Accelerated Wirtinger Flow With Score-Based Image Priors for Holographic Phase Retrieval in Poisson-Gaussian Noise Conditions

Phase retrieval (PR) is a crucial problem in many imaging applications. This study focuses on holographic phase retrieval in situations where the measurements are degraded by a combination of Poisson and Gaussian noise, as commonly occurs in optical imaging systems. We propose a new algorithm called “AWFS” that uses accelerated Wirtinger flow (AWF) with a learned score function as a 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 one version of the proposed algorithm. The results of our simulation experiments on three different datasets show the following. 1) By using the PG likelihood model, a practical version of the proposed algorithm improves reconstruction compared to algorithms based solely on Gaussian or Poisson likelihoods. 2) The proposed score-based image prior method leads to better reconstruction quality than a method based on denoising diffusion probabilistic model (DDPM), as well as a plug-and-play alternating direction method of multipliers (PnP-ADMM) and regularization by denoising (RED).