Physical Model-Inspired Deep Unrolling Network for Solving Nonlinear Inverse Scattering Problems

In this article, to bridge the gap between the traditional model-based methods and data-driven deep learning schemes, we propose a physical model-inspired deep unrolling network for solving nonlinear inverse scattering problems, termed PM-Net. The proposed end-to-end network is formed by two consequent steps. First, an augmented Lagrangian method is introduced to transform a constrained objective function to be an unconstrained optimization. In addition, it is further decomposed into four quasi-linear subproblems. Second, we unfold the iterative scheme into a layer-wise deep neural network. Each subproblem is mapped into a module of the deep unrolling network. In PM-Net, these variables including the weight, the regularization of contrast, and other parameters are learned and updated alternately by corresponding network layers. PM-Net effectively combines neural networks with the knowledge of underlying physics as well as traditional techniques. Unlike existing networks, PM-Net explicitly exploits contrast source and contrast modules. Compared to traditional iterative methods, the performance of PM-Net is comparable or even better than subspace-based optimization method in the high noise-level circumstance. Compared to the state-of-the-art learning approaches, not only less network parameters need to be learned, but also better performance is achieved by PM-Net.