Electromagnetic (EM) field prediction is a fundamental problem with many practical applications, such as radar cross-section estimation, indoor positioning, and WiFi access point planning. In this thesis, we explore the ideas of EM field prediction in indoor scattering environments using surface integral formulation. In doing so, we do not assume prior knowledge of the permittivities or the exact geometry of the scattering objects. However, we assume that the region between the scatterers is homogeneous.

A novel approach based on Huygens' principle and compressive sensing is developed to predict the electromagnetic (EM) fields in arbitrary scattering environments by making a few field measurements. We develop two methods for EM field prediction based on the type of field measurements (i) compressive sensing-based subspace optimization method (CS-SOM) when source distribution (incident field) is known (ii) total field compressive sensing-based subspace optimization method (TCS-SOM) when source distribution is unknown. We validate and test the methods by performing numerical experiments on synthetically generated scattering environments which mimic the indoor scattering scenario. Further, we identify the best measurement locations in the environment, which reduces the prediction error to approximately half of the error obtained when using random locations.

To conclude, we present two applications of the proposed methods in the area of (i) microwave imaging and (ii) subsurface radar imaging. Most microwave inverse imaging algorithms rely on measurements of the total and the incident electric field to estimate the dielectric properties of an unknown scattering object. With TCS-SOM, we jointly estimate the incident field and relative permittivity of a heterogeneous dielectric object from measurements of the total electric field alone. Finally, we extend the optimal sensor location strategy for subsurface radar imaging of a two-layered background medium imaged via a multi-frequency, multi-monostatic configuration. For both the applications we quantify the performance via extensive numerical simulations and experimental data.

Keywords : Microwave Imaging, Compressive Sensing, Inverse Scattering, Sensor Placement, Sensor location, Subsurface Imaging, Ground Penetrating Radars