An Adaptive Multiscaling Imaging Technique Based on a Fuzzy-logic Strategy for Dealing with the Uncertainty of Noisy Scattering Data

Inverse scattering data, even though collected in a controlled-environment, are usually corrupted by 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 information content available from the measurements, an innovative inversion scheme based on the integration of an adaptive multiscale procedure and a fuzzy-logic (FL)-based strategy is proposed. The main goal of the approach is to reduce the complexity of the problem as well as to improve the robustness of the inversion procedure allowing an accurate retrieval of the profile under test. The approach is based on an adaptive, coarse-to-fine successive representation of the unknown object obtained through a sequence of reconstructions where suitable weighting coefficients are defined through a FL. Key elements of the theoretical analysis are given and several numerical examples, concerned with synthetic and experimental test cases, illustrate the consequences of the proposed approach in terms of both resolution accuracy and robustness as well as computational costs.