A direct sampling method for simultaneously recovering electromagnetic inhomogeneous inclusions of different nature

Abstract

In this work, we propose a novel direct sampling method (DSM) to recover the support of two different types of electromagnetic inhomogeneous inclusions simultaneously, with only one or two sets of noisy boundary measurement data. The DSM leverages upon an important mutually almost orthogonality property between the fundamental solutions of the forward problem and some proper families of probing functions. Two proper families of probing functions that possess desired properties are proposed to reconstruct the support of inhomogeneous inclusions accurately in the direction that is parallel to or vertical to the measurement surface separately. For the two families of probing functions, the mutually almost orthogonality property is carefully verified through both theoretical justifications and numerical experiments. The novel DSM is fast to compute, effective under limited measurement data, and very stable and robust against random noise of reasonable size. All these features are verified through extensive numerical experiments.