On an artificial neural network for inverse scattering problems

In this paper, we consider artificial neural networks for inverse scattering problems. As a working model, we consider the inverse problem of recovering a scattering object from the (possibly) limited-aperture radar cross section (RCS) data collected corresponding to a single incident field. This nonlinear and ill-posed inverse problem is practically important and highly challenging due to the severe lack of information. From a geometrical and physical point of view, the low-frequency data should be able to resolve the unique identifiability issue, but meanwhile lose the resolution. On the other hand, the machine learning can be used to break through the resolution limit. By combining the two perspectives, we develop a fully connected neural network (FCNN) for the inverse problem. Extensive numerical results show that the proposed method can produce stunning reconstructions. The proposed strategy can be extended to tackling other inverse scattering problems with limited measurement information.