Unrolled Optimization With Deep Learning-Based Priors for Phaseless Inverse Scattering Problems

Inverse scattering problems (ISPs), such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly nonlinear and ill-posed under extremely strong scattering conditions such as when the objects have very high permittivity or are large in size. In this work, we propose an end-to-end reconstruction framework using unrolled optimization with deep priors to solve PD-ISPs under very strong scattering conditions. We incorporate an approximate linear-physics-based model into our optimization framework along with a deep learning (DL)-based prior and solve the resulting problem using an iterative algorithm which is unfolded into a deep network. This network not only learns data-driven regularization but also overcomes the shortcomings of approximate linear models and learns nonlinear features. More important, unlike the existing PD-ISP methods, the proposed framework learns optimum values of all the tunable parameters (including multiple regularization parameters) as a part of the framework. Results from simulations and experiments are shown for the use case of indoor imaging using 2.4-GHz phaseless Wi-Fi measurements, where the objects exhibit extremely strong scattering and low absorption. Results show that the proposed framework outperforms the existing model-driven and data-driven techniques by a significant margin and provides up to 20 times higher validity range.