Contrast Source Extended Born Inversion in Noncanonical Scenarios Via FEM Modeling

The contrast source extended Born formulation of the electromagnetic scattering is based on a simple rewriting of standard source type integral equations and allows enhancing the reliability of the inverse problem´s solution, especially when losses are present in the scenario. The method has been developed in the framework of integral equations, so that its application has been so far limited to canonical scenarios, where the Green´s function is available. To overcome this drawback, in this work we consider a generalization of the contrast source extended Born scheme based on a finite element formalism, which opens the way to a much more flexible algorithm, capable of handling noncanonical configurations. Additionally, we also propose a new hybrid strategy that simultaneously exploits both the well-known contrast source formulation and the contrast source extended Born one and it is capable to achieve improved imaging performance with respect to both of them. Numerical examples are reported to illustrate the performance of the proposed inversion methods.