论文标题
低级矩阵恢复的噪声折叠分析
An analysis of noise folding for low-rank matrix recovery
论文作者
论文摘要
关于低级别矩阵恢复的先前工作集中在矩阵无噪声且测量结果被噪声损坏的情况上。但是，在实际应用中，矩阵本身通常受到测量之前的随机噪声的干扰。 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.此外，本文讨论了在设置中低级矩阵的重建，基于关联的空空间属性提供了足够的条件，以保证稳健的恢复并获得测量的数量。此外，对于非高斯噪声场景，我们进一步探索并给出相应的结果。另一方面，进行的仿真实验显示了噪声方差对恢复性能的影响，另一方面证明了所提出的模型的可验证性。
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.
