低秩相位恢复
Low Rank Phase Retrieval
摘要：
本文提出了两种求解低秩相位恢复（LRPR）问题的迭代算法。LRPR是指从其列的随机线性投影的仅幅度（无相）测量恢复低秩矩阵$\X$。这两种方法包括一个频谱初始化步骤，然后通过迭代算法，以最大限度地提高观测数据的可能性。我们获得样本的复杂性界限，我们提出的初始化方法，以提供一个很好的近似真实的$\X$。当秩足够低时，这些界限明显低于现有的单矢量相位恢复算法所需的界限。通过大量的实验，我们表明，同样是真实的建议完整的算法。
英文摘要：
We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both methods consist of a spectral initialization step followed by an iterative algorithm to maximize the observed data likelihood. We obtain sample complexity bounds for our proposed initialization approach to provide a good approximation of the true $\X$. When the rank is low enough, these bounds are significantly lower than what existing single vector phase retrieval algorithms need. Via extensive experiments, we show that the same is also true for the proposed complete algorithms.
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