  Nonlinear electromagnetic (EM) inverse scattering is a quantitative and
super-resolution imaging technique, in which more realistic interactions
between the internal structure of scene and EM wavefield are taken into account
in the imaging procedure, in contrast to conventional tomography. However, it
poses important challenges arising from its intrinsic strong nonlinearity,
ill-posedness, and expensive computation costs. To tackle these difficulties,
we, for the first time to our best knowledge, exploit a connection between the
deep neural network (DNN) architecture and the iterative method of nonlinear EM
inverse scattering. This enables the development of a novel DNN-based
methodology for nonlinear EM inverse problems (termed here DeepNIS). The
proposed DeepNIS consists of a cascade of multi-layer complexvalued residual
convolutional neural network (CNN) modules. We numerically and experimentally
demonstrate that the DeepNIS outperforms remarkably conventional nonlinear
inverse scattering methods in terms of both the image quality and computational
time. We show that DeepNIS can learn a general model approximating the
underlying EM inverse scattering system. It is expected that the DeepNIS will
serve as powerful tool in treating highly nonlinear EM inverse scattering
problems over different frequency bands, involving large-scale and
high-contrast objects, which are extremely hard and impractical to solve using
conventional inverse scattering methods.
