Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior

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. We calculate the gradient of the log-likelihood function for PR and provide an implementable estimate for it. Additionally, we introduce a generative prior in our regularization framework by using score matching to capture information about the gradient of image prior distributions. 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 leads to improved reconstruction quality over 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).