Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior
This work addresses a specific noise model in optical imaging, offering incremental improvements for phase retrieval applications.
The authors tackled holographic phase retrieval under combined Poisson and Gaussian noise by proposing the AWFS algorithm, which uses accelerated Wirtinger flow with a score-based generative prior, and demonstrated improved reconstruction over methods using only Gaussian or Poisson likelihoods, as well as better performance than DDPM, PnP-ADMM, and RED in simulations on three datasets.
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).