基于模糊递归和最优硬阈值的局部投影降噪算法

doi:10.12305/j.issn.1001-506X.2023.03.01

摘要/Abstract

摘要：

针对原始局部投影降噪算法的局部邻域选取问题和子空间划分问题, 提出了一种基于模糊递归图和最优硬阈值准则的局部投影降噪算法。首先，利用模糊递归图确定局部邻域范围; 然后，再对邻域矩阵进行奇异值分解, 并利用最优硬阈值准则对局部邻域的信号子空间和噪声子空间进行划分; 最后，进行投影去噪。Lorenz信号的仿真结果表明, 所提方法能够提高信噪比并降低均方误差, 恢复原始吸引子的形态结构。对实测含噪心电图信号进行处理后, 信噪比显著提高, 验证了本方法的有效性。

关键词: 局部投影, 模糊递归图, 最优硬阈值准则, 降噪, 混沌信号

Abstract:

For the local neighborhood selection problem and subspace partition problem of the original local projective (LP) noise reduction algorithm, an improved LP noise reduction algorithm based on fuzzy recurrence plot and optimal hard threshold criterion is proposed. Firstly, the local neighborhood is determined by fuzzy recurrence plot. Then, the singular value decomposition (SVD) is implemented to local neighborhood matrix, and signal subspace and noise subspace in local neighborhood is partitioned by optimal hard threshold criterion. Finally, the projection for denoising is performed. The denoising results of Lorenz signal show that the proposed algorithm can improve the signal to noise ratio, reduce the mean square error, and recovery the morphological structure of the original attractor. After processing the measured noisy electrocardiogram (ECG) signal, the signal to noise ratio is significantly improved, which shows the effectiveness of the proposed algorithm.

Key words: local projection, fuzzy recurrence plot, optimal hard threshold, noise reduction, chaotic signal

中图分类号:

TN911.7

王东, 崔忠马, 陈文东, 舒勤. 基于模糊递归和最优硬阈值的局部投影降噪算法[J]. 系统工程与电子技术, 2023, 45(3): 621-628.

Dong WANG, Zhongma CUI, Wendong CHEN, Qin SHU. Local projective noise reduction algorithm based on fuzzy recurrence and optimal hard threshold[J]. Systems Engineering and Electronics, 2023, 45(3): 621-628.

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方法	李雅普诺夫指数	关联维数	耗时/s
原始信号	1.657 96	2.065 44	-
本文方法	1.722 05	2.135 53	10.823
标准局部投影	1.443 18	2.511 27	4.878
递归局部投影	1.564 47	2.235 61	6.453
基于小波的局部投影	1.544 73	2.215 46	8.613
基于EMD的局部投影	1.556 42	2.226 54	8.456
K均值局部投影	1.577 46	2.151 46	9.862
平滑子空间局部投影	1.486 25	2.496 54	5.061

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