  Phase retrieval (PR) is an important component in modern computational
imaging systems. Many algorithms have been developed over the past half
century. Recent advances in deep learning have opened up a new possibility for
robust and fast PR. An emerging technique, called deep unfolding, provides a
systematic connection between conventional model-based iterative algorithms and
modern data-based deep learning. Unfolded algorithms, powered by data learning,
have shown remarkable performance and convergence speed improvement over the
original algorithms. Despite their potential, most existing unfolded algorithms
are strictly confined to a fixed number of iterations when employing
layer-dependent parameters. In this study, we develop a novel framework for
deep unfolding to overcome the existing limitations. Even if our framework can
be widely applied to general inverse problems, we take PR as an example in the
paper. Our development is based on an unfolded generalized expectation
consistent signal recovery (GEC-SR) algorithm, wherein damping factors are left
for data-driven learning. In particular, we introduce a hypernetwork to
generate the damping factors for GEC-SR. Instead of directly learning a set of
optimal damping factors, the hypernetwork learns how to generate the optimal
damping factors according to the clinical settings, thus ensuring its
adaptivity to different scenarios. To make the hypernetwork work adapt to
varying layer numbers, we use a recurrent architecture to develop a dynamic
hypernetwork, which generates a damping factor that can vary online across
layers. We also exploit a self-attention mechanism to enhance the robustness of
the hypernetwork. Extensive experiments show that the proposed algorithm
outperforms existing ones in convergence speed and accuracy, and still works
well under very harsh settings, that many classical PR algorithms unstable or
even fail.
