Simultaneous high-order contrast source inversion of dielectric and magnetic targets

Magnetic contrast agents have been recently proposed as a method of improving the capabilities of microwave imaging for cancer diagnosis, detection and treatment monitoring. In order to exploit these contrast agents, electromagnetic inversion algorithms should be based on forward solvers capable of predicting the scattered fields from both dielectric and magnetic targets. To this end we have developed a high-order, nonlinear inversion algorithm for the simultaneous inversion of magnetic and dielectric targets using the contrast source inversion (CSI) formulation of the inverse problem. The inverse solver uses a high-order, time-harmonic, discontinuous Galerkin formulation of Maxwell´s equations and supports unstructured discretizations of dielectric, magnetic and perfectly conducting media. The resulting CSI formulation is an unstructured, high-order extension of an existing dielectric and magnetic CSI formulation (A. Abubakar and P. M. van den Berg, J. Comput. Phys., 195(1), 236-262, 2004), and extends FEM-CSI (A. Zakaria, C. Gilmore and J. LoVetri, Inverse Probl., 26(11), 115010, 2010) to both high-order and magnetic materials. In this work we will focus on the modifications to the CSI formulation required to support independent expansion orders for the contrast, contrast sources and fields. High-order contrast expansions effectively decouple the solution from the underlying discretization and, for the same level of accuracy, reduce the number of degrees of freedom in the iterative inversion process. An exact radiating boundary condition has been implemented for open problems and, at the cost of computational time and memory, yields an error-controllable forward solver for electromagnetic inversion. The reconstructions of both dielectric and/or magnetic targets will be presented for two-dimensional image reconstruction of synthetic and experimental data.