Enhancement of the Contrast Source Inversion Method Using Fuzzy Logic

The problem of determining the proprieties of an unknown object by means of electromagnetic waves probing the object is intrinsically instable with respect to the presence of noise and measurement errors on scattering data. In several practical condition in the framework of medical imaging, non-destructive testing, and sub-surface inspection, these errors are unavoidable and the ill-posedness of the system leads to inaccurate reconstructions of the scenario under test. In [1], an innovative fuzzy-logic-based strategy has been proposed for properly taking into account the presence of the noise and errors on the data. Such a system provides, in an unsupervised way, two series of coefficients that can be used as weighting parameters of the arising cost function to be minimized. In that paper, the mathematical formulation was presented considering the contrast and the fields equations. In this work, a further assessment of the proposed fuzzy-logic approach is carried out operating with data and state equations expressed in terms of the contrast and the contrast sources as suggested in [2]. Selected results from the numerical simulations are reported to assess the performances of the system with single and multi-frequency data with and without total-variation-based regularization. This is the author's version of the final version available at IEEE.