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Novel Sampling Methods for Electromagnetic Inverse Scattering Theory

电磁逆散射理论的新颖采样方法

基本信息

批准号：
2208293
负责人：
Dinh-Liem Nguyen
金额：
$ 19.85万
依托单位：
Kansas State University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-08-01 至 2025-07-31
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2208293&HistoricalAwards=false
关键词：
Novel Sampling Methods Electromagnetic Inverse

项目摘要

The inverse electromagnetic scattering problem (IESP) aims to determine an unknown object from the electromagnetic fields scattered by that object. The IESP has been an active research topic in the engineering, mathematics, and physics communities for the past three decades due to its impact on a wide range of applications including radar, nondestructive testing, medical imaging, and geophysical exploration. However, solving the IESP is very challenging since this problem is in general highly nonlinear and severely ill-posed. Therefore, although computational algorithms have been extensively studied for the IESP, there is still a high demand for algorithms with improved efficiency and robustness. The project addresses this demand by developing new and highly efficient sampling-type algorithms for the IESP in the context of optics and radar. This project will also involve the training of undergraduate and graduate students in computational mathematics. Solving the IESP involves proper sampling methods to construct an approximate indicator function for the unknown scattering object. Ideally these sampling methods are fast, non-iterative, and do not require a priori information about the scattering object. In this project, the principal investigator and graduate students will develop new sampling-type methods for the IESP for both the Helmholtz equation and the system of Maxwell's equations in different types of scattering media, including infinite periodic media, small and point-like objects, bounded inhomogeneous media, and nonlinear media. In addition to the aforementioned features, the sampling-type methods that will be developed in this project will be simple to implement and extremely robust against noise in the data. The resolution and stability analysis of these sampling-type methods and their validation by experimental data will be investigated. The new methods are expected to provide a promising alternative tool to solve the IESP in optics and radar.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

电磁散射逆问题（IESP）的目的是确定一个未知的目标，从该目标散射的电磁场。在过去的三十年里，IESP一直是工程，数学和物理界的一个活跃的研究课题，因为它对雷达，无损检测，医学成像和地球物理勘探等广泛的应用产生了影响。然而，解决IESP是非常具有挑战性的，因为这个问题通常是高度非线性和严重不适定的。因此，虽然计算算法已被广泛研究的IESP，仍然有一个高的需求，提高效率和鲁棒性的算法。该项目通过在光学和雷达的背景下为IESP开发新的高效采样型算法来满足这一需求。该项目还将涉及在计算数学方面对本科生和研究生的培训。解决IESP涉及到适当的采样方法来构建一个近似的指示函数的未知散射对象。理想地，这些采样方法是快速的、非迭代的，并且不需要关于散射对象的先验信息。在这个项目中，首席研究员和研究生将开发新的采样类型的方法IESP的亥姆霍兹方程和麦克斯韦方程组在不同类型的散射介质，包括无限周期性介质，小和点状物体，有界非均匀介质和非线性介质。除了上述功能外，本项目中将开发的采样类型方法将易于实现，并且对数据中的噪声非常强大。这些采样类型的方法和实验数据验证的分辨率和稳定性分析将进行研究。新方法有望为解决光学和雷达领域的IESP问题提供一种有前途的替代工具。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。