Signal denoising method based on matrix rank minimization and statistical modification

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (15) : 38-44.

LI Wen-feng1, 2 ,XU Ai-qiang1, DAI Hao-min1, WANG Feng3

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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

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LI Wen-feng1, 2,XU Ai-qiang1, DAI Hao-min1, WANG Feng3. Signal denoising method based on matrix rank minimization and statistical modification[J]. Journal of Vibration and Shock, 2015, 34(15): 38-44

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