In this study, we present a phase retrieval solution that aims to recover signals from noisy phaseless measurements. A recently proposed scheme known as generalized expectation consistent signal recovery (GEC-SR), has shown better accuracy, speed, and robustness than many existing methods. However, sensing high-resolution images with large transform matrices presents a computational burden for GEC-SR, thereby limiting its applications to areas, such as real-time implementation. Moreover, GEC-SR does not support distributed computing, which is an important requirement to modern computing. To address these issues, we propose a novel decentralized algorithm called “deGEC-SR” by leveraging the core framework of GEC-SR. deGEC-SR exhibits excellent performance similar to GEC-SR but runs tens to hundreds of times faster than GEC-SR. We derive the theoretical state evolution for deGEC-SR and demonstrate its accuracy using numerical results. Analysis allows quick generation of performance predictions and enriches our understanding on the proposed algorithm.

中文翻译：

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相位检索的分散期望一致信号恢复

在这项研究中，我们提出了一种相位检索解决方案，旨在从嘈杂的无相测量中恢复信号。最近提出的一种称为广义期望一致信号恢复 (GEC-SR) 的方案显示出比许多现有方法更好的准确性、速度和鲁棒性。然而，使用大型变换矩阵感知高分辨率图像给 GEC-SR 带来了计算负担，从而将其应用限制在实时实现等领域。而且，GEC-SR 不支持分布式计算，这是现代计算的一个重要要求。为了解决这些问题，我们利用 GEC-SR 的核心框架提出了一种名为“deGEC-SR”的新型去中心化算法。deGEC-SR 表现出与 GEC-SR 相似的出色性能，但运行速度比 GEC-SR 快数十到数百倍。我们推导出 deGEC-SR 的理论状态演变，并使用数值结果证明其准确性。分析允许快速生成性能预测并丰富我们对所提出算法的理解。