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

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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.