基于矩阵秩最小化和统计修正的信号降噪方法研究

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摘要针对奇异值分解在信号降噪时有效秩的选择问题，提出一种基于矩阵秩最小化和统计修正的信号降噪方法。首先，利用矩阵秩最小化理论将奇异值有效秩选择问题转化为秩的约束优化问题；然后，通过凸优化求解，得到干净信号的Hankel矩阵，实现一次降噪；最后，根据奇异值子集标准差对干净信号Hankel矩阵进行统计修正，进一步优化降噪效果。模拟信号和真实信号的实验结果表明：该方法可以有效的消除脉冲干扰和高斯噪声，能够最大限度的降低信号均方误差，提高信噪比，增强了奇异值分解在信号降噪中的通用性。

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	李文峰1
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	许爱强1
	戴豪民1
	王丰3

关键词 ：奇异值分解, 奇异值扰动理论, 矩阵秩最小化, 奇异值子集标准差

Abstract：According to the selection problem of effective rank in the singular value decomposition for signal denoising, a signal denoising method based on matrix rank minimization and statistical modification is proposed. Firstly, effective rank selection problem of singular value decomposition is transformed into a constrained optimization problem of rank by using matrix rank minimization theory. Secondly, the Hankel matrix of the clean signal is obtained by convex optimization for the realization of the first noise reduction. Lastly, the clean signal Hankel matrix is carried through statistical correction based on every subset standard deviation of the singular value for further optimize the noise reduction effect. The simulation signal and real signal experimental results show: the method can effectively eliminate the pulse noise and Gaussian noise. In the same time, the method can reduce the maximum signal mean square error and improve the signal-to-noise ratio. So the method can enhance the universality of the singular value decomposition in signal denoising.

Key words： Singular Value Decomposition Matrix Perturbation Theory Matrix Rank Minimization Subset Standard Deviation of the Singular Value

收稿日期: 2014-12-19 出版日期: 2015-08-15

引用本文:

李文峰1，2，许爱强1，戴豪民1，王丰3. 基于矩阵秩最小化和统计修正的信号降噪方法研究[J]. 振动与冲击, 2015, 34(15): 38-44.
LI Wen-feng1, 2,XU Ai-qiang1, DAI Hao-min1, WANG Feng3. Signal denoising method based on matrix rank minimization and statistical modification. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(15): 38-44.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2015/V34/I15/38

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