Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies

The aim of this paper is twofold. First, why and how exploitation of multifrequency information is of great usefulness in inverse scattering problems is discussed. Second, three different solution strategies, all based on a recently introduced approach, are presented, discussed, and compared in the actual case of noise affected data in the two-dimensional (2D) scalar case. The first one is a (nonlinear) frequency-hopping technique, which favorably compares with approaches of the same kind that use linear inversion steps. As a second approach, the contemporary use of the different frequencies data is considered. Contrary to common assumptions, it is shown that such an approach may perform better than the previous one, the different performances between the two being dictated by the spatial frequency content of the unknown contrast. Finally, a hybrid and, to the best of the authors' knowledge, novel strategy, which exploits the advantages of the the previous ones, is introduced and discussed.