本文應用經驗模態分解法針對非穩態與非線性訊號之良好解析度，以 及最小平方法在數學領域上之最佳化技術成功有效濾除心電訊號中所存 在之雜訊成分。在訊號分解上，經驗模態分解法能將訊號中所隱含的成 分由高頻至低頻拆解出來，其中本質模態函數屬於高頻部份，殘餘值則 屬於低頻部份，因此整個訊號拆解的過程為一濾波的動作。而重建的部 份則利用最小平方法來進行，先求出欲重建的各個本質模態函數需要相 乘的權重係數，再乘上相對應的本質模態函數並相加之後，即可得到重 建訊號。本研究亦在最小平方法與部分重建法之間利用均方誤差針對訊 號重建效果做了相關比較，最後實驗驗證雜訊干擾小的情況下，使用最 小平方法可以達到較佳的重建效果；當雜訊干擾較為強烈時，訊號源會 近似雜訊，則採用過程較簡單的部分重建法即可獲得與過程較複雜的最 小平方法同樣甚至更佳效果。
本文所提出之雜訊濾除方法雖然已能有效的濾除心電訊號中雜訊成 分，但經驗模態分解法還存在著許多限制與缺點，期望未來能有更多研 究者針對此領域繼續深入探討及改善演算法，為全民福祉做出更大的貢 獻。
參考文獻
[1] 行政院衛生署
http://www.doh.gov.tw/cht2006/index_populace.aspx [2] 基本心電圖圖例簡介
http://www.dcbiomed.com/material/ECG3CH.pdf
[3] J.A.V. Alste, T.S. Schilder, “Removal of Base Line Wander and Power Line Interference from the ECG by an Efficient FIR Filter with a Reduced Number of Taps”, IEEE transactions on biomedical engineering, Vol. Bme-32. No. 12, Dec. 1985, pp.1052-1060.
[4] A. Gutierrez, P.R. Hernandez, M. Lara, S. Perez, “A QRS Detection Algorithm Based on Haar Wavelet”, Computers in Cardiology 1998 Sep. 1998, pp.353-356.
[5] A. Haar, “Zur theorie der orthogonalen funktionen-systeme”, Math. Ann., vol. 69, 1910, pp.331-373.
[6] I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
[7] H. Xing, M. Huang, “A New QRS Detection Algorithm Based on Empirical Mode Decomposition”, Bioinformatics and biomedical engineering, May 2008, pp.693-696.
[8] D. Davis (1991), 基本心電圖判讀 (黃天守、陳清輝編譯)，台北：眾 文圖書股份有限公司。(原著出版於 1985)
[9] http://www.adam.com/democontent/hie/images/en/1135.jpg
[10] http://static.howstuffworks.com/gif/adam/images/en/ecg-electrode-place ment-picture.jpg
[11] G.M. Friesen, T.C. Jannett, M.A. Jadallah, S.L. Yates, S.R. Quint, H.T.
Algorithm”, IEEE transactions on biomedical engineering, Vol. 37. No.
1. January, 1990, pp.85-98.
[12] G.D. Clifford, F. Azuaje, P.E. mcSharry, Advanced method and tools for ECG data analysis, Artech House, INC. 685 Canton Street Norwood.
[13] S.K. Mitra, Digital signal processing, McGraw.Hill international 3rd edtion 2006.
[14] A.G. Kleber, M.J. Janse, F.J. van Capelle, D. Durrer, “Mechanism and time course of S-T and T-Q segment changes during acute regional ischemia in the pig determined by extracellular and intracellular recordings”, Circ. Res., Vol. 42, 1978, pp.603-613.
[15] R. Coronel, J.R. DE Groot, M.J. Janse, “Laplacian electrograms and the interpretation of complex ventricular activation patterns during ventricular fibrillation”, J Cardiovasc Electrophysiol, Vol. 11, 2000, pp.1119-1128.
[16] N. E. Huang, Z. Shen, S. R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C.
Yen, C.C. Tung, H.H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis”, Proc. R. Soc. Lond. A, Vol. 454, 1998, pp.903-995.
[17] N. E. Huang, M. C. Wu, S. R. Long, S.S.P. Shen, W. Qu, P. Gloersen, K.L. Fan, “A Confidence Limit for the Empirical Mode Decomposition and Hilbert Spectrum Analysis”, Proc. R. Soc. Lond. A, Vol. 459, 2003, pp.2317-2345.
[18] P. Gonçalvés, P. Abry, G. Rilling, P. Flandrin, “Fractal Dimension Estimation: Empirical Mode Decomposition Versus Wavelets”, IEEE International Conference on Acoustics, Speech and Signal Processing
[19] V. Kamath, Y.C. Lai, L. Zhu, “Empirical Mode Decomposition and Blind Source Separation Methods for Antijamming with GPS Signals”, IEEE Position Location and Navigation Symposium PLANS 2006, Apr.
2006, pp.335-341.
[20] B. Weng, B.V. Manuel, K.E. Barner, “ECG Denoising Based on The Empirical Mode Decomposition”, IEEE International Conference on Engineering in Medicine and Biology Society EMBS 2006, 30 Aug.-3 Sep. 2006, pp.1-4.
[21] Y. Ye, J. Garcia-Casado, J.L. Martines-de-Juan, et al., “Combined Method for Artifact Reduction in Surface Eletroenterogram”, IEEE International Conference on Engineering in Medicine and Biology Society EMBS 2007, 23-26 Aug. 2007.
[22] S. Liu, Q. He, R.X. Gao, F. Patty, “Empirical Mode Decomposition Applied to Tissue Artifact Removal from Respiratory Signal”, IEEE International Conference on Engineering in Medicine and Biology Society EMBS 2008, Aug. 2008, pp.3624-3627.
[23] Md.K.I. Molla, K. Hirose, N. Minematsu, K. Hasan, “Voiced/Unvoiced Detection of Speech Signals Using Empirical Mode Decomposition Model”, IEEE International Conference on Information and Communication Technology ICICT '07, Mar. 2007, pp.311-314.
[24] K. Khaldi, A.O. Boudraa, A. Bouchikhi, M.T.H. Alouane, E.H.S Diop, ”Speech Signal Noise Reduction by EMD”, IEEE International Symposium on Communications, Control and Signal Processing ISCCSP 2008, Mar. 2008, pp.1155-1158.
Conference on Systems, Signals and Image Processing IWSSIP 2008, Jun.
2008, pp.101-104.
[26] R. Srinivasan, R. Rengaswamy, R. Miller, “A Modified Empirical Mode Decomposition (EMD) Process for Oscillation Characterization in Control Loops”, Control Engineering Practice, Vol. 15, No. 9, Sep. 2007, pp.1135-1148
[27] J.F. Khan, R.R. Adhami, S.M.A. Bhuiyan, K.E. Barner, “Empirical Mode Decomposition Based Interest Point Detector”, IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2008, 30 Mar. - 4 Apr. 2008, pp.1317-1320.
[28] Y.X. Huang, F.G. Schmitt, Z.M. Lu, et al., “An Amplitude-Frequency Study of Turbulent Scaling Intermittency Using Empirical Mode Decomposition and Hilbert Spectral Analysis”, A Letters Journal Exploring The Frontiers of Physics, Vol. 84, Nov. 2008, pp.1-6.
[29] V. Agarwal, L.H. Tsoukalas, “Denoising Electrical Signal via Empirical Mode Decomposition”, 2007 iREP Symposium- Bulk Power System Dynamics and Control- VII, Revitalizing Operational Reliability, Aug.
2007, pp.1-6.
[30] G. Rilling, P. Flandrin, P. Gonçalvés, “On Empirical Mode Decomposition and Its Algorithms”, IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, Jun. 2003.
[31] J. Cheng, D. Yu, Y. Yang, “Research on the Intrinsic Mode Function (IMF) Criterion in EMD Method”, Mechanical Systems and Signal Processing, Vol. 20, No.4, May 2006, pp.817-824.
[32] B. Xuan, Q. Xie, S. Peng, “EMD Sifting Based on Bandwidth”, IEEE
[33] Y. Kopsinis, S. McLaughlin, “Enhanced Empirical Mode Decomposition Using a Novel Sifting-Based Interpolation Points Detection”, IEEE Workshop on Statistical Signal Processing SSP 2007, Aug. 2007, pp.725-729.
[34] Y. Kopsinis, S. McLaughlin, “Investigation of The Empirical Mode Decomposition Based on Genetic Algorithm Optimization Schemes”, IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2007, Vol. 3, Apr. 2007, pp.1397-1400.
[35] Y. Kopsinis, S. McLaughlin, “Investigation and Performance Enhancement of The Empirical Mode Decomposition on a Heuristic Search Optimization Approach”, IEEE Transaction on Signal Processing, Vol. 56, No.1, Jan. 2008, pp.1-13.
[36] Y. Kopsinis, S. McLaughlin, “Improve EMD Using Doubly-Iterative Sifting and High Order Spline Interpolation”, EURASIP Journal on Advances in Signal Processing, Vol. 2008, Mar. 2008 , pp.1-8.
[37] Z. Zhao, Y. Wang, “A New Method for Processing End Effect in Empirical Mode Decomposition”, IEEE International Conference on Circuits and Systems for Communications ICCSC 2007, July 2007, pp.841-845.
[38] M.C. Peel, G.E. Amirthanathan, G.G.S. Pegram, “Issue with The Application of Empirical Mode Decomposition Analysis”, MODSIM 2005 International Congress on Modelling and Simulation, Dec. 2005, pp.1681-1687.
[39] G. Rilling, P. Flandrin, “One or Two Frequency? The Empirical Mode
[40] 維基百科
http://zh.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E5%B9%B3
%E6%96%B9%E6%B3%95
[41] S. Ma, K. Li, “Fast parametric time-frequency modeling of nonstationary signals”, Applied mathematics and computation 205, 2008 pp.170–177.
[42] J. Pan, W.J. Tompkins, “ A Real Time QRS detection Algorithm”, IEEE Transaction on Biomedical Engineering, Vol. Bme-32, No. 3, March 1985, pp.230-236.
[43] MIT/BIH 心律不整資料庫
http://www.physionet.org/physiobank/database/mitdb