  Phase retrieval (PR), a long-established challenge for recovering a
complex-valued signal from its Fourier intensity-only measurements, has
attracted considerable attention due to its widespread applications in digital
imaging. Recently, deep learning-based approaches were developed that achieved
some success in single-shot PR. These approaches require a single Fourier
intensity measurement without the need to impose any additional constraints on
the measured data. Nevertheless, vanilla deep neural networks (DNN) do not give
good performance due to the substantial disparity between the input and output
domains of the PR problems. Physics-informed approaches try to incorporate the
Fourier intensity measurements into an iterative approach to increase the
reconstruction accuracy. It, however, requires a lengthy computation process,
and the accuracy still cannot be guaranteed. Besides, many of these approaches
work on simulation data that ignore some common problems such as saturation and
quantization errors in practical optical PR systems. In this paper, a novel
physics-driven multi-scale DNN structure dubbed PPRNet is proposed. Similar to
other deep learning-based PR methods, PPRNet requires only a single Fourier
intensity measurement. It is physics-driven that the network is guided to
follow the Fourier intensity measurement at different scales to enhance the
reconstruction accuracy. PPRNet has a feedforward structure and can be
end-to-end trained. Thus, it is much faster and more accurate than the
traditional physics-driven PR approaches. Extensive simulations and experiments
on a practical optical platform were conducted. The results demonstrate the
superiority and practicality of the proposed PPRNet over the traditional
learning-based PR methods.
