Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.

翻译：相位恢复是从傅里叶幅度测量中恢复真实信号的非线性逆问题，广泛应用于天文成像、X射线晶体学、显微术等领域。由于相位引入的多义性以及大量可能图像与给定测量结果相匹配，该问题高度病态。为此，学界长期以来通过引入结构先验来改进解的质量，包括稀疏先验和基于深度学习的生成模型。然而，这类先验往往受限于表征能力或对略微不同分布的泛化性。近期，利用去噪器作为非凸优化算法正则化项的研究展现出良好的性能与泛化能力。本文提出一种方法，通过将去噪器隐式学习的先验融入经典交替最小化框架来解决相位恢复问题。与现有基于去噪的高性能相位恢复算法相比，本文方法在分布内图像的傅里叶测量中表现出竞争性性能，并在分布外图像上取得显著改进。