  Exploring the idea of phase retrieval has been intriguing researchers for
decades, due to its appearance in a wide range of applications. The task of a
phase retrieval algorithm is typically to recover a signal from linear
phaseless measurements. In this paper, we approach the problem by proposing a
hybrid model-based data-driven deep architecture, referred to as Unfolded Phase
Retrieval (UPR), that exhibits significant potential in improving the
performance of state-of-the art data-driven and model-based phase retrieval
algorithms. The proposed method benefits from versatility and interpretability
of well-established model-based algorithms, while simultaneously benefiting
from the expressive power of deep neural networks. In particular, our proposed
model-based deep architecture is applied to the conventional phase retrieval
problem (via the incremental reshaped Wirtinger flow algorithm) and the sparse
phase retrieval problem (via the sparse truncated amplitude flow algorithm),
showing immense promise in both cases. Furthermore, we consider a joint design
of the sensing matrix and the signal processing algorithm and utilize the deep
unfolding technique in the process. Our numerical results illustrate the
effectiveness of such hybrid model-based and data-driven frameworks and
showcase the untapped potential of data-aided methodologies to enhance the
existing phase retrieval algorithms.
