经验模态分解及其模态混叠消除的研究进展
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摘要
由Huang提出的经验模态分解(Empirical Mode Decomposition,EMD)算法是一种数据驱动的自适应非线性时变信号分析方法,可以把数据分解成具有物理意义的少数几个固有模态函数(Intrinsic Mode Function,IMF)分量。然而模态混叠会导致错假的时频分布,使IMF失去物理意义,严重影响了EMD分解的准确性与实用性。分别针对一维和多维EMD抑制模态混叠,总结归纳了相关研究取得的主要成果,指出了各方法抑制效果的改进及仍有的不足。最后讨论了相关研究及应用未来的发展趋势。
The Empirical Mode Decomposition( EMD) algorithm proposed by Huang is a data driven adaptive analysis method for nonlinear time-varying signals. The signals can be decomposed into a few Intrinsic Mode Functions( IMFs) components with physical meaning. However, Mode Mixing( MM) can lead to wrong or false components in time frequency distributions, and then cause the decomposed IMFs losing their physical meaning. This seriously affects the EMD accuracies and applications. This study reviews methods of the MM suppression in one-dimensional and multi-dimensional EMD algorithms. The results improvements and limita-tions in related researches are summarized. Finally, the future development trend of related researches and applications are dis-cussed.
The Empirical Mode Decomposition( EMD) algorithm proposed by Huang is a data driven adaptive analysis method for nonlinear time-varying signals. The signals can be decomposed into a few Intrinsic Mode Functions( IMFs) components with physical meaning. However, Mode Mixing( MM) can lead to wrong or false components in time frequency distributions, and then cause the decomposed IMFs losing their physical meaning. This seriously affects the EMD accuracies and applications. This study reviews methods of the MM suppression in one-dimensional and multi-dimensional EMD algorithms. The results improvements and limita-tions in related researches are summarized. Finally, the future development trend of related researches and applications are dis-cussed.
引文
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[3]GRIFFIN D,LIM J S.Signal estimation from modified short-time Fourier transform[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1984,32(2):236-243.
[4]LOUGHLIN P J,PITTON J W,ATLAS L E.Bilinear timefrequency representations:new insights and properties[J].IEEE Transactions on Signal Processing,1993,41(2):750-767.
[5]QIAN S E,CHEN D P.Discrete Gabor transform[J].IEEETransactions on Signal Processing,1993,41(7):2429-2438.
[6]MALLAT S G.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[7]ALMEIDA L B.The fractional Fourier transform and timefrequency representations[J].IEEE Transactions on Signal Processing,1994,42(11):3084-3091.
[8]ROEPSTORFF G.Fourier decomposition[M].Path Integral Approach to Quantum Physics.Springer Berlin Heidelberg,1994.
[9]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[J].Mathematical,Physical and Engineering Sciences,1998,454(1971):903-995.
[10]HUANG N E,WU Z H,LONG S R,et al.On instantaneous frequency[J].Advances in Adaptive Data Analysis,2009,1(2):177-229.
[11]HEISENBERG W.譈ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[J].Zeitschrift Für Physik,1927,43(3-4):172-198.
[12]CHENG J S,YU D J,YANG Y.Research on the intrinsic mode function(IMF)criterion in EMD method[J].Mechanical Systems and Signal Processing,2006,20(4):817-824.
[13]HUANG N E,WU M L C,LONG S R,et al.A confidence limit for the empirical mode decomposition and hilbert spectral analysis[J].Mathematical,Physical and Engineering Sciences,2003,459(2037):2317-2345.
[14]WANG G,CHEN X Y,QIAO F L,et al.On intrinsic mode function[J].Advances in Adaptive Data Analysis,2010,2(3):277-293.
[15]HU X Y,PENG S L,HWANG W L.EMD revisited:a new understanding of the envelope and resolving the mode-mixing problem in AM-FM signals[J].IEEE Transactions on Signal Processing,2012,60(3):1075-1086.
[16]SU Y X,LIU Z G,LI K L,et al.A new method for end effect of EMD and its application to harmonic analysis[J].Advanced Technology of Electrical Engineering and Energy,2008,27(2):33.
[17]WU Z H,HUANG N E.Ensemble empirical mode decomposition:a noise-assisted data analysis method[J].Ad vances in Adaptive Data Analysis,2009,1(1):1793-5369.
[18]FLANDRIN P,RILLING G,GONCALVES P.Empirical mode decomposition as a filter bank[J].IEEE Signal Processing Letters,2004,11(2):112-114.
[19]WU Z H,HUANG N E.A study of the characteristics of white noise using the empirical mode decomposition method[J].Mathematical,Physical and Engineering Sciences,2004,460(2046):1597-1611.
[20]HUANG N E,SHEN S S P.Hilbert-Huang transform and its applications[M].World Scientific,2005.
[21]HELSKE J,LUUKKO P.Ensemble empirical mode decomposition(EEMD)and its completevariant(CEEMDAN)[J].International Journal of Public Health,2015,60(5):1-9.
[22]YEH J R,SHIEH J S,HUANG N E.Complementary ensemble empirical mode decomposition:a novel noise enhanced data analysis method[J].Advances in Adaptive Data Analysis,2010,2(2):135-156.
[23]COLOMINAS M A,SCHLOTTHAUER G,TORRES M E.Improved complete ensemble EMD:a suitable tool for biomedical signal processing[J].Biomedical Signal Processing and Control,2014,14(1):19-29.
[24]TORRES M E,COLOMINAS M A,SCHLOTTHAUER G,et al.A complete ensemble empirical mode decomposition with adaptive noise[C].2011 IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP),2011:4144-4147.
[25]COLOMINAS M A,SCHLOTTHAUER G,TORRES M E,et al.Noise-assisted emd methods in action[J].Advances in Adaptive Data Analysis,2012,4(4):1793-5369.
[26]COLOMINAS M A,SCHLOTTHAUER G,FLANDRIN P,et al.Descomposición empírica en modos por conjuntos completa con ruido adaptativo y aplicaciones biomédicas[C].XVIII Congreso Argentino de Bioingeniería SABI 2011-VII Jornadas de Ingeniería Clínica.2011.
[27]HUMEAU-HEURTIER A,ABRAHAM P,MAHE G.Analysis of laser speckle contrast images variability using a novel empirical mode decomposition:comparison of results with laser Doppler flowmetry signals variability[J].IEEE Transactions on Medical Imaging,2015,34(2):618-627.
[28]REHMAN N U,MANDIC D P.Multivariate empirical mode decomposition[J].Mathematical,Physical and Engineering Sciences,2010,466(2117):1291-1302.
[29]REHMAN N U,MANDIC D P.Filter bank property of multivariate empirical mode decomposition[J].IEEE Transactions on Signal Processing,2011,59(5):2421-2426.
[30]REHMAN N U,PARK C,HUANG N E,et al.EMD via MEMD:multivariate noise-aided computation of standard EMD[J].Advances in Adaptive Data Analysis,2013,5(2):1793-5369.
[31]MANDIC D P,REHMAN N U,WU Z H,et al.Empirical mode decomposition-based time-frequency analysis of multivariate signals:the power of adaptive data analysis[J].IEEE Signal Processing Magazine,2013,30(6):74-86.
[32]CUI J J,FREEDEN W.Equidistribution on the Sphere[M].Society for Industrial and Applied Mathematics,1997,18(2):595-609.
[33]PARK C,LOONEY D,REHMAN N U,et al.Classification of motor imagery BCI using multivariate empirical mode decomposition[J].IEEE Transactions on Neural Systems and Rehabilitation Engineering,2013,21(1):10-22.
[34]LOONEY D,MANDIC D P.Multiscale image fusion using complex extensions of EMD[J].IEEE Transactions on Signal Processing,2009,57(4):1626-1630.
[2]BIRKHOFF G.A limitation of fourier analysis[J].Journal of Mathematics and Mechanics,1967,17(5):443-447.
[3]GRIFFIN D,LIM J S.Signal estimation from modified short-time Fourier transform[J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1984,32(2):236-243.
[4]LOUGHLIN P J,PITTON J W,ATLAS L E.Bilinear timefrequency representations:new insights and properties[J].IEEE Transactions on Signal Processing,1993,41(2):750-767.
[5]QIAN S E,CHEN D P.Discrete Gabor transform[J].IEEETransactions on Signal Processing,1993,41(7):2429-2438.
[6]MALLAT S G.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,1989,11(7):674-693.
[7]ALMEIDA L B.The fractional Fourier transform and timefrequency representations[J].IEEE Transactions on Signal Processing,1994,42(11):3084-3091.
[8]ROEPSTORFF G.Fourier decomposition[M].Path Integral Approach to Quantum Physics.Springer Berlin Heidelberg,1994.
[9]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[J].Mathematical,Physical and Engineering Sciences,1998,454(1971):903-995.
[10]HUANG N E,WU Z H,LONG S R,et al.On instantaneous frequency[J].Advances in Adaptive Data Analysis,2009,1(2):177-229.
[11]HEISENBERG W.譈ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik[J].Zeitschrift Für Physik,1927,43(3-4):172-198.
[12]CHENG J S,YU D J,YANG Y.Research on the intrinsic mode function(IMF)criterion in EMD method[J].Mechanical Systems and Signal Processing,2006,20(4):817-824.
[13]HUANG N E,WU M L C,LONG S R,et al.A confidence limit for the empirical mode decomposition and hilbert spectral analysis[J].Mathematical,Physical and Engineering Sciences,2003,459(2037):2317-2345.
[14]WANG G,CHEN X Y,QIAO F L,et al.On intrinsic mode function[J].Advances in Adaptive Data Analysis,2010,2(3):277-293.
[15]HU X Y,PENG S L,HWANG W L.EMD revisited:a new understanding of the envelope and resolving the mode-mixing problem in AM-FM signals[J].IEEE Transactions on Signal Processing,2012,60(3):1075-1086.
[16]SU Y X,LIU Z G,LI K L,et al.A new method for end effect of EMD and its application to harmonic analysis[J].Advanced Technology of Electrical Engineering and Energy,2008,27(2):33.
[17]WU Z H,HUANG N E.Ensemble empirical mode decomposition:a noise-assisted data analysis method[J].Ad vances in Adaptive Data Analysis,2009,1(1):1793-5369.
[18]FLANDRIN P,RILLING G,GONCALVES P.Empirical mode decomposition as a filter bank[J].IEEE Signal Processing Letters,2004,11(2):112-114.
[19]WU Z H,HUANG N E.A study of the characteristics of white noise using the empirical mode decomposition method[J].Mathematical,Physical and Engineering Sciences,2004,460(2046):1597-1611.
[20]HUANG N E,SHEN S S P.Hilbert-Huang transform and its applications[M].World Scientific,2005.
[21]HELSKE J,LUUKKO P.Ensemble empirical mode decomposition(EEMD)and its completevariant(CEEMDAN)[J].International Journal of Public Health,2015,60(5):1-9.
[22]YEH J R,SHIEH J S,HUANG N E.Complementary ensemble empirical mode decomposition:a novel noise enhanced data analysis method[J].Advances in Adaptive Data Analysis,2010,2(2):135-156.
[23]COLOMINAS M A,SCHLOTTHAUER G,TORRES M E.Improved complete ensemble EMD:a suitable tool for biomedical signal processing[J].Biomedical Signal Processing and Control,2014,14(1):19-29.
[24]TORRES M E,COLOMINAS M A,SCHLOTTHAUER G,et al.A complete ensemble empirical mode decomposition with adaptive noise[C].2011 IEEE International Conference on Acoustics,Speech and Signal Processing(ICASSP),2011:4144-4147.
[25]COLOMINAS M A,SCHLOTTHAUER G,TORRES M E,et al.Noise-assisted emd methods in action[J].Advances in Adaptive Data Analysis,2012,4(4):1793-5369.
[26]COLOMINAS M A,SCHLOTTHAUER G,FLANDRIN P,et al.Descomposición empírica en modos por conjuntos completa con ruido adaptativo y aplicaciones biomédicas[C].XVIII Congreso Argentino de Bioingeniería SABI 2011-VII Jornadas de Ingeniería Clínica.2011.
[27]HUMEAU-HEURTIER A,ABRAHAM P,MAHE G.Analysis of laser speckle contrast images variability using a novel empirical mode decomposition:comparison of results with laser Doppler flowmetry signals variability[J].IEEE Transactions on Medical Imaging,2015,34(2):618-627.
[28]REHMAN N U,MANDIC D P.Multivariate empirical mode decomposition[J].Mathematical,Physical and Engineering Sciences,2010,466(2117):1291-1302.
[29]REHMAN N U,MANDIC D P.Filter bank property of multivariate empirical mode decomposition[J].IEEE Transactions on Signal Processing,2011,59(5):2421-2426.
[30]REHMAN N U,PARK C,HUANG N E,et al.EMD via MEMD:multivariate noise-aided computation of standard EMD[J].Advances in Adaptive Data Analysis,2013,5(2):1793-5369.
[31]MANDIC D P,REHMAN N U,WU Z H,et al.Empirical mode decomposition-based time-frequency analysis of multivariate signals:the power of adaptive data analysis[J].IEEE Signal Processing Magazine,2013,30(6):74-86.
[32]CUI J J,FREEDEN W.Equidistribution on the Sphere[M].Society for Industrial and Applied Mathematics,1997,18(2):595-609.
[33]PARK C,LOONEY D,REHMAN N U,et al.Classification of motor imagery BCI using multivariate empirical mode decomposition[J].IEEE Transactions on Neural Systems and Rehabilitation Engineering,2013,21(1):10-22.
[34]LOONEY D,MANDIC D P.Multiscale image fusion using complex extensions of EMD[J].IEEE Transactions on Signal Processing,2009,57(4):1626-1630.
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