Hybridizable Discontinuous Galerkin Method Contrast Source Inversion of 2-D and 3-D Dielectric and Magnetic Targets

Abstract

We present a microwave imaging algorithm capable of simultaneously reconstructing electric and magnetic targets from both electric and magnetic field measurement data, with support for arbitrary imaging system boundaries and inhomogeneous background media. A high-order time-harmonic discontinuous Galerkin method (DGM) forward solver is adopted within a contrast source inversion (CSI) algorithm formulated for electric and magnetic targets. Due to its high-order capabilities, the DGM forward solver effectively decouples the contrast and field discretizations without introducing a dual mesh. The drawback of standard DGM forward solvers, namely, their high computational cost, is addressed by a hybridizable DGM (HDGM) formulation. Synthetic and experimental results for both DGM-CSI and HDGM-CSI are presented for a variety of 2-D and 3-D measurement configurations and both dielectric and magnetic targets. HDGM-CSI is shown to have imaging performance comparable to FEM-CSI for dielectric targets, and significant additional flexibility that will enable future electromagnetic imaging applications and system design.