Fuzzy-Logic Reasoning for Estimating the Reliability of Noisy Data in Inverse Scattering Problems

Inverse scattering data, even though collected in a controlled environment, are usually corrupted by electromagnetic noise, which strongly affects the effectiveness of the reconstruction techniques because of the intrinsic ill-positioning of the problem. In order to limit the effects of the noise on the retrieval procedure and to fully exploit the limited information content available from the measurements, an innovative inversion scheme based on the integration of an adaptive multi-scale procedure and a fuzzy-logic-based decision strategy is proposed. The approach is based on an adaptive, coarse-to-fine successive representation of the unknown object obtained through a sequence of nonlinear reconstructions where suitable weighting coefficients are defined using fuzzy logic. Numerical examples from synthetic and experimental test cases are given to illustrate the advantages brought by the proposed approach in terms of reconstruction quality.