A common approach for compressing large-scale data is through matrix sketching. In this work, we consider the problem of recovering low-rank matrices from two noisy linear sketches using the double sketching scheme discussed in Fazel et al. (2008), which is based on an approach by Woolfe et al. (2008). Using tools from non-asymptotic random matrix theory, we provide the first theoretical guarantees characterizing the error between the output of the double sketch algorithm and the ground truth low-rank matrix. We apply our result to the problems of low-rank matrix approximation and low-tubal-rank tensor recovery.

翻译：数据压缩的常见方法是通过矩阵素描。本文考虑利用Fazel等人（2008）讨论的双重素描方案（基于Woolfe等人（2008）的方法）从两个含噪线性素描中恢复低秩矩阵的问题。借助非渐近随机矩阵理论工具，我们首次给出理论保证，刻画了双重素描算法输出与真实低秩矩阵之间的误差。我们将该结果应用于低秩矩阵近似和低管秩张量恢复问题。