Support Reconstruction of Dielectric and Metallic Targets via the Contraction Integral Equation

A new method for support reconstruction is proposed based on the contraction integral equation, a smart rewriting of the scattering equations introduced to alleviate the nonlinearity of the inverse scattering problem. Within such a model, in the case of strong and/or metallic targets, or by a suitable choice of a hyperparameter, the inherent auxiliary function encoding the target properties is expected to assume values close to one inside the target and zero outside. Hence, its retrieval, which is achieved herein using a contrast source inversion method, allows the reconstruction of the support of the obstacle at hand. The achievable performance is tested against simulated and experimental data, including nonconvex dielectric and metallic targets. The cases of multifrequency inversion and dispersive targets are also addressed.