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According to the characteristics of empirical mode decomposition and denoise of independent component analysis, an adaptive denoising method of chaotic signal is proposed based on independent component analysis and empirical mode decomposition. First, the chaotic signal is decomposed into a set of intrinsic mode functions by empirical mode decomposition; then, the multi-dimensional input vectors are constructed based on the translation invariant empirical mode decomposition, and the noise of each intrinsic mode function is removed through the constructed multi-dimensional input vectors and the independent component analysis; finally, the denoisied chaotic signal is obtained by accumulating and reconstructing all the processed intrinsic mode functions. Both the chaotic signal generated by Lorenz map with different level Gaussian noises, and the observed monthly series of sunspots are respectively used for noise reduction using the proposed method. The results of numerical experiments show that the proposed method is efficient. It can better correct the positions of data points in phase space and approximate the real chaotic attractor trajectories more closely．
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Keywords:
- independent component analysis /
- empirical mode decomposition /
- chaotic signal /
- denoising
[1] Li G L, Chen X Y 2008 Acta Electronica Sinica 36 1814 (in Chinese) [李冠林, 陈希有 2008 电子学报 36 1814]
[2] Vicha T, Dohnal M 2008 Chaos, Solitons & Fractals 38 70
[3] Dedieu H, Kisel A 1999 International Journal of Circuit Theory and Applications 27 577
[4] Jako Z, Kis G 2000 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47 1720
[5] Schreiber T 1993 Physical Review E 47 2401
[6] Han M, Liu Y H, Shi Z W, Xiang M 2007 Journal of System Simulation 19 364 (in Chinese) [韩敏, 刘玉花, 史志伟, 项牧 2007 系统仿真学报 19 364]
[7] Leontitsis A, Bountis T, Pagge J 2004 Chaos 14 106
[8] Huang X G, Xu J X, He D H 1999 Acta Phys. Sin. 48 1810 (in Chinese) [黄显高, 徐健学, 何岱海, 夏军利 1999 48 1810]
[9] Murguia J S, Campos C E 2006 Revista Mexicana De Fisica 52 155
[10] Liu Y X, Yang G S, Jia Q 2011 Acta Electronica Sinica 39 13 (in Chinese) [刘云侠, 杨国诗, 贾群 2011 电子学报 39 13]
[11] Zhang L, Bao P, Wu X 2005 IEEE Transactions on Circuits and Systems for Video Technology 15 469
[12] Zhang H, Chen X H, Yang H Y 2011 Oil Geophysical Prospecting 46 70 (in Chinese) [张华, 陈小宏, 杨海燕 2011 石油地球物理勘探 46 70]
[13] Huang N E, Shen Z, Long S R 1998 Proc. of the Royal Society of London A454 903
[14] Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008 57 6139]
[15] An X L, Jiang D X, Zhao M H, Liu C 2011 Communications in Nonlinear Science and Numerical Simulation 17 1036
[16] Boudraa A, Cexus J 2007 IEEE Transaction on Instrumentation and Measurement 56 2196
[17] Olufemi A, Vladimir A, Auroop R 2011 IEEE Sensors Journal 11 2565
[18] Kopsinis Y, Mclaughli S 2009 IEEE Transactions on Signal Processing 57 1351
[19] Hyvarinen A, Oja E 2000 Neural Networks 13 411
[20] Li P J, Jin H R, Song B Q 2008 Acta Scientiarum Naturalium Universitatis Pekinensis 4 45(in Chinese) [李培军, 金慧然, 宋本钦 2008 北京大学学报(自然科学版) 4 45]
[21] Zhang Z S, Yu J, Yan Q, Meng Y S, Zhao Z 2011 Acta Geodaetica et Cartographica Sinica 40 289 (in Chinese) [张中山, 余洁, 燕琴, 孟云闪, 赵争 2011 测绘学报 40 289]
[22] Li H, Sun Y L 2007 Journal of Beijing University of Posts andTelecommunicatios 30 33 (in Chinese) [李洪, 孙云莲 2007 北京邮电大学学报 30 33]
[23] Aapo H 1999 IEEE Transactions on Neural Networks 10 626
[24] Zhao H W, Norden E H 2004 Proc. R. Soc. Lond. A8 460 1597
[25] Schlotthauer G, Torres M E, Rufiner H L, Flandrin P 2009 Advances in Adaptive Data Analysis 1 11
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[1] Li G L, Chen X Y 2008 Acta Electronica Sinica 36 1814 (in Chinese) [李冠林, 陈希有 2008 电子学报 36 1814]
[2] Vicha T, Dohnal M 2008 Chaos, Solitons & Fractals 38 70
[3] Dedieu H, Kisel A 1999 International Journal of Circuit Theory and Applications 27 577
[4] Jako Z, Kis G 2000 IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47 1720
[5] Schreiber T 1993 Physical Review E 47 2401
[6] Han M, Liu Y H, Shi Z W, Xiang M 2007 Journal of System Simulation 19 364 (in Chinese) [韩敏, 刘玉花, 史志伟, 项牧 2007 系统仿真学报 19 364]
[7] Leontitsis A, Bountis T, Pagge J 2004 Chaos 14 106
[8] Huang X G, Xu J X, He D H 1999 Acta Phys. Sin. 48 1810 (in Chinese) [黄显高, 徐健学, 何岱海, 夏军利 1999 48 1810]
[9] Murguia J S, Campos C E 2006 Revista Mexicana De Fisica 52 155
[10] Liu Y X, Yang G S, Jia Q 2011 Acta Electronica Sinica 39 13 (in Chinese) [刘云侠, 杨国诗, 贾群 2011 电子学报 39 13]
[11] Zhang L, Bao P, Wu X 2005 IEEE Transactions on Circuits and Systems for Video Technology 15 469
[12] Zhang H, Chen X H, Yang H Y 2011 Oil Geophysical Prospecting 46 70 (in Chinese) [张华, 陈小宏, 杨海燕 2011 石油地球物理勘探 46 70]
[13] Huang N E, Shen Z, Long S R 1998 Proc. of the Royal Society of London A454 903
[14] Yang Y F, Ren X M, Qin W Y, Wu Y F, Zhi X Z 2008 Acta Phys. Sin. 57 6139 (in Chinese) [杨永锋, 任兴民, 秦卫阳, 吴亚锋, 支希哲 2008 57 6139]
[15] An X L, Jiang D X, Zhao M H, Liu C 2011 Communications in Nonlinear Science and Numerical Simulation 17 1036
[16] Boudraa A, Cexus J 2007 IEEE Transaction on Instrumentation and Measurement 56 2196
[17] Olufemi A, Vladimir A, Auroop R 2011 IEEE Sensors Journal 11 2565
[18] Kopsinis Y, Mclaughli S 2009 IEEE Transactions on Signal Processing 57 1351
[19] Hyvarinen A, Oja E 2000 Neural Networks 13 411
[20] Li P J, Jin H R, Song B Q 2008 Acta Scientiarum Naturalium Universitatis Pekinensis 4 45(in Chinese) [李培军, 金慧然, 宋本钦 2008 北京大学学报(自然科学版) 4 45]
[21] Zhang Z S, Yu J, Yan Q, Meng Y S, Zhao Z 2011 Acta Geodaetica et Cartographica Sinica 40 289 (in Chinese) [张中山, 余洁, 燕琴, 孟云闪, 赵争 2011 测绘学报 40 289]
[22] Li H, Sun Y L 2007 Journal of Beijing University of Posts andTelecommunicatios 30 33 (in Chinese) [李洪, 孙云莲 2007 北京邮电大学学报 30 33]
[23] Aapo H 1999 IEEE Transactions on Neural Networks 10 626
[24] Zhao H W, Norden E H 2004 Proc. R. Soc. Lond. A8 460 1597
[25] Schlotthauer G, Torres M E, Rufiner H L, Flandrin P 2009 Advances in Adaptive Data Analysis 1 11
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