Solving Full-Wave Nonlinear Inverse Scattering Problems by Deep Learning Schemes

Abstract

This paper aims to solve a full-wave inverse scattering problem, which is a quantitative imaging problem, i.e., to reconstruct the permittivities of dielectric scatterers from the knowledge of measured scattering data. Scatterers are represented in pixel basis, which is a versatile approach since the value of permittivity of each pixel is an independent parameter. This paper compares three different deep learning schemes in solving full-wave nonlinear ISPs. It is well known that in order to make machine learning more powerful when solving a particular problem, researchers must have a deep understanding of the corresponding forward problem. The same applies to inverse scattering problems. The concept of induced current plays an essential role in the proposed CNN technique, which enables us to design architecture of learning machine such that unnecessary computational effort spent in learning wave physics is minimized or avoided. Several representative tests are carried out, and it is demonstrated that the proposed CNN scheme outperforms a brute-force application of CNN.