Learning approach to inverse scattering problems with special boundary conditions and inhomogeneous background

This article reviews the physics inspired machine learning inverse scattering algorithms developed by the authors for solving mixed boundary condition problem and inhomogeneous background problem, both of which are seldom studied though have found wide applications in practical scenarios such as ground penetrating radar, biomedical imaging and through wall imaging. The difficulty lies in mixed boundary problem is how to choose the parameter representing both PEC and dielectric scatterers as well as how to distinguish them. And the difficulty lies in the inhomogeneous background problem is how to suppress the unwanted artifacts due to the multiple scattering between the scatterers and the background. In this article, a T-matrix based inversion method is proposed to image PEC and dielectric scatterers together, which automatically distinguish the two kinds of scatterers, as the T-matrix naturally contains the information of boundary conditions. The inhomogeneous background problem is solved by generative adversarial neural network (GAN). By introducing the attention scheme into the GAN, the artifacts due to multiple scattering effect between the background and the scatterers are suppressed with a great improvement of resolution. The machine learning part is guided by the physics rather than working as a black box. Therefore, the proposed machine learning approach has a strong generalization ability. Numerical results and experimental results have shown the advantages of the proposed machine learning methods over conventional iterative methods in both image resolution, accuracy and imaging speed.