Phase retrieval (PR) is a crucial problem in many imaging applications. This study focuses on resolving the holographic phase retrieval problem in situations where the measurements are affected by a combination of Poisson and Gaussian noise, which commonly occurs in optical imaging systems. To address this problem, we propose a new algorithm called "AWFS" that uses the accelerated Wirtinger flow (AWF) with a score function as generative prior. Specifically, we formulate the PR problem as an optimization problem that incorporates both data fidelity and regularization terms. We calculate the gradient of the log-likelihood function for PR and determine its corresponding Lipschitz constant. Additionally, we introduce a generative prior in our regularization framework by using score matching to capture information about the gradient of image prior distributions. We provide theoretical analysis that establishes a critical-point convergence guarantee for the proposed algorithm. The results of our simulation experiments on three different datasets show the following: 1) By using the PG likelihood model, the proposed algorithm improves reconstruction compared to algorithms based solely on Gaussian or Poisson likelihood. 2) The proposed score-based image prior method, performs better than the method based on denoising diffusion probabilistic model (DDPM), as well as plug-and-play alternating direction method of multipliers (PnP-ADMM) and regularization by denoising (RED).

翻译：相位恢复（PR）是许多成像应用中的关键问题。本研究聚焦于在测量受泊松噪声和高斯噪声联合影响（这在光学成像系统中普遍存在）的情况下，解决全息相位恢复问题。针对该问题，我们提出了一种名为“AWFS”的新算法，该算法采用加速Wirtinger流（AWF）并结合分数函数作为生成先验。具体而言，我们将PR问题建模为一个包含数据保真项和正则化项的优化问题。我们计算了PR对数似然函数的梯度，并确定了其对应的Lipschitz常数。此外，我们在正则化框架中引入生成先验，通过分数匹配捕捉图像先验分布梯度的信息。我们提供了理论分析，为所提算法建立了临界点收敛性保证。在三个不同数据集上的仿真实验结果如下：1）通过使用泊松-高斯似然模型，所提算法相比仅基于高斯或泊松似然的算法提高了重建质量。2）所提出的基于分数的图像先验方法，其性能优于基于去噪扩散概率模型（DDPM）、即插即用交替方向乘子法（PnP-ADMM）以及通过去噪正则化（RED）的方法。