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Microwave imaging of inhomogeneous objects made of a finite number of dielectric and conductive materials from experimental data

We deal with an electromagnetic inverse scattering problem where the goal is to characterize unknown objects from measurements of the scattered fields that result from their interaction with a known interrogating wave in the microwave frequency range. This nonlinear and ill-posed inverse problem is tackled from experimental data collected in a laboratory-controlled experiment led at the Institut Fresnel (Marseille, France), which consist of the time-harmonic scattered electric field values measured at several discrete frequencies. The modelling of the wave–object interaction is carried out through a domain integral representation of the fields in a 2D-TM configuration. The inverse scattering problem is solved by means of an iterative algorithm tailored for objects made of a finite number of different homogeneous dielectric and/or conductive materials. The latter a priori information is introduced via a Gauss–Markov field for the distribution of the contrast with a hidden Potts–Markov field for the class of materials in the Bayesian estimation framework. In this framework, we first derive the posterior distributions of all the unknowns and, then, an appropriate Gibbs sampling algorithm is used to generate samples and estimate them. The proposed Bayesian inversion method is applied to both a linear case derived from diffraction tomography and the full nonlinear problem.