Evolutionary Techniques For Inverse Scattering: Current Trends and Envisaged Developments

The possibility of sensing a given region from the measurements of the scattered field when it is illuminated through low‐power microwave electromagnetic waves is still a topic of great interest due to the wide range of applications in many different areas of medical, industrial, and civil engineering. For instance, let us consider problems related to biomedical engineering, non‐invasive thermometry, non‐destructive testing and evaluation, geophysical analysis, remote sensing, and archeology. Although this list is certainly non‐exhaustive, it is sufficient to justify the great attention devoted to the solution of inverse scattering problems both from a theoretical and algorithmic point of view, as demonstrated by the large amount of papers and books available in the scientific literature. The issues that actually limit the proliferation of practical imaging systems are the intrinsic theoretical difficulties (i.e., ill‐posedness and non‐linearity), which characterize an inverse scattering problem. The ill‐posedness can be avoided by using additional (a‐priori) information directly taken from the physics of the problem at hand. This strategy allows one to avoid the reconstruction of artifacts and obtain the so‐called regularized solutions. Concerning the non‐linearity of the inverse scattering model, it must be considered to take into account the multiple‐scattering effects, since linear approximations (e.g., Born‐like approaches) can be rarely applied to real objects. Accordingly, many non‐linear inversion techniques have been proposed for the optimization of a suitable cost function taking into account the mismatch between the measured data and the reconstructed ones. Originally, various deterministic approaches based on steepest‐descent algorithms [e.g., conjugate‐gradients (CG)] were proposed [1]. Although they have shown to provide successful results, they suffer the presence of local minima when initial solution does not belong to the “attraction basin” of the global optimum.