Inverse Problems in 3D Full wave Electromagnetics

Abstract

An inverse problem in Electromagnetics (EM) refers to the process of reconstructing the physical system by processing the measured data of its electromagnetic properties. Inverse problems are typically ill-posed, and this makes them far more challenging than the typically well-posed forward problem. The solution of such inverse problems finds applications in nondestructive testing and evaluation, biomedical imaging, geophysical exploration etc. This thesis addresses some inverse problems specific to the area of electromagnetics, arising in three different scenarios. The first problem is 3-D quantitative imaging primarily targeted towards bio-medical applications. The task is to retrieve the dielectric properties, location and the shape of an unknown object from the measured scattered field. The unknown object is modeled by discretization into several voxels, with each voxel having its own dielectric property. As the inverse problem is non-linear, typically an iterative optimization process is adopted, and a forward problem needs to be solved at every iteration. The total time for reconstruction depends on the forward solver time and the number of iterations. In many cases, the number of unknowns to be reconstructed is prohibitively large. Further, the non-convergence or false-convergence of the optimization process presents its own challenge. This thesis proposes two methodologies to solve these challenges. In the first approach a multilevel methodology is proposed where voxels are hierarchically decomposed into smaller voxels based on an appropriate indicator, leading to a non-uniform multilevel voxel structure aimed at reducing the eventual number of unknowns to be solved for, also enabling faster convergence. In the second approach, a two-stage framework is proposed comprising of Machine Learning classification followed by optimization (ML-OPT). The first stage generates an appropriate adaptive grid for the optimization process and provides a suitable initial guess aiding convergence to the global minima...