A new algorithm of signal de-noising based on sparse AR model

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (6) : 127-131.

The actual signal always contains noises by different surroundings and collected devices. And the noise has different forms. So the signal de-noise algorithm is a significant important pre-processing. The paper proposes a new de-noise algorithm which is based on sparse optimization. The algorithm assumes that coefficients of signal’s AR model are sparse and the impact of noise effect on coefficient of AR model is equilibrium distribution. A sparse AR model is built by the signal with noises. The AR coefficients matrix is created by noised signal. Take the matrix as the over-completed sparse basis. One underdetermined equation set is obtained by cramped out some rows from the over-completed sparse basis randomly. Then the sparse AR coefficients are solved by sparse optimization algorithm. And the above processing is repeated many times to obtain many sparse AR coefficients. At last, the AR coefficients are averaged, and the de-noised signal is reconstructed by the averaged AR coefficients. A bidirectional algorithm is proposed by the above de-noise algorithm. The original signal and its inversion signal are de-noised and averaged. For general multi-frequency signals with lager noises, many simulation experiments are tested. It indicates that the de-noising effect obtained by using the algorithm in this paper is better than the classical wavelet de-noising algorithm and median filtering de-noising algorithm. The algorithm in this paper is applied to de-noising step for the vibration signal of the bridge cable, and practice shows that algorithm in this paper has excellent effect.

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Abstract

The actual signal always contains noises by different surroundings and collected devices. And the noise has different forms. So the signal de-noise algorithm is a significant important pre-processing. The paper proposes a new de-noise algorithm which is based on sparse optimization. The algorithm assumes that coefficients of signal’s AR model are sparse and the impact of noise effect on coefficient of AR model is equilibrium distribution. A sparse AR model is built by the signal with noises. The AR coefficients matrix is created by noised signal. Take the matrix as the over-completed sparse basis. One underdetermined equation set is obtained by cramped out some rows from the over-completed sparse basis randomly. Then the sparse AR coefficients are solved by sparse optimization algorithm. And the above processing is repeated many times to obtain many sparse AR coefficients. At last, the AR coefficients are averaged, and the de-noised signal is reconstructed by the averaged AR coefficients. A bidirectional algorithm is proposed by the above de-noise algorithm. The original signal and its inversion signal are de-noised and averaged. For general multi-frequency signals with lager noises, many simulation experiments are tested. It indicates that the de-noising effect obtained by using the algorithm in this paper is better than the classical wavelet de-noising algorithm and median filtering de-noising algorithm. The algorithm in this paper is applied to de-noising step for the vibration signal of the bridge cable, and practice shows that algorithm in this paper has excellent effect.

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multi-frequency signal / AR model / sparse representation / over-completed sparse base

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SONG Huan-huan，YE Qing-wei，WANG Xiao-dong，ZHOU Yu. A new algorithm of signal de-noising based on sparse AR model[J]. Journal of Vibration and Shock, 2015, 34(6): 127-131

References

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