Analysis and Design of Computational Systems for Three-Dimensional Electromagnetic Modeling and Inversion

三维电磁建模与反演计算系统的分析与设计

• 批准号: 9987779
• 负责人: Michael Zhdanov
• 金额: $ 25万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-15 至 2003-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9987779&HistoricalAwards=false
• 关键词: Analysis; Design; Computational; Systems; Three

This proposal contributes to the development of the underlying physical and mathematical methods and principles of a new technology of electromagnetic (EM) imaging the objects in nontransparent media based on EM forward and inverse problem solutions. EM inverse methods are widely used in different technical and engineering applications, including determining the internal defects in the metal or concrete constructions, for studying the underground geological structures in mineral, hydrocarbons and groundwater exploration, in the solution of environmental clean up problems, for imaging of the internal structure of human body in medical applications, in remote sensing, etc. The image reconstruction is based on the numerical solution of the inverse scattering EM problem. This problem requires development intelligent computational systems for EM forward modeling and inversion in inhomogeneous media. These problems are extremely difficult, especially in three-dimensional case. In this proposal we suggest to analyze and design the computational systems which make the numerical methods more flexible and more powerful tool for the solution of practical forward and inverse problems in media with a complex distribution of EM parameters. This system will be based on applying compression and numerical image enhancement and sharpening in the solution of EM problems. The compression allows transforming the original Maxwell's equations into a compressed domain, and the solution is obtained there in a compact form. Using compression, we convert the original dense matrix of the forward and inverse problems to a sparse matrix. This reduces the memory required for storage and speeds up computations.Image processing and restoration is one of the important problems in EM imaging. It requires developing a stable inverse problem solution that at the same time can produce a sharp and focused image of the target. We plan to consider a new way of focusing EM images using specially selected stabilizing functionals. In particular, we will use a new stabilizing functional, which minimizes the area where strong model parameter variations and discontinuity occur. We plan to demonstrate that focusing stabilizer will help to generate a stable solution of EM inverse problem for complex objects, and will help to generate much more ''focused'' EM images than conventional methods. In summary, the main goal of this project is to develop new methods and ideas that will result in a new enabling technology for EM inverse imaging.This new technology will address the following problems: 1) to increase the resolution and stability of inverse imaging by applying regularization method based on focusing stabilizers; 2) to speed up computations and to enable solution of large EM forward and inverse problems using data and image parameters compression technique; 3) to enable general application for solution of different type of scientific and engineering problems involving inverse EM imaging of the objects in nontransparent media.The proposed work will be significant for several reasons includinga) fast and accurate computational system for 3-D EM forward modeling in the media withthe arbitrary distribution of conductivity will be constructed using compressionprinciples;b) a new generation of fast 3-D EM inversion techniques will be developed based oncompression and focusing stabilizing functionals;c) improved methods for analysis, design and evaluation of electromagnetic data in complexstructures will be developed.

该提案有助于开发基于电磁正向和逆向问题解决方案对非透明介质中的物体进行电磁 (EM) 成像的新技术的基础物理和数学方法和原理。电磁反演方法广泛应用于不同的技术和工程应用，包括确定金属或混凝土结构的内部缺陷，用于研究矿物、碳氢化合物和地下水勘探中的地下地质结构，解决环境清理问题，用于医疗应用中的人体内部结构成像、遥感等。图像重建基于反散射电磁问题的数值解。这个问题需要开发智能计算系统，用于非均匀介质中的电磁正演建模和反演。这些问题非常困难，尤其是在三维情况下。 在本提案中，我们建议分析和设计计算系统，使数值方法更加灵活，成为解决具有复杂电磁参数分布的介质中的实际正向和逆向问题的工具。该系统将基于在解决电磁问题时应用压缩和数值图像增强和锐化。压缩允许将原始麦克斯韦方程转换为压缩域，并以紧凑形式获得解。使用压缩，我们将正向和逆向问题的原始稠密矩阵转换为稀疏矩阵。这减少了存储所需的内存并加快了计算速度。图像处理和恢复是电磁成像中的重要问题之一。它需要开发一个稳定的反问题解决方案，同时可以产生清晰且聚焦的目标图像。我们计划考虑一种使用专门选择的稳定功能来聚焦电磁图像的新方法。特别是，我们将使用一种新的稳定泛函，它可以最大限度地减少模型参数变化和不连续性发生的区域。我们计划证明聚焦稳定器将有助于为复杂物体生成电磁反问题的稳定解决方案，并将有助于生成比传统方法更多“聚焦”的电磁图像。总之，该项目的主要目标是开发新的方法和想法，从而产生一种新的电磁逆成像使能技术。这项新技术将解决以下问题：1）通过应用基于聚焦稳定器的正则化方法来提高逆成像的分辨率和稳定性； 2) 使用数据和图像参数压缩技术加速计算并能够解决大型电磁正向和反演问题； 3）使涉及非透明介质中物体的逆电磁成像的不同类型的科学和工程问题的解决成为可能。所提出的工作将具有重要意义，原因包括：a）将使用压缩原理构建具有任意电导率分布的介质中的快速准确的3-D EM正演建模计算系统；b）将开发基于压缩和聚焦稳定的新一代快速3-D EM反演技术 泛函；c) 将开发复杂结构中电磁数据分析、设计和评估的改进方法。