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. This approach is aimed at detecting breast tumors where the optimization algorithm can aim for higher resolution in the suspected tumor region, while using lower resolution elsewhere. The second problem is in the domain of high-speed circuits and is focused on synthesis of transmission line physical parameters given the desired electrical parameters like characteristic impedance and propagation constant. A forward solver is used to train Neural network for several different configurations for analysis and an optimization algorithm is used for synthesis. The third problem is focused on finding the source of radiation in an electronic system e.g. an automotive ECU, given the measured field at the antenna in the radiated emissions setup. The source of radiation can be from common mode current on the cable harness or from the Design Under Test (DUT). A method based on Huygens box is proposed to quantify the radiation from cable and DUT at each frequency. On each cell of the Huygens box the value of electric field computed at the observation point taking the Electric Current (J) and Magnetic Current (M) on that cell as sources and this information on the Huygens box is used to quantify the radiation. Some part of the presented work is used via technology-transfer at Simyog Technology Pvt. Ltd., an IISc incubated startup, to develop a simulation software called Compliance-scope which allows the hardware designer to predict the EMI/EMC performance of electronics modules from an early design stage.