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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.
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Keywords:
- nonuniformly sampled bivariate empirical mode decomposition /
- noise assisted /
- noise energy estimate
[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 物理学报 62 020501]
[4] Qu J L, Wang X F, Qiao Y C, Gao F, Di Y Z 2014 Chin. Phys. Lett. 31 020503
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[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
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[16] [17] Fu M J, Zhuang J J, Hou F Z, Zhan Q B, Shao Y 2010 Chin. Phys. B 19 058701
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[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
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[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 物理学报 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 物理学报 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 物理学报 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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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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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