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

这一建议有助于发展一种基于电磁正问题和反问题解的非透明介质中目标的电磁成像新技术的基本物理和数学方法和原理。电磁逆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，研究矿产、油气和地下水勘探中的地下地质结构，解决环境清理问题，医学应用中的人体内部结构成像，遥感等，图像重建是基于逆散射电磁问题的数值解。这就需要开发用于非均匀介质中电磁正演和反演的智能计算系统。这些问题是极其困难的，特别是在三维情况下。在这个方案中，我们建议分析和设计计算系统，使数值方法更灵活，更强大的工具来解决具有复杂电磁参数分布的介质中的实际正问题和反问题。该系统将基于应用压缩和数字图像增强和锐化来解决电磁问题。这种压缩允许将原始的麦克斯韦方程转换到一个压缩的区域，并在那里以紧凑的形式获得解。通过压缩，我们将正问题和反问题的原始稠密矩阵转化为稀疏矩阵。图像处理和复原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，同时可以产生目标的清晰和聚焦的图像。我们计划考虑一种使用特别选择的稳定泛函来聚焦EM图像的新方法。特别是，我们将使用一个新的稳定化泛函，它最小化了发生强烈模型参数变化和不连续的区域。我们计划展示聚焦稳定器将有助于产生复杂目标的电磁反问题的稳定解，并且将有助于产生比传统方法更多的聚焦的电磁图像。综上所述，本项目的主要目标是开发一种新的方法和思路，以产生一种新的电磁反成像使能技术。这一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反成像的分辨率和稳定性；2)加快计算速度，利用数据和图像参数压缩技术来解决大型电磁正反问题；3)使不同类型的科学和工程问题能够被广泛地应用于解决涉及非透明介质中目标的反电磁成像的问题。所提出的工作将具有重要意义，原因包括a)将利用压缩原理构建用于电导率任意分布的介质中的三维电磁正演的快速而准确的计算系统；b)将基于压缩和聚焦稳定泛函发展新一代快速三维电磁反演技术；c)将发展复杂结构中电磁数据的分析、设计和评价的改进方法。

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.