Topological derivative strategy for one-step iteration imaging of arbitrary shaped thin, curve-like electromagnetic inclusions

In this manuscript, a fast imaging of thin, curve-like electromagnetic inclusions completely hidden in the homogeneous domain with smooth boundaries is considered. By creating an electromagnetic inclusion of a small diameter and applying the asymptotic expansion formula in the existence of such an inclusion, the topological derivative is successfully derived. Based on this derivative, a one-step iteration imaging algorithm is designed by solving an adjoint problem. Various numerical experiments of single and multiple inclusions demonstrate the viability and limitation of the designed algorithm.