  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).
