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

• URL: http://arxiv.org/abs/2305.07712v2
• Date: Wed, 20 Sep 2023 20:03:08 GMT
• Title: Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior
• Authors: Zongyu Li, Jason Hu, Xiaojian Xu, Liyue Shen and Jeffrey A. Fessler
• Abstract summary: 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 determine the Lipschitz constant. We provide theoretical analysis that establishes a critical-point convergence guarantee for the proposed algorithm.
• Score: 19.231581775644617
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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).

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