相位降噪与矢径分解组合的矢量序列分解方法
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摘要
基于矢量序列相位与矢径的统计分布差异,本文提出一种TV (Total Variation)相位降噪和EMD (EmpiricalMode Decomposition)矢径分解组合的矢量序列降噪、分解方法。利用TV细致的演化特点进行相位降噪,其中引入最大信杂比准则,以优化选择调整参数和迭代次数;利用EMD适用于非线性非平稳分解的特点,将矢径分解为多个IMFS(Intrin-sic Mode Function),其中加入了非负判别,以保证重构矢量的相位不会发生跳变。然后,将降噪相位和分解的IMFS一一对应,重构矢量。考虑到历史继承性,该方法称为VEMD(Vector Empirical Mode Decomposition)方法。以高斯噪声污染的2个人工信号(线性调频信号、正弦+线性调频信号)和实测海杂波数据验证了本文所提出方法的性能。
The instantaneous frequency analysis of the vector time series has the fundamentality strongly application requirements such as in the sea clutter and underwater echo analysis.The de-noising is an inevitable critical step for the instantaneous frequency,due to it has the noise sensitive property.It is challenge that extracting signal from the noising polluted signal for it is the‘ill-problem'.Specially,it is more difficulty for the sea clutter because of the nonlinear and non-stationary caused by the sea surface.Concerned with the difference of the statistical distribution between the phase and the amplitude of vector-series signal,this article proposed a method to de-noise and decompose a vector-series signal byusing TV based phase de-noising and EMD based amplitude decomposition.TV method is applied for phase de-noising with the advantage of precise evolution,while the criterion of maximum SNR(signal to noise ratio)guides the selections of the parameters of regularization and iteration number.Specific to non-stationary and nonlinear signal decomposition,EMD method is applied to decompose the amplitudes into a number of intrinsic mode functions(IMFs),within which the non-negative criterion is introduced in the decomposition to avoid phase disorder.The vector-series signal is reconstructed using the de-noised phaseseroes and the IMFs of the amplitude series by one-to-one correspondence.The proposed method is called VEMD(Vector Empirical Mode Decomposition)by taking account of the historic inheritance.The effectiveness of the proposed method is illustrated through experiments on the examples of linear frequency modulation signal and linear plus sine frequency modulation signal,both of which are polluted with the Gaussian noise,as well as real IPIX radar clutter signal.
The instantaneous frequency analysis of the vector time series has the fundamentality strongly application requirements such as in the sea clutter and underwater echo analysis.The de-noising is an inevitable critical step for the instantaneous frequency,due to it has the noise sensitive property.It is challenge that extracting signal from the noising polluted signal for it is the‘ill-problem'.Specially,it is more difficulty for the sea clutter because of the nonlinear and non-stationary caused by the sea surface.Concerned with the difference of the statistical distribution between the phase and the amplitude of vector-series signal,this article proposed a method to de-noise and decompose a vector-series signal byusing TV based phase de-noising and EMD based amplitude decomposition.TV method is applied for phase de-noising with the advantage of precise evolution,while the criterion of maximum SNR(signal to noise ratio)guides the selections of the parameters of regularization and iteration number.Specific to non-stationary and nonlinear signal decomposition,EMD method is applied to decompose the amplitudes into a number of intrinsic mode functions(IMFs),within which the non-negative criterion is introduced in the decomposition to avoid phase disorder.The vector-series signal is reconstructed using the de-noised phaseseroes and the IMFs of the amplitude series by one-to-one correspondence.The proposed method is called VEMD(Vector Empirical Mode Decomposition)by taking account of the historic inheritance.The effectiveness of the proposed method is illustrated through experiments on the examples of linear frequency modulation signal and linear plus sine frequency modulation signal,both of which are polluted with the Gaussian noise,as well as real IPIX radar clutter signal.
引文
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[6]Rilling G,Flandrin P,Goncalves P,et al.Bivariate empirical mode decomposition[J].IEEE Signal Processing Letters,2007,14(12):936-939.
[7]Looney D,Mandic D P.Multiscale image fusion using complex extensions of EMD[J].IEEE Transactions on Signal Processing,2009,57(4):1626-1630.
[8]Güntürkün U.Bivariate empirical mode decomposition for cognitive radar scene analysis[J].IEEE Signal Processing Letters,2015,22(5):603-607.
[9]Selesnick I.Total Variation Denoising(an MM Algorithm)[CP/OL].[2017-05-15].http://cnx.org/content/m44934/1.4/
[2]Rudin L I,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms[J].Physica D:Nonlinear Phenomena,1992,60(1-4):259-268.
[3]Sinding K M,Drapaca C S,Tittmann B R.Digital signal processing methods for ultrasonic echoes[J].IEEE Transactions on Ultrasonics,Ferroelectrics,and Frequency Control,2016,63(8):1172-1176.
[4]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[C].//Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Sciences.London:The Royal Society of London,1998,454(1971):903-995.
[5]Altaf M U B,Gautama T,Tanaka T,et al.Rotation invariant complex empirical mode decomposition[C].//Acoustics,Speech and Signal Processing.Honolulu,Hawaii:ASSP 2007,IEEE International Conference,2007:1009-1012.
[6]Rilling G,Flandrin P,Goncalves P,et al.Bivariate empirical mode decomposition[J].IEEE Signal Processing Letters,2007,14(12):936-939.
[7]Looney D,Mandic D P.Multiscale image fusion using complex extensions of EMD[J].IEEE Transactions on Signal Processing,2009,57(4):1626-1630.
[8]Güntürkün U.Bivariate empirical mode decomposition for cognitive radar scene analysis[J].IEEE Signal Processing Letters,2015,22(5):603-607.
[9]Selesnick I.Total Variation Denoising(an MM Algorithm)[CP/OL].[2017-05-15].http://cnx.org/content/m44934/1.4/