This note provides a significantly simpler and shorter proof of our sample complexity guarantee for solving the low rank column-wise sensing problem using the Alternating Gradient Descent (GD) and Minimization (AltGDmin) algorithm. AltGDmin was developed and analyzed for solving this problem in our recent work. We also provide an improved guarantee.

翻译：本文为使用交替梯度下降（GD）与最小化（AltGDmin）算法解决低秩列向感知问题，给出了显著更简洁、更短的样本复杂度保证证明。AltGDmin算法是在我们近期工作中为解决该问题而开发并分析的。此外，本文还提供了改进后的保证条件。