AWFSD: Accelerated Wirtinger Flow with Score-based Diffusion Image Prior for Poisson-Gaussian Holographic Phase Retrieval

Phase retrieval (PR) is an essential problem in a number of coherent imaging systems. This work aims at resolving the holographic phase retrieval problem in real world scenarios where the measurements are corrupted by a mixture of Poisson and Gaussian (PG) noise that stems from optical imaging systems. To solve this problem, we develop a novel algorithm based on Accelerated Wirtinger Flow that uses Score-based Diffusion models as the generative prior (AWFSD). In particular, we frame the PR problem as an optimization task that involves both a data fidelity term and a regularization term. We derive the gradient of the PG log-likelihood function along with its corresponding Lipschitz constant, ensuring a more accurate data consistency term for practical measurements. We introduce a generative prior as part of our regularization approach by using a score-based diffusion model to capture (the gradient of) the image prior distribution. We provide theoretical analysis that establishes a critical-point convergence guarantee for the proposed AWFSD algorithm. Our simulation experiments demonstrate that: 1) The proposed algorithm based on the PG likelihood model enhances reconstruction compared to that solely based on either Gaussian or Poisson likelihood. 2) The proposed AWFSD algorithm produces reconstructions with higher image quality both qualitatively and quantitatively, and is more robust to variations in noise levels when compared with state-of-the-art methods for phase retrieval.