改进低秩列感知问题的采样复杂度，提升算法效率。
Noisy Low Rank Column-wise Sensing
- 提出改进的AltGDmin算法，降低采样需求。
- 采样复杂度比现有最优结果提升max(r, log(1/ε))/r倍。
- 首次系统对比同问题不同命名下的理论成果。
本文研究用于求解噪声低秩列感知（Noisy Low Rank Column-wise Sensing, LRCS）问题的AltGDmin算法。我们的样本复杂度保证相较于现有最优结果提升了max(r, log(1/ε))/r倍，其中r为未知矩阵的秩，ε为最终期望精度。第二项贡献是详细比较了所有研究与LRCS数学形式完全相同但名称不同的工作所给出的理论保证。
原文摘要 · Abstract (English)
This letter studies the AltGDmin algorithm for solving the noisy low rank column-wise sensing (LRCS) problem. Our sample complexity guarantee improves upon the best existing one by a factor $\max(r, \log(1/ε))/r$ where $r$ is the rank of the unknown matrix and $ε$ is the final desired accuracy. A second contribution of this work is a detailed comparison of guarantees from all work that studies the exact same mathematical problem as LRCS, but refers to it by different names.
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