演技术；同时为了对所提出的方法进行对比验证，在项目实施过程中增加了对传统FDTD方的改进和研究。所提出的三维共形Fourier变换算法和正演方法具有谱精度，可以在极低频的探测频率下仍旧能很好的反应实际情况，所提出三维反演算法可以得到15%以下的反演精度。.在本项目的全部或部分支持下，在国内外重要学术期刊和国际会议上发表相关学术论文17篇，其中期刊论文13篇，全部为SCI检索(JCR二区7篇，JCR三区3篇，JCR4四区3篇)，会议论文4篇，全部为EI检索。以本项目为第一标注的期刊论文5篇，会议论文1篇。以项目负责人为第一作者或通讯作者的期刊论文三篇（JCR二区2篇，JCR四区1篇），会议论文1篇。以项目负责人或参与者为第一作者或通讯作者的期刊论文11篇，会议论文2篇。.由于三维电磁逆散射的庞大计算复杂度，目前得到应用的地球物理勘探仪器中所携带的软件以一维或者一维和二维组合成的伪三维计算成像为主。本项目所研究的三维问题的三维稀疏目标探测的电磁逆散射问题高效求解方法对于提高地球物理勘探的效率和成像质量是一项非常重要而有意义的工作。