标题： 低秩矩阵恢复中的噪声折叠分析 显示英文标题

标题： An analysis of noise folding for low-rank matrix recovery

摘要： 以往关于低秩矩阵恢复的工作主要集中在矩阵无噪声且测量值受噪声影响的场景中。 然而，在实际应用中，矩阵本身在测量之前通常会受到随机噪声的干扰。 本文简要研究了这一场景，并证明了对于压缩感知中常用的大多数测量方案，这两个模型是等价的，其中区别在于与（\ref{eq.3}）相关的噪声比$mn/M$大一个因子，其中$m,~n$是矩阵的维度，$M$是测量次数。 此外，本文讨论了该设置下低秩矩阵的重建，基于关联的零空间性质提出了保证鲁棒恢复的充分条件，并得到了测量次数。 此外，针对非高斯噪声场景，我们进一步进行了探讨并给出了相应的结果。 仿真实验一方面展示了噪声方差对恢复性能的影响，另一方面验证了所提出模型的可行性。 显示英文摘要

摘要： Previous work regarding low-rank matrix recovery has concentrated on the scenarios in which the matrix is noise-free and the measurements are corrupted by noise. However, in practical application, the matrix itself is usually perturbed by random noise preceding to measurement. This paper concisely investigates this scenario and evidences that, for most measurement schemes utilized in compressed sensing, the two models are equivalent with the central distinctness that the noise associated with (\ref{eq.3}) is larger by a factor to $mn/M$, where $m,~n$ are the dimension of the matrix and $M$ is the number of measurements. Additionally, this paper discusses the reconstruction of low-rank matrices in the setting, presents sufficient conditions based on the associating null space property to guarantee the robust recovery and obtains the number of measurements. Furthermore, for the non-Gaussian noise scenario, we further explore it and give the corresponding result. The simulation experiments conducted, on the one hand show effect of noise variance on recovery performance, on the other hand demonstrate the verifiability of the proposed model.