二次测量回归的Reweighted Wirtinger Flow算法及收敛性分析
The Reweighted Wirtinger Flow Algorithm and Convergence for Quadratic Measurement Regression
DOI: 10.12677/aam.2024.1311479, PDF,    科研立项经费支持
作者: 单晓雅：河北工业大学理学院，天津
关键词: 二次测量；信号恢复；RWF方法；局部收敛性；Quadratic Measurement； Signal Recovery； RWF Method； Local Convergence
摘要: 二次测量回归模型在众多研究领域中受到了广泛关注，例如相位恢复、电力系统状态估计、未标记距离几何问题等。本文重点研究如何在二次测量回归模型中有效地恢复未知信号。我们使用了加权Wirtinger Flow (Reweighted Wirtinger Flow, RWF)方法来重建真实信号，并证明了该方法在一定条件下能够收敛至局部极小点。数值实验结果表明，样本量较小时，该算法在信号恢复成功率和计算速度方面表现优异。
Abstract: Quadratic measurement regression models have received extensive attention in many research fields, such as phase recovery, power system state estimation, and unlabeled distance geometry problems. This paper focuses on how to recover the unknown signal effectively in the secondary measurement model. Reweighted Wirtinger Flow (RWF) method is used to reconstruct real signals, and it is proved that the proposed method can converge to local minima under certain conditions. Numerical experiment results show that the proposed algorithm has excellent performance in signal recovery success rate and computational efficiency.
文章引用：单晓雅. 二次测量回归的Reweighted Wirtinger Flow算法及收敛性分析[J]. 应用数学进展, 2024, 13(11): 4966-4974. https://doi.org/10.12677/aam.2024.1311479

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