泊松相位恢复中Wirtinger Flow的收敛性分析
Convergence analysis of Wirtinger Flow for Poisson phase retrieval
AI总结：
针对泊松相位恢复问题，本文开展Wirtinger Flow算法的收敛性分析，提出无需额外处理的低复杂度框架，证明其无噪线性收敛与有界噪声鲁棒性，还提出高效增量式变体且保证高概率收敛。
摘要：
本文针对成像应用中的基础问题——泊松相位恢复，对Wirtinger Flow（WF）算法开展了严格的理论收敛性分析。不同于以往依赖截断或额外调整来处理异常值的分析方法，本文的框架无需剔除测量值或引入额外计算步骤，从而降低了整体复杂度。我们证明，在无噪声条件下WF可线性收敛至真实信号，且在泊松相位恢复的有界噪声场景下仍具备鲁棒性与稳定性。此外，我们提出了一种增量式WF变体，该变体显著提升了计算效率，且在合适条件下能以高概率保证收敛至真实信号。
英文摘要：
This paper presents a rigorous theoretical convergence analysis of the Wirtinger Flow (WF) algorithm for Poisson phase retrieval, a fundamental problem in imaging applications. Unlike prior analyses that rely on truncation or additional adjustments to handle outliers, our framework avoids eliminating measurements or introducing extra computational steps, thereby reducing overall complexity. We prove that WF achieves linear convergence to the true signal under noiseless conditions and remains robust and stable in the presence of bounded noise for Poisson phase retrieval. Additionally, we propose an incremental variant of WF, which significantly improves computational efficiency and guarantees convergence to the true signal with high probability under suitable conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
