  The problem of phase retrieval (PR) involves recovering an unknown image from
limited amplitude measurement data and is a challenge nonlinear inverse problem
in computational imaging and image processing. However, many of the PR methods
are based on black-box network models that lack interpretability and
plug-and-play (PnP) frameworks that are computationally complex and require
careful parameter tuning. To address this, we have developed PRISTA-Net, a deep
unfolding network (DUN) based on the first-order iterative shrinkage
thresholding algorithm (ISTA). This network utilizes a learnable nonlinear
transformation to address the proximal-point mapping sub-problem associated
with the sparse priors, and an attention mechanism to focus on phase
information containing image edges, textures, and structures. Additionally, the
fast Fourier transform (FFT) is used to learn global features to enhance local
information, and the designed logarithmic-based loss function leads to
significant improvements when the noise level is low. All parameters in the
proposed PRISTA-Net framework, including the nonlinear transformation,
threshold parameters, and step size, are learned end-to-end instead of being
manually set. This method combines the interpretability of traditional methods
with the fast inference ability of deep learning and is able to handle noise at
each iteration during the unfolding stage, thus improving recovery quality.
Experiments on Coded Diffraction Patterns (CDPs) measurements demonstrate that
our approach outperforms the existing state-of-the-art methods in terms of
qualitative and quantitative evaluations. Our source codes are available at
\emph{https://github.com/liuaxou/PRISTA-Net}.
