在現今社會裡，心臟病具有很高的致死率，其中以急性冠心症（ACS）最為嚴重，能迅速診斷，適當的治療是極為重要的。本論文為達輔助心電圖（ECG）辨識及診斷疾病之目的，應用小波散射轉換（WST）由ECG擷取特徵值，並用非線性支持向量機（SSVM）對心肌梗塞和心肌健康的訊號進行辨識及分類。
本研究以類似深度學習方法使用心電圖中心肌梗塞與正常的波形特徵值作為基礎，利用Mallat等人所提出的小波散射網路為模型，採用監督式學習，對所有受測心電圖進行標記後，讓小波散射網路擷取不同標記的波型特徵，接著使用所得的特徵係數對非線性支持向量機進行訓練，用統計風險最小化的原則來決定一個分類的超平面（hyperplane）。訓練完成後，任何新的未知心電圖中波形由本模型擷取特徵係數後，使用本模型分類的超平面即可辨識。
本論文主要貢獻為提供可準確識別心電圖中心肌梗塞與正常的波形特徵值之方法。貢獻分為三部分：1.結合連續小波散射轉換和非線性支持向量機識別時變系統。 2.應用小波散射轉換配合分段擷取特徵值以識別心電圖之波形。 3.發展基於小波散射轉換的特徵值作為診斷心電圖中心肌梗塞及異常結構損傷之方法。
在前處理的階段，我們也提出一種偵測心電圖中R峰的離散小波轉換（DWT）方法，此方法在Long-Term ST Database（LTSTdb）上做測試，其召回率（recall）和精確率（precision）為98.5%和98.2%均高於Pan–Tompkins演算法的97.7%和97.6%。進一步我們使用Wilson Central Terminal ECG Database （WCTECGdb）裡診斷為STEMI和NSTEMI的病人心電圖波形和Physikalisch-Technische Bundesanstalt Diagnostic ECG Database（PTBdb）裡的健康心電圖波形，進行兩種實驗。一，將ECG訊號直接分割為數個5秒的片段，交由小波散射網路模型進行訓練，對訓練完成的模型進行辨識分類測試，此方法證實可以達到87%的準確度（accuracy）。二，對ECG訊號做前處理，先偵測R峰位置，將ECG分段為數個單一心跳，再交由小波散射網路模型分類辨識，結果發現可以達到高達95%的準確度，而進一步來說，因為ACS可再細分為ST段抬高型心肌梗塞（STEMI）和非ST段抬高型心肌梗塞（NSTEMI），所以我們亦將STEMI和NSTEMI的病人ECG訊號抽取出來，利用主成分分析（PCA）降維後搭配SSVM做分類，得到的準確度則為73%。

Nowadays, one of the leading causes of mortality is heart disease. Among all heart diseases, acute coronary syndrome (ACS) is the most serious. An electrocardiogram (ECG) is a common way to diagnose non-ST-segment elevation myocardial infarction (NSTEMI) and ST-segment elevation myocardial infarction (STEMI) for ACS. The present study aims to help with the diagnose by proposing a new method of feature extraction and classification of ECG signal by a combination of wavelet scattering transform (WST) and smooth support vector machine (SSVM).
By using convolution with wavelet, activating nonlinearity with modulus and pooling with low-pass filter, wavelet scattering network model recently developed by Mallat et al. was based on rigorous mathematical theory and excellent feature extraction ability for audio and image classification. The methodology for both training and inference of such wavelet scattering network model for detection and classification of myocardial infarction (MI) and normal ECG signal is presented.
The main contribution of this thesis is providing a wavelet scattering network model to accurately detect the MI signals. Our contribution has three parts: 1. Combining wavelet scattering transform and smooth support vector machine for ECG time series identification. 2. Application of wavelet scattering transform for feature extraction of ECG signals. 3. Developing waveform classifier for MI based on wavelet scattering transform feature extraction.
Also, based on discrete wavelet transform, we proposed a new R-peak detection method for ECG signal preprocessing. The method had been verified on Long-Term ST Database (LTSTdb) with 98.5% recall and 98.2% precision, which was slightly higher than the current Pan-Tompkins algorithm’s 97.7% recall and 97.6% precision. Furthermore, we verified our proposed wavelet scattering network model with Wilson Central Terminal ECG Database (WCTECGdb) and Physikalisch-Technische Bundesanstalt Diagnostic ECG Database (PTBdb). We conducted 2 experiments. The first one was splitting ECG signal to several 5-second segments and the second one was splitting ECG signal to several beats. We demonstrated that our proposed method for detecting MI greatly reduced the computational complexity while the classification accuracy of about 87% and 95% were comparable to the traditional deep convolution neural network. In addition, we wanted to differentiate STEMI and NSTEMI as well. We used Principal Component Analysis (PCA) to reduce the dimension of ECG signals from STEMI and NSTEMI and used SSVM to classify. We found that we had 73% accuracy.

Contents
1 Introduction ....................................................1
2 Basic Theorem and Background Knowledge...........................3
2.1 Wavelet Scattering Transform ..................................3
2.2 About Electrocardiogram (ECG) Signal ..........................11
3 Methodology .....................................................13
3.1 ECG Signal Classification Framework ...........................13
3.1.1 Basic Classification Framework ..............................13
3.1.2 ECG Database ................................................14
3.2 Feature Extraction ............................................15
3.2.1 Wavelet Scattering Network Model ............................15
3.2.2 R Peaks Detection ...........................................19
3.2.3 Segmentation ................................................24
3.3 Dimension Reduction and Classification .......................25
3.4 Evaluation Index ..............................................26
4 Experiments and Results .........................................26
4.1 Myocardial Infarction Classification in PTBdb .................26
4.2 Results of R Peaks Detection ..................................27
4.3 Myocardial Infarction (including NSTEMI and STEMI) Classification in PTBdb and WCTECGdb .............................................29
5 Discussion ......................................................30
References ........................................................34

[1] Yi-Heng Li, Yu-Chen Wang, Yi-Chih Wang, Ju-Chi Liu, Cheng-Han Lee, Chun-Chi Chen, I-Chang Hsieh, Feng-You Kuo, Wei-Chun Huang, Shih-Hsien Sung, et al. 2018 Guidelines of the Taiwan Society of Cardiology, Taiwan Society of Emergency Medicine and Taiwan Society of Cardiovascular Interventions for the management of non ST-segment elevation acute coronary syndrome. Journal of the Formosan Medical Association, 117(9):766-790, 2018.
[2] https://www.cardiosmart.org/heart-conditions/guidelines/heart-attackguidelines.
[3] Muhammad Arif, Ijaz A Malagore, and Fayyaz A Afsar. Detection and localization of myocardial infarction using k-nearest neighbor classifier. Journal of medical systems, 36(1):279-289, 2012.
[4] Li Sun, Yanping Lu, Kaitao Yang, and Shaozi Li. Ecg analysis using multiple instance learning for myocardial infarction detection. IEEE transactions on biomedical engineering, 59(12):3348-3356, 2012.
[5] Naser Safdarian, Nader Jafarnia Dabanloo, and Gholamreza Attarodi. A new pattern recognition method for detection and localization of myocardial infarction using t-wave integral and total integral as extracted features from one cycle of ecg signal. Journal of Biomedical Science and Engineering, 2014, 2014.
[6] LN Sharma, RK Tripathy, and Samarendra Dandapat. Multiscale energy and eigenspace approach to detection and localization of myocardial infarction. IEEE transactions on biomedical engineering, 62(7):1827-1837, 2015.
[7] U Rajendra Acharya, Hamido Fujita, Vidya K Sudarshan, Shu Lih Oh,
Muhammad Adam, Joel EW Koh, Jen Hong Tan, Dhanjoo N Ghista,
Roshan Joy Martis, Chua K Chua, et al. Automated detection and localization of myocardial infarction using electrocardiogram: a comparative study of different leads. Knowledge-Based Systems, 99:146-156, 2016.
[8] U Rajendra Acharya, Hamido Fujita, Shu Lih Oh, Yuki Hagiwara, Jen Hong Tan, and Muhammad Adam. Application of deep convolutional neural network for automated detection of myocardial infarction using ecg signals. Information Sciences, 415:190-198, 2017.
[9] Tahsin Reasat and Celia Shahnaz. Detection of inferior myocardial infarction using shallow convolutional neural networks. In 2017 IEEE Region 10 Humanitarian Technology Conference (R10-HTC), pages 718-721. IEEE, 2017.
[10] Nils Strodthoff and Claas Strodthoff. Detecting and interpreting myocardial infarction using fully convolutional neural networks. Physiological measurement, 40(1):015001, 2019.
[11] Kai Feng, Xitian Pi, Hongying Liu, and Kai Sun. Myocardial infarction classification based on convolutional neural network and recurrent neural network. Applied Sciences, 9(9):1879, 2019.
[12] Gong Zhang, Yujuan Si, Di Wang,Weiyi Yang, and Yongjian Sun. Automated detection of myocardial infarction using a gramian angular field and principal component analysis network. IEEE Access, 7:171570-171583, 2019.
[13] Stephane Mallat. Group invariant scattering. Communications on Pure and Applied Mathematics, 65(10):1331-1398, 2012.
[14] Joakim Anden and Stephane Mallat. Deep scattering spectrum. IEEE Transactions on Signal Processing, 62(16):4114-4128, 2014.
[15] Joakim Anden and Stephane Mallat. Multiscale scattering for audio classification. In ISMIR, pages 657-662. Miami, FL, 2011.
[16] Joan Bruna and Stephane Mallat. Classification with scattering operators. In CVPR 2011, pages 1561-1566. IEEE, 2011.
[17] Leif Sornmo and Pablo Laguna. Electrocardiogram (ecg) signal processing. Wiley encyclopedia of biomedical engineering, 2006.
[18] Adam Pleister, Helina Selemon, Shane M Elton, and Terry S Elton. Circulating mirnas: novel biomarkers of acute coronary syndrome? Biomarkers in medicine, 7(2):287-305, 2013.
[19] Ary L Goldberger, Luis AN Amaral, Leon Glass, Jerey M Hausdorff, Plamen Ch Ivanov, Roger G Mark, Joseph E Mietus, George B Moody, Chung-Kang Peng, and H Eugene Stanley. Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals. circulation [Online], 101(23):e215-e220, 2000.
[20] Franc Jager, Alessandro Taddei, George B Moody, Michele Emdin, G Antolic, Roman Dorn, Ales Smrdel, Carlo Marchesi, and Roger G Mark. Long-term st database: a reference for the development and evaluation of automated ischaemia detectors and for the study of the dynamics of myocardial ischaemia. Medical and Biological Engineering and Computing, 41(2):172-182, 2003.
[21] Gargiulo G. Moeinzadeh, H. Wilson central terminal ecg database (version 1.0.1). https://doi.org/10.13026/f73z-an96., 2019.
[22] Gaetano D Gargiulo, Paolo Bifulco, Mario Cesarelli, Alistair L McEwan, Hossein Moeinzadeh, Aiden O'Loughlin, Ibrahim M Shugman, Jonathan C Tapson, and Aravinda Thiagalingam. On the "zero of potential of the electric field produced by the heart beat". a machine capable of estimating this underlying persistent error in electrocardiography. Machines, 4(4):18, 2016.
[23] Kreiseler D. Schnabel A. Bousseljot, R. Nutzung der ekg-signaldatenbank cardiodat der ptb uber das internet. Biomedizinische Technik / Biomedical Engineering, 40(s1):317-318, 1995.
[24] Bedionita Soro and Chaewoo Lee. A wavelet scattering feature extraction approach for deep neural network based indoor fingerprinting localization. Sensors, 19(8):1790, 2019.
[25] https://www.di.ens.fr/data/scattering/.
[26] Gael de Lannoy, Arnaud De Decker, and Michel Verleysen. A supervised wavelet transform algorithm for r spike detection in noisy ecgs. In International Joint Conference on Biomedical Engineering Systems and Technologies, pages 256-264. Springer, 2008.
[27] N. V. Thakor, J. G. Webster, and W. J. Tompkins. Estimation of qrs complex power spectra for design of a qrs filter. IEEE Transactions on Biomedical Engineering, BME-31(11):702-706, 1984.
[28] Paul S Addison. Wavelet transforms and the ecg: a review. Physiological measurement, 26(5):R155, 2005.
[29] Stephane Mallat. A wavelet tour of signal processing. Elsevier, 1999.
[30] Ingrid Daubechies. Ten lectures on wavelets. SIAM, 1992.
[31] http://wavelets.pybytes.com/wavelet/db4/.
[32] Jiapu Pan and Willis J Tompkins. A real-time qrs detection algorithm. IEEE transactions on biomedical engineering, (3):230-236, 1985.
[33] Hooman Sedghamiz (2020). Complete pan tompkins implementation ecg qrs detector. https://www.mathworks.com/matlabcentral/fileexchange/45840-complete-pan-tompkins-implementation-ecg-qrs-detector.
[34] Hooman Sedghamiz. Matlab implementation of pan tompkins ecg qrs detector. Code Available at the File Exchange Site of MathWorks, 2014.
[35] R. Sameni, M. B. Shamsollahi, C. Jutten, and G. D. Clifford. A nonlinear bayesian filtering framework for ecg denoising. IEEE Transactions on Biomedical Engineering, 54(12):2172-2185, 2007.
[36] Karl Pearson. Liii. on lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11):559-572, 1901.
[37] Yuh-Jye Lee and Olvi L Mangasarian. Ssvm: A smooth support vector machine for classification. Computational optimization and Applications, 20(1):5-22, 2001.
[38] Chien-Ming Huang, Yuh-Jye Lee, Dennis KJ Lin, and Su-Yun Huang. Model selection for support vector machines via uniform design. Computational Statistics & Data Analysis, 52(1):335-346, 2007.