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This paper presents a new approach to handle the nonlinear microwave tomography equations for dielectric materials. The electromagnetic tomography equations are rewritten in the framework of an equivalent wire grid model loaded with resistors and capacitors to represent the permittivity and conductivity of the material. The validation of the model is performed using near-field measurements at a frequency of 2.45 GHz on devices under test made of dielectric plates of various shapes surrounded by an unbounded free-space medium. The reconstruction algorithm is based on the contrast source inversion (CSI) technique. Here, we introduce an enhanced version of the CSI cost function by adding extra regularization terms; in addition, minimization is carried out using a logarithmic barrier constraint in order to avoid nonphysical permittivity and conductivity values. The distributions of those physical properties retrieved with experimental data, for nonhomogeneous dielectric structures of known composition, are in good agreement with the expected ones. The imaging resolution is limited by the density of the wire grid meshing.