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.

逆电磁散射问题（IESP）旨在从该物体散射的电磁场确定一个未知物体。在过去的三十年中，IESP一直是工程，数学和物理社区中的一个积极研究主题，因为它对包括雷达，无损测试，医学成像和地球物理探索等广泛应用的影响。但是，解决IESP非常具有挑战性，因为这个问题通常是高度非线性的，并且严重不良。因此，尽管已经对IESP进行了广泛研究了计算算法，但对具有提高效率和鲁棒性的算法的需求仍然很高。该项目通过在光学和雷达的背景下为IESP开发新的，高效的采样类型算法来解决这一需求。该项目还将涉及计算数学的本科和研究生的培训。求解IESP涉及适当的采样方法，以构建未知散射对象的近似指示器函数。理想情况下，这些抽样方法是快速，非著作，并且不需要有关散射对象的先验信息。在该项目中，主要研究人员和研究生将为Helmholtz方程式IESP开发新的采样型方法，以及在不同类型的散射媒体中的Maxwell方程系统，包括无限型和点状的物体，包括无限元素的媒体和非线性媒体。除了上述功能外，该项目中将开发的采样型方法将非常易于实现，并且对数据中的噪声非常强大。将研究这些采样类型方法的分辨率和稳定性分析及其通过实验数据进行验证。预计新方法将提供一个有希望的替代工具来解决ISP的光学和雷达。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准通过评估来获得支持的。