论文标题
通过随机kaczmarz方法对复合物值的相位检索
Phase retrieval of complex-valued objects via a randomized Kaczmarz method
论文作者
论文摘要
本文研究了复杂值对象的相位检索问题的随机Kaczmarz算法的收敛性。尽管已研究了该算法的实现情况}，但其对复杂值情况的概括是非平凡的，并且已被视为一个猜想。本文建立了算法的收敛与目标函数的凸度之间的联系。基于连接，它表明，当传感向量是从单位球体均匀采样的，并且传感向量的数量$ m $满足$ m> o（n \ log n）$作为$ n，m \ rightArrow \ infty $，那么该算法具有很好的初始化，可以使线性转化为有线性的转化，从而使求解具有高概率。
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.
