三维稀疏目标探测的电磁逆散射问题高效求解方法研究

项目名称： 三维稀疏目标探测的电磁逆散射问题高效求解方法研究

项目编号： No.61301008

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 无线电电子学、电信技术

项目作者： 朱春辉

作者单位： 厦门大学

项目金额： 26万元

中文摘要： 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。

中文关键词： 三维共性傅里叶变换；混合谱元法；三维正演；三维反演；快速高精度

英文摘要： 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

英文关键词： 3D-CFT；mixed-spectral element method；3D forward scattering；3D inverse scattering；fast and high accurate