  The solution of nonlinear electromagnetic (EM) inverse scattering problems is
typically hindered by several challenges such as ill-posedness, strong
nonlinearity, and high computational costs. Recently, deep learning has been
demonstrated to be a promising tool in addressing these challenges. In
particular, it is possible to establish a connection between a deep
convolutional neural network (CNN) and iterative solution methods of nonlinear
EM inverse scattering. This has led to the development of an efficient
CNN-based solution to nonlinear EM inverse problems, termed DeepNIS. It has
been shown that DeepNIS can outperform conventional nonlinear inverse
scattering methods in terms of both image quality and computational time. In
this work, we quantitatively evaluate the performance of DeepNIS as a function
of the number of layers using structure similarity measure (SSIM) and
mean-square error (MSE) metrics. In addition, we probe the dynamic evolution
behavior of DeepNIS by examining its near-isometry property. It is shown that
after a proper training stage the proposed CNN is near optimal in terms of the
stability and generalization ability.
