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

TL;DR

This paper introduces a novel algorithm for holographic phase retrieval under combined Poisson and Gaussian noise, leveraging score-based priors and providing theoretical convergence guarantees, with improved reconstruction performance demonstrated through simulations.

Contribution

It proposes the AWFS algorithm that integrates a score-based image prior into phase retrieval, addressing mixed noise conditions with theoretical convergence analysis.

Findings

Improved reconstruction accuracy over Gaussian or Poisson-only models.

Score-based prior outperforms DDPM, PnP-ADMM, and RED methods.

Theoretical guarantee of critical-point convergence.

Abstract

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).