基于随机Kaczmarz方法的复值目标相位恢复
Phase retrieval of complex-valued objects via a randomized Kaczmarz method
摘要：
本文研究了复值物体相位恢复问题的随机Kaczmarz算法的收敛性。虽然这个算法已经研究了实值的情况下，其推广到复值的情况下是不平凡的，并已离开作为一个猜想。本文建立了算法的收敛性与目标函数的凸性之间的联系。在此基础上，证明了当感知矢量在单位球面上均匀采样，且感知矢量个数$m$满足$m>O(n\log n)$为$n, m\rightarrow\infty$时，该算法在良好的初始化条件下，以高概率线性收敛到解.
英文摘要：
This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the complex-valued case is nontrivial and has been left as a conjecture. This paper establishes the connection between the convergence of the algorithm and the convexity of an objective function. Based on the connection, it demonstrates that when the sensing vectors are sampled uniformly from a unit sphere and the number of sensing vectors $m$ satisfies $m>O(n\log n)$ as $n, m\rightarrow\infty$, then this algorithm with a good initialization achieves linear convergence to the solution with high probability.
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。
