  Inverse scattering problems, 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 non-linear 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-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 non-linear features. More important,
unlike existing PD-ISP methods, the proposed framework learns optimum values of
all 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 existing model-driven and
data-driven techniques by a significant margin and provides up to 20 times
higher validity range.
