Phase Retrieval by Alternating Minimization With Random Initialization
Phase Retrieval by Alternating Minimization With Random Initialization
复制标题
DOI：
10.1109/tit.2020.2971211
复制
发表时间：
2018-12
影响因子：
2.5
通讯作者：
Teng Zhang
中科院分区：
文献类型：
--
作者：
Teng Zhang
我们考虑相位检索问题，其目标是从复正态分布中独立采样的$m$传感向量的无相标量积中重建$n$维复向量。我们证明，对于某些$M>0$，如果${m}\geq Mn^{3/2}\log ^{7/2}n$，则经典的随机初始化交替最小化算法以高概率成功为$n,m\rightarrow \infty $。这是证明中的猜想的一步，该猜想在$m=O(n)$时算法成功。分析依赖于一种能够解耦算法迭代和传感向量之间依赖关系的方法。
We consider the phase retrieval problem, where the goal is to reconstruct an $n$ -dimensional complex vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that, if ${m}\geq Mn^{3/2}\log ^{7/2}n$ for some $M>0$ , then the classical algorithm of alternating minimization with random initialization succeeds with high probability as $n,m\rightarrow \infty $ . This is a step toward proving the conjecture in, which conjectures that the algorithm succeeds when $m=O(n)$ . The analysis depends on an approach that enables the decoupling of the dependency between the algorithmic iterates and the sensing vectors.