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鉴于非均匀采样复数据经验模态分解（NSBEMD）相对传统分解方法的优势和噪声的NSBEMD特性，提出了一种基于噪声辅助NSBEMD的混沌信号自适应降噪方法. 该方法首先以含噪混沌信号和高斯白噪声分别为实、虚部来构造复数据并进行NSBEMD，然后根据虚部各IMF的能量来估算实部各IMF中包含的噪声能量，最后根据噪声能量的估计值对实部IMF进行奇异值分解（SVD）降噪. 噪声估计实验验证了噪声能量估计方法的可行性，而Lorenz信号和太阳黑子月平均数的降噪实验则表明，相对于现有EMD降噪方法，本文方法能够进一步消除噪声，更清晰地恢复出混沌吸引子的拓扑结构.
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关键词:
- 非均匀采样复数据经验模态分解 /
- 噪声辅助 /
- 噪声能量估计
According to the advantages of nonuniformly sampled bivariate empirical mode decomposition and the characteristics of noise after it, an adaptive chaotic signal denoising method is proposed based on the noise-assisted nonuniformly sampled bivariate empirical mode decomposition. Firstly, a complex signal is constructed for the noise-assisted nonuniformly sampled bivariate empirical mode decomposition, by using noisy chaotic signal and gaussian white noise as the real part and imaginary part respectively; secondly, the noise energy of each intrinsic mode function in the real part is estimated according to the energy of each intrinsic mode function in the imaginary part; and finally, from the above results, each intrinsic mode function in the real part is denoised by using the singular value decomposition. Noise energy estimate numerical experiment validates the feasibility of this method, and the denoising tests for Lorenz signal and monthly sunspot data indicate that our method shows advantages in both noise reduction and chaotic attractor topological configuration reversion.-
Keywords:
- nonuniformly sampled bivariate empirical mode decomposition /
- noise assisted /
- noise energy estimate
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[40] Altaf M U B, Gautama T, Tanaka T 2007 IEEE ICASSP 3 1009
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[44] Ahrabian A, Rehman N U, Mandic E 2013 IEEE Signal Process Lett. 20 245
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[48] Qu J L, Wang X F, Gao F, Zhou Y P, Zhang X F 2014 Acta Phys. Sin. 63 110201 (in Chinese)[曲建岭, 王小飞, 高峰, 周玉平, 张翔宇 2014 63 110201]
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[51] [52] [53] Flandrin P 2004 Int. J. Wavelets Multiresolution Inf. Process. 2 1
[54] [55] Perrin E, Harba R, Jennane R 2002 IEEE Signal Process Lett. 9 382
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[1] Zhang Y 2013 Chin. Phys. B 22 050502
[2] [3] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 020501 (in Chinese)[王文波, 张晓东, 汪祥莉 2013 62 020501]
[4] Qu J L, Wang X F, Qiao Y C, Gao F, Di Y Z 2014 Chin. Phys. Lett. 31 020503
[5] [6] Schreiber T 1993 Phys. Rev. E 47 2401
[7] [8] [9] Dedieu H, Kisel A 1999 Int. J. Circuit Theory Appl. 27 577
[10] Deng K, Zhang L, Luo M K 2011 Chin. Phys. Lett. 28 020502
[11] [12] [13] Xu L Q, Hu L Q, Li E Z 2012 Chin. Phys. B 21 055208
[14] [15] Xie Z B, Feng J C 2009 Chin. Phys. Lett. 26 030501
[16] [17] Fu M J, Zhuang J J, Hou F Z, Zhan Q B, Shao Y 2010 Chin. Phys. B 19 058701
[18] [19] Tang J 2014 Acta Phys. Sin. 63 049701 (in Chinese)[唐洁 2014 63 049701]
[20] Boudraa A, Cexus J 2007 IEEE Trans. Instrum. Measur. 56 2196
[21] [22] [23] Khan J, Bhuiyan S, Murphy G, Alam M 2011 Opt. Pattern Recognit. 8055 805504
[24] Chacko A, Ari S 2012 IEEE ICAESM Nagapattinam, Tamil Nadu, March, 30-31, 2012 p6
[25] [26] [27] Olufemi A, Vladimir A, Auroop R 2011 IEEE Sensors J. 11 2565
[28] [29] Kopsinis Y, McLaughlin S 2009 IEEE Trans. Signal Process. 57 1351
[30] [31] Wang W B, Zhang X D, Wang X L 2013 Acta Phys. Sin. 62 069701 (in Chinese)[王文波, 张晓东, 汪祥莉 2013 62 069701]
[32] [33] Wang W B, Wang X L 2013 Acta Phys. Sin. 62 209701 (in Chinese)[王文波, 汪祥莉 2013 62 209701]
[34] [35] Hassan M, Boudaoud S, Terrien J, Karlsson B, Marque C 2011 IEEE Trans. Biomed. Eng. 58 2441
[36] [37] Sweeney K T, McLoone S F 2013 IEEE Trans. Biomed. Eng. 60 97
[38] [39] Tanaka T, Mandic D P 2006 IEEE Signal Process Lett. 14 101
[40] Altaf M U B, Gautama T, Tanaka T 2007 IEEE ICASSP 3 1009
[41] [42] [43] Rilling G, Flandrin P, Gonalves P 2007 IEEE Signal Process Lett. 14 936
[44] Ahrabian A, Rehman N U, Mandic E 2013 IEEE Signal Process Lett. 20 245
[45] [46] [47] Wu Z H, Huang N E 2009 Advances in Adaptive Data Analysis 1 1
[48] Qu J L, Wang X F, Gao F, Zhou Y P, Zhang X F 2014 Acta Phys. Sin. 63 110201 (in Chinese)[曲建岭, 王小飞, 高峰, 周玉平, 张翔宇 2014 63 110201]
[49] [50] Wu Z, Huang N E 2004 Proc. R. Soc. London, Ser. A 460 1597
[51] [52] [53] Flandrin P 2004 Int. J. Wavelets Multiresolution Inf. Process. 2 1
[54] [55] Perrin E, Harba R, Jennane R 2002 IEEE Signal Process Lett. 9 382
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