论文标题
从排名一测量的噪声盲恢复的稳健性
On the robustness of noise-blind low-rank recovery from rank-one measurements
论文作者
论文摘要
我们证明了有关从不确定的线性测量值重建低级矩阵的众所周知的凸噪声优化公式的鲁棒性的新结果。我们的结果适用于对称排名良好的测量值，如相位检索问题的配方。 我们通过确定I.I.D定义的高概率排名一级测量运算符来获得这些结果。高斯矢量显示出所谓的Schatten-1商特性，该特性对应于其核标准图像（Schatten-1）单位球的下限。 我们通过比较噪声盲和噪声吸引公式的解决方案的数值实验来补充分析。这些实验证实，噪声优化方法表现出与噪声吸引的配方相当的鲁棒性。 关键字：低级别矩阵恢复，相位检索，商特性，噪声，稳健性，核标准最小化
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measurements. Our results are applicable for symmetric rank-one measurements as used in a formulation of the phase retrieval problem. We obtain these results by establishing that with high probability rank-one measurement operators defined by i.i.d. Gaussian vectors exhibit the so-called Schatten-1 quotient property, which corresponds to a lower bound for the inradius of their image of the nuclear norm (Schatten-1) unit ball. We complement our analysis by numerical experiments comparing the solutions of noise-blind and noise-aware formulations. These experiments confirm that noise-blind optimization methods exhibit comparable robustness to noise-aware formulations. Keywords: low-rank matrix recovery, phase retrieval, quotient property, noise-blind, robustness, nuclear norm minimization
