论文标题
在低级汉克尔矩阵上
On Low-Rank Hankel Matrix Denoising
论文作者
论文摘要
线性系统中的低复杂性假设通常可以表示为具有广义Hankel结构的数据矩阵中的等级缺陷。这使得通过估计基本结构的低级别矩阵来降低数据。但是，在估计无噪声矩阵方面，不能保证标准的低级别近似方法表现良好。在本文中，回顾了通过单数值收缩来构成基质的最新结果。提出了一种新的方法来通过在结构化的低级别近似值中使用数据驱动的奇异值收缩来修改结构化的低级别近似值，以解决低级Hankel基质去核问题。在输入输出轨迹denoisis和脉冲响应中，它在数值上显示了deno的问题，即所提出的方法在估计低秩矩阵近似算法和deNoso的现有算法之间的无噪声矩阵方面表现最好。
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank matrix. However, standard low-rank approximation approaches are not guaranteed to perform well in estimating the noise-free matrix. In this paper, recent results in matrix denoising by singular value shrinkage are reviewed. A novel approach is proposed to solve the low-rank Hankel matrix denoising problem by using an iterative algorithm in structured low-rank approximation modified with data-driven singular value shrinkage. It is shown numerically in both the input-output trajectory denoising and the impulse response denoising problems, that the proposed method performs the best in terms of estimating the noise-free matrix among existing algorithms of low-rank matrix approximation and denoising.
