基于共识均衡与深度神经网络的相位恢复

Phase Retrieval Based on Consensus Equilibrium and Deep Neural Networks

摘要: 相位恢复是计算成像中典型非线性非凸逆问题，旨在从幅值测量中恢复信号相位，噪声会显著降低重构精度与成像质量。共识平衡通过平衡方程统一数据拟合与正则化约束，可将正则化反演的最大后验估计转化为方程求解。本文提出适用于数据驱动模型的通用多映射融合框架，并从理论上推导共识平衡方程，证明其解在特定条件下为标准最大后验估计的扩展，为框架提供理论依据。同时设计对应求解算法，将共识平衡思想与深度学习结合，提出兼具可解释性与数据驱动优势的去噪相位恢复方法。

Abstract: Phase retrieval is a typical nonlinear non-convex inverse problem in computational imaging, aiming to recover signal phase from intensity measurements, where noise significantly degrades reconstruction accuracy and imaging quality. Consensus balance unifies data fitting and regularization constraints through balance equations, enabling the transformation of maximum a posteriori estimation of regularized inversion into equation solving. This paper proposes a general multi-mapping fusion framework for data-driven models, theoretically derives the consensus balance equation, and proves that its solution is an extension of the standard maximum a posteriori estimation under specific conditions. A corresponding solving algorithm is designed, and by integrating consensus balance with deep learning, a denoising phase retrieval method with both interpretability and data-driven advantages is proposed.