在傳統經驗模態分解的分解過程中，容易受到間歇性訊號的影響而產生混模現象，造成分解出的本質模態函數失去真正的物理意義。本文提出了，能快速且穩定地改善混模現象。所提出的改良型經驗模態分解藉由訊號中每一個波的時間尺度進行分配，能直接得到改善混模現象的結果。此外，本文亦對現有文獻中較少探討的二維影像資料的混模現象進行探討，申明二維混模現象的定義與二維混模現象的檢視方法。

In the sifting process of the traditional empirical mode decomposition (EMD), intermittence causes mode mixing phenomenon. The intrinsic mode function (IMF) with the mode mixing phenomenon loses its original real physical meaning. In the current study, an improved EMD based on time scale allocation method has been proposed to improve the decomposition of the mode mixing phenomenon fast and stably. Additionally, the 2D version of our method has been extended to improve the decomposition of the mode mixing phenomenon in the 2D image data. Experimental results show that the improved EMD not only improves the decomposition of the mode mixing phenomenon correctly regardless for 1D signal or 2D image, but also exhibits great performance in quality and computation time. Furthermore, this thesis discusses the mode mixing phenomenon for 2D image data directly rather than extending the definition form 1D to 2D.

[1] N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, et al., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 454, pp. 903-995, 1998.
[2] Z. Peng, W. T. Peter, and F. Chu, “A comparison study of improved Hilbert–Huang transform and wavelet transform: application to fault diagnosis for rolling bearing,” Mechanical Systems and Signal Processing, vol. 19, no. 5, pp. 974-988, 2005.
[3] P. Flandrin, G. Rilling, and P. Goncalves, “Empirical mode decomposition as a filter bank,” Signal Processing Letters, IEEE, vol. 11, no. 2, pp. 112-114, 2004.
[4] Y. Lei, J. Lin, Z. He, and M. J. Zuo, “A review on empirical mode decomposition in fault diagnosis of rotating machinery,” Mechanical Systems and Signal Processing, vol. 35, no. 1, pp. 108-126, 2013.
[5] N. E. Huang, Z. Shen, and S. R. Long, “A new view of nonlinear water waves: the Hilbert Spectrum 1,” Annual Review of Fuid Mechanics, vol. 31, no. 1, pp. 417-457, 1999.
[6] T. Jing-tian, Z. Qing, T. Yan, L. Bin, and Z. Xiao-kai, “Hilbert-Huang transform for ECG de-noising,” Bioinformatics and Biomedical Engineering, 2007. ICBBE 2007. The 1st International Conference on, pp. 664-667, 2007.
[7] J. C. Nunes, Y. Bouaoune, E. Delechelle, O. Niang, and P. Bunel, “Image analysis by bidimensional empirical mode decomposition,” Image and Vision Computing, vol. 21, no. 12, pp. 1019-1026, 2003.
[8] Y. Zhang, Z. Sun, and W. Li, “Texture synthesis based on direction empirical mode decomposition,” Computers and Graphics, vol. 32, no. 2, pp. 175-186, 2008.
[9] J. Riffi, A. Mohamed Mahraz, and H. Tairi, “Medical image registration based on fast and adaptive bidimensional empirical mode decomposition,” Image Processing, IET, vol. 7, no. 6, pp. 567-574, 2013.
[10] J. M. Hughes, D. Mao, D. N. Rockmore, Y. Wang, and Q. Wu, “Empirical mode decomposition analysis for visual stylometry,” Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 34, no. 11, pp. 2147-2157, 2012.
[11] X. Chen, A. Song, J. Li, Y. Zhu, X. Sun, and H. Zeng, “Texture Feature Extraction Method for Ground Nephogram Based on Hilbert Spectrum of Bidimensional Empirical Mode Decomposition,” Journal of Atmospheric and Oceanic Technology, vol. 31, no. 9, pp. 1982-1994, 2014.
[12] H. Ali, M. Hariharan, S. Yaacob, and A. H. Adom, “Facial emotion recognition using empirical mode decomposition,” Expert Systems with Applications, vol. 42, no. 3, pp. 1261-1277, 2015.
[13] R. Deering and J. F. Kaiser, “The use of a masking signal to improve empirical mode decomposition,” Acoustics, Speech, and Signal Processing, 2005. Proceedings.(ICASSP'05). IEEE International Conference on, vol. 4, pp. iv/485-iv/488 Vol. 4, 2005.
[14] N. Senroy, S. Suryanarayanan, and P. F. Ribeiro, “An improved Hilbert–Huang method for analysis of time-varying waveforms in power quality,” Power Systems, IEEE Transactions on, vol. 22, no. 4, pp. 1843-1850, 2007.
[15] X. Hu, S. Peng, and W.-L. Hwang, “EMD revisited: A new understanding of the envelope and resolving the mode-mixing problem in AM-FM signals,” Signal Processing, IEEE Transactions on, vol. 60, no. 3, pp. 1075-1086, 2012.
[16] B. Tang, S. Dong, and T. Song, “Method for eliminating mode mixing of empirical mode decomposition based on the revised blind source separation,” Signal Processing, vol. 92, no. 1, pp. 248-258, 2012.
[17] Z. Wu and N. E. Huang, “Ensemble empirical mode decomposition: a noise-assisted data analysis method,” Advances in Adaptive Data Analysis, vol. 1, no. 1, pp. 1-41, 2009.
[18] M. E. Torres, M. A. Colominas, G. Schlotthauer, and P. Flandrin, “A complete ensemble empirical mode decomposition with adaptive noise,” Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE international conference on, pp. 4144-4147, 2011.
[19] M. A. Colominas, G. Schlotthauer, and M. E. Torres, “Improved complete ensemble EMD: A suitable tool for biomedical signal processing,” Biomedical Signal Processing and Control, vol. 14, pp. 19-29, 2014.
[20] Z. Wu, N. E. Huang, and X. Chen, “The multi-dimensional ensemble empirical mode decomposition method,” Advances in Adaptive Data Analysis, vol. 1, no. 3, pp. 339-372, 2009.
[21] A. Humeau-Heurtier, G. Mahé, and P. Abraham, “Multi-dimensional complete ensemble empirical mode decomposition with adaptive noise applied to laser speckle contrast images,” Medical Imaging, IEEE Transactions on, vol. 34, no. 10, pp. 2103-2117, 2015.