| Summary: | In this paper, we consider the imaging of targets with a multi-frequency microwave experiment and investigate the best way to take advantage of the frequency-diversity data for reconstructing the three-dimensional permittivity of the objects from the scattered field data. We derive two inversion procedures where the permittivity is estimated iteratively so as to minimize an adequate cost functional. In the first approach, known as the frequency hopping procedure, the inversion scheme is run on a single frequency dataset, starting from the lowest frequency, and its final result is used as an initial guess for the inversion performed on the next frequency dataset. In the second approach, the inversion procedure is applied to the full multi-frequency data. We show on various targets taken from the Fresnel database, that the best reconstructions are obtained when the inversion procedure acts on the full data. The reconstruction can be further ameliorated by modifying the weight of the different frequencies in the cost functional.
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