隨著世界人口高齡化的現象與健康意識的抬頭，遠距居家看護系統逐漸受到重視，為了避免心電圖資訊因為長期監測而產生的龐大資料量造成網路頻寬與儲存空間的負擔，本論文提出利用壓縮感知為基礎的心電壓縮演算法，使用者可視儲存裝置容、生理訊號觀測品質等不同環境與需求，調整不同壓縮比例。且壓縮感知理論在編碼端與解碼端的運算量不對等，編碼端的運算量會低於解碼端，因此可以降低編碼端的運算量。
本論文提出一個有效的心電圖資料壓縮方法，心電圖訊號壓縮演算法採用壓縮感知(Compressive sensing)結合霍夫曼編碼(Huffman coding)的方式，並藉由K-SVD演算法訓練字典，取代壓縮感知中固定形式的基底，屬有失真性壓縮 (Lossy Compression)。壓縮感知理論限制，壓縮訊號需在特定已知基底下具有稀疏性(sparse)，才能還原出原始訊號，分為壓縮與解壓縮兩個階段，壓縮流程中，首先將ECG訊號依照R波所在位置進行分割，將各區段內插為256點後，去掉各別區段的平均值，將處理後的訊號使用測量矩陣進行壓縮，壓縮過後的訊號進行片段後項差分，降地壓縮訊號動態範圍，接著量化訊號，最後使用霍夫曼編碼進一步的增加壓縮率。在還原過程中，使用K-SVD演算法訓練過完備的字典矩陣，使用此字典做為還原時的稀疏表示字典，取代原本固定形式的還原基底，所提出的壓縮演算法使用MIT-BIH 心律不整資料庫的48組心律不整資料作為測試訊號，平均壓縮比(CR)為30.26、失真率(PRD)為1.54。

As the world population aging phenomenon and the rise of health consciousness, remote home care system gradually be taken seriously. In order to avoid the huge amount of data because of long-term monitoring of ECG information arising from the burden of network bandwidth and storage space, this paper proposes the use of ECG compression algorithm based compressed sensing,the user depending on storage capacity, physiological signal quality observations different environments and needs, adjust different compression ratio.
This paper presents a valid ECG data compression method can be applied to health care in remote ECG management system to save storage space and reduce data transfer times. ECG signal compression algorithm in compressed sensing combined with Huffman coding method. It is divided into two stages, the compression and decompression. The compression process, the ECG R-wave signal in accordance with the position where the split, each zone 256 as interpolation points, remove the average value of the individual segments, the signal processed is compressed using the measurement matrix. After the signal compression performed Segment backward difference. Then quantization signal. Finally, Huffman coding increases the compression ratio. During the decompression process,use of K-SVD algorithm train Personal dictionary matrix, this dictionary as sparse restores the dictionary, to replace the original fixed-form orthogonal basis.The proposed algorithms were evaluated by using all patterns from MIT-BIH arrhythmia database,the average compression ratio (CR) is 30.26, distortion (PRD) is 1.54

[1] 行政院衛生署. Available: http://www.mohw.gov.tw/cht/DOS/DisplayStatisticFile.aspx?d=49775&s=1
[2] IMS Research. Available: http://www.imsresearch.com
[3] Cunningham, Textbook of Veterinary Physiology, 2002.
[4] 心電圖，維基百科. Available: http://zh.wikipedia.org/zhtw/%E5%BF%83%E9%9B%BB%E5%9C%96#cite_note-1
[5] "ECG-Learning Center."
[6] A. Camm, M. Malik, J. Bigger, G. Breithardt, S. Cerutti, R. Cohen, et al., "Heart rate variability. Standards of measurement, physiological interpretation, and clinical use," European Heart Journal, vol. 17, pp. 354-381, 1996.
[7] 除顫器，A+醫學百科. Available: http://cht.a-hospital.com/w/除顫器
[8] B.-U. Köhler, C. Hennig, and R. Orglmeister, "The principles of software QRS detection," Engineering in Medicine and Biology Magazine, IEEE, vol. 21, pp. 42-57, 2002.
[9] B. C. YU, C. S. Liu, M. LEE, C. Y. CHEN, and B. N. CHIANG, "A Nonlinear Digital Filter For Cardiac QRS Complex Detection," Journal of Clinical Engineering, vol. 10, pp. 193-201, 1985.
[10] G. B. Moody and R. G. Mark, "The impact of the MIT-BIH arrhythmia database," Engineering in Medicine and Biology Magazine, IEEE, vol. 20, pp. 45-50, 2001.
[11] A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, et al., "Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals," Circulation, vol. 101, pp. e215-e220, 2000.
[12] R. E. Hermes, D. B. Geselowitz, and G. C. Oliver, "Development, distribution, and use of the American Heart Association database for ventricular arrhythmia detector evaluation," Computers in cardiology, pp. 263-266, 1980.
[13] A. Taddei, A. Biagini, G. Distante, M. Emdin, M. Mazzei, P. Pisani, et al., "The European ST-T database: development, distribution and use," in Computers in Cardiology 1990, Proceedings., 1990, pp. 177-180.
[14] B. Singh, A. Kaur, and J. Singh, "A Review of ECG Data Compression Techniques," International Journal of Computer Applications, vol. 116, 2015.
[15] B. S. Kashin, "Diameters of some finite-dimensional sets and classes of smooth functions," Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, vol. 41, pp. 334-351, 1977.
[16] E. J. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," Information Theory, IEEE Transactions on, vol. 52, pp. 489-509, 2006.
[17] D. L. Donoho, "Compressed sensing," Information Theory, IEEE Transactions on, vol. 52, pp. 1289-1306, 2006.
[18] E. J. Candes and T. Tao, "Near-optimal signal recovery from random projections: Universal encoding strategies?," Information Theory, IEEE Transactions on, vol. 52, pp. 5406-5425, 2006.
[19] R. G. Baraniuk, "Compressive sensing," IEEE signal processing magazine, vol. 24, 2007.
[20] E. J. Candès, "The restricted isometry property and its implications for compressed sensing," Comptes Rendus Mathematique, vol. 346, pp. 589-592, 2008.
[21] E. J. Candes and T. Tao, "Decoding by linear programming," Information Theory, IEEE Transactions on, vol. 51, pp. 4203-4215, 2005.
[22] E. J. Candè and M. B. Wakin, "An introduction to compressive sampling," Signal Processing Magazine, IEEE, vol. 25, pp. 21-30, 2008.
[23] T. T. Cai, L. Wang, and G. Xu, "New bounds for restricted isometry constants," Information Theory, IEEE Transactions on, vol. 56, pp. 4388-4394, 2010.
[24] E. Candes and J. Romberg, "Sparsity and incoherence in compressive sampling," Inverse problems, vol. 23, p. 969, 2007.
[25] R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, "A simple proof of the restricted isometry property for random matrices," Constructive Approximation, vol. 28, pp. 253-263, 2008.
[26] L. Bregman, "The method of successive projection for finding a common point of convex sets(Theorems for determining common point of convex sets by method of successive projection)," Soviet Mathematics, vol. 6, pp. 688-692, 1965.
[27] J. A. Tropp and A. C. Gilbert, "Signal recovery from random measurements via orthogonal matching pursuit," Information Theory, IEEE Transactions on, vol. 53, pp. 4655-4666, 2007.
[28] W. Dai and O. Milenkovic, "Subspace pursuit for compressive sensing signal reconstruction," Information Theory, IEEE Transactions on, vol. 55, pp. 2230-2249, 2009.
[29] S. Qaisar, R. M. Bilal, W. Iqbal, M. Naureen, and S. Lee, "Compressive sensing: From theory to applications, a survey," Communications and Networks, Journal of, vol. 15, pp. 443-456, 2013.
[30] M. Aharon, M. Elad, and A. Bruckstein, "K-SVD: An algorithm for designing of overcomplete dictionaries for sparse representation Technion—Israel Inst. of Technology, 2005," Tech. Ref.
[31] J. A. Hartigan and M. A. Wong, "Algorithm AS 136: A k-means clustering algorithm," Journal of the Royal Statistical Society. Series C (Applied Statistics), vol. 28, pp. 100-108, 1979.
[32] K. Engan, S. O. Aase, and J. Hakon Husoy, "Method of optimal directions for frame design," in Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on, 1999, pp. 2443-2446.
[33] A. Mishra, F. Thakkar, C. Modi, and R. Kher, "ECG signal compression using compressive sensing and wavelet transform," in Engineering in Medicine and Biology Society (EMBC), 2012 Annual International Conference of the IEEE, 2012, pp. 3404-3407.
[34] L. F. Polania, R. E. Carrillo, M. Blanco-Velasco, and K. E. Barner, "Compressed sensing based method for ECG compression," in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, 2011, pp. 761-764.
[35] L. F. Polania and K. E. Barner, "Multi-scale dictionary learning for compressive sensing ECG," in Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), 2013 IEEE, 2013, pp. 36-41.
[36] 戴佩真, "利用差分 QRS 波之無失真/失真性心電訊號壓縮演算法與無線心電圖量測系統實現," 2013.
[37] ImpulseAdventure - JPEG Huffman Coding Tutorial. Available: http://www.impulseadventure.com/photo/jpeg-huffman-coding.html
[38] Y. Zigel, A. Cohen, and A. Katz, "The weighted diagnostic distortion (WDD) measure for ECG signal compression," Biomedical Engineering, IEEE Transactions on, vol. 47, pp. 1422-1430, 2000.
[39] R. Kumar and I. Saini, "Empirical wavelet transform based ECG signal compression," IETE Journal of Research, vol. 60, pp. 423-431, 2014.
[40] C. M. Fira and L. Goras, "An ECG signals compression method and its validation using NNs," Biomedical Engineering, IEEE Transactions on, vol. 55, pp. 1319-1326, 2008.
[41] J. Chen, F. Wang, Y. Zhang, and X. Shi, "ECG compression using uniform scalar dead-zone quantization and conditional entropy coding," Medical Engineering & Physics, vol. 30, pp. 523-530, 2008.
[42] A. Bilgin, M. W. Marcellin, and M. I. Altbach, "Compression of electrocardiogram signals using JPEG2000," Consumer Electronics, IEEE Transactions on, vol. 49, pp. 833-840, 2003.
[43] A. Khalaj and H. M. Naimi, "New efficient fractal based compression method for electrocardiogram signals," in Electrical and Computer Engineering, 2009. CCECE'09. Canadian Conference on, 2009, pp. 983-986.
[44] M. Abo-Zahhad, A. F. Al-Ajlouni, S. M. Ahmed, and R. J. Schilling, "A new algorithm for the compression of ECG signals based on mother wavelet parameterization and best-threshold levels selection," Digital Signal Processing, vol. 23, pp. 1002-1011, 2013.