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{this https URL}.

从有限的幅度测量数据中恢复未知图像的相位恢复问题是计算成像和图像处理中具有挑战性的非线性逆问题。我们提出的 PRISTA-Net 是一个基于深度展开网络（DUN）和第一阶迭代收缩阈值算法（ISTA）的网络，通过可学习的非线性转换来处理稀疏先验的近端点映射子问题，并利用注意力机制聚焦于包含图像边缘、纹理和结构的相位信息。实验结果表明，该方法在定性和定量评估方面优于现有的最先进方法。