A new hybrid FEM-IE inversion method for helmholtz scalar problems

In this work, we introduce a novel inversion method to tackle 2-D scalar inverse scattering problems in non-canonical configurations. This kind of problems is relevant to several applications, such as for instance biomedical imaging, wherein the imaging device is hosted into a casing. The proposed approach is a hybrid method which exploits the integral equation (IE)-based contrast source extended Born (CS-EB) method together with a finite element method (FEM) framework to model the Green´s functions required in the integral operators. While the choice of FEM is motivated by its well known flexibility in describing wave propagation in complex (non-conventional) scenario, the choice of CS-EB is related to its capability of providing reliable inversion results in presence of lossy media. Such a circumstance is assessed by means of synthetic experiments, which show that the proposed FEM-CS-EB method outperforms a similar hybrid scheme exploiting FEM and the widely adopted contrast source inversion (CSI) method.