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A dissertation submitted in fulfilment of the requirement for the degree of Doctor of Philosophy


Academic year: 2022

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A dissertation submitted in fulfilment of the requirement for the degree of Doctor of Philosophy

(Mechatronics Engineering)

Kulliyyah of Engineering

International Islamic University Malaysia





Though various techniques have been suggested for the analysis of ECG signals, interpretation of these signals, especially as they affect human health, has posed some difficulties. Consequently, the best way of interpreting these physiological signals by electric measurements from the body surface in terms of cardiac electric activity remains an active research topic till today. This research tackles three problems related to ECG analysis namely, parametric modeling, period normalization (interpolation) and classification of arrhythmias. In order to model the signal, each heartbeat is first mapped into a new domain where the transform coefficients vector would be sparse. The coefficients vector is then approximated to a sum of damped sinusoids. The transform matrix is generated based on the combination of linear prediction (LP) and the singular values decomposition (SVD) of the LPC filter impulse response matrix. This approach leads to relatively satisfactory compression ratio (CR) as compared to existing techniques. Though parametric modeling of ECG signals has a central role in real time transmission and classification of heart abnormalities (arrhythmias), the compression ratios achieved are not suitable for storage purpose. Therefore, 2D ECG compression schemes are adopted where the beats of differing periods should be equalized to the same period length and then arranged in an image matrix before the application of image compression algorithm.

Limitations of the existing techniques for ECG period equalization are highlighted and a new frequency domain approach for period normalization has been developed. The proposed approach is signal dependent and able to adapt to the signal characteristics.

An analytical model to generate basis functions has also been developed. The merits of the proposed technique are appreciated when compared to other techniques commonly used in the literature. Finally, an algorithm for arrhythmia classification that conforms to the recommended practice of the Association for the Advancement of Medical Instrumentation (AAMI) is presented. Three inter-patient classification scenarios have been considered namely, detection of ventricular ectopic beats (VEBs), detection of supraventricular ectopic beats (SVEBs) and the multiclass recommended taxonomy.A novel set of features extraction via the application of orthogonal transformation of the ECG signal has been developed. These features in conjunction with some commonly used features are fed into the Regularized Least Squares Classifier (RLSC) with linear kernel. The proposed classification scheme shows good separation capability between the classes of ECG arrhythmias as it has achieved a Balanced Classification Rate (BCR) of 83.9 % for the multiclass scenario which is comparable to the state-of-the-art performance of automatic arrhythmia classification algorithms.



ﺚﺤﺒﻟا ﺺﺨﻠﻣ

، تارﺎﺷﻹا ﻩﺬﻫ ﲑﺴﻔﺗ لاﺰﻳ ﻻ ،ﺐﻠﻘﻟا ﻂﻴﻄﲣ تارﺎﺷإ ﻞﻴﻠﺤﺘﻟ ﺔﻔﻠﺘﳐ تﺎﻴﻨﻘﺗ حاﱰﻗا ﻦﻣ ﻢﻏﺮﻟا ﻰﻠﻋ ﻩﺬﻫ ﲑﺴﻔﺘﻟ ﺔﻘﻳﺮﻃ ﻞﻀﻓأ نﺈﻓ ، ﱄﺎﺘﻟ5و .ت5ﻮﻌﺼﻟا ﺾﻌﺑ حﺮﻄﻳ ، نﺎﺴﻧﻹا ﺔﺤﺻ ﻰﻠﻋ ﺮﺛﺆﺗ ﺎAأو ﺔﺻﺎﺧ ﺮﻬﻜﻟا طﺎﺸﻨﻟا ﺔﻓﺮﻌﳌ ﻢﺴﳉا ﺢﻄﺳ ﻰﻠﻋ ﺔﺳﺎﻘﳌاا ﺔﻴﺟﻮﻟﻮﻳﺰﻴﻔﻟا تارﺎﺷﻹا ﻞﻜﺸﻳ لاﺰﻳ ﻻ ﺐﻠﻘﻟا ﰲ ﻲﺋ5

ﻲﻫو ﺐﻠﻘﻟا ﻂﻴﻄﲣ ﻞﻴﻠﺤﺘﺑ ﻖﻠﻌﺘﺗ ﻞﻛﺎﺸﻣ ثﻼﺛ لوﺎﻨﺘﻳ ﺚﺤﺒﻟا اﺬﻫ.مﻮﻴﻟا ﱴﺣ ﻂﺸﻧ ﺚﲝ عﻮﺿﻮﻣ ﻲﺿ[ﺮﻟا ﻞﻴﺜﻤﺘﻟا ﻞﺟأ ﻦﻣ . ﺐﻠﻘﻟا ت5ﺮﺿ مﺎﻈﺘﻧا مﺪﻋ ﻒﻴﻨﺼﺗو ،ءﺎﻔﻴﺘﺳﻻا ، ةرﺎﺷﻼﻟ ﻲﺿ[ﺮﻟا ﻞﻴﺜﻤﺘﻟا نﻮﻜﺗ ﺚﻴﺣ ﺪﻳﺪﺟ لﺎﳎ ﰲ ﺔﻀﺒﻧ ﻞﻛ ﻞﻴﺜﲤ ﻻوا ﻢﺘﻳ ، ةرﺎﺷﻼﻟ لﺎeا ﰲ عﺎﻌﺸﻟا تﻼﻣﺎﻌﻣ ﺐﻠﻏا

ﻢﺘﻳ .ةﺪﻣﺎﺨﺘﻣ ﺔﻴﺒﻴﺟ تﺎﻴﻨﺤﻨﻣ عﻮﻤﳎ ﱃا ﺔﻠﻳﻮﺤﺘﻟا ﻦﻋ ﺞﺗﺎﻨﻟا عﺎﻌﺸﻟا ﺐﻳﺮﻘﺗ ﻢﺘﻳ ﺎﻫﺪﻌﺑ.ةﲑﻐﺻ ﺪﻳﺪﳉا ) ﻲﻄﳋا ﺆﺒﻨﺘﻟا لﺎﻤﻌﺘﺳ5 ﻞﻳﻮﺤﺘﻟا ﺔﻓﻮﻔﺼﻣ ءﺎﺸﻧإ LP

) و ( SVD ﱰﻠﻔﻠﻟ ( LPC ﺔﻘﻳﺮﻄﻟا ﻩﺬﻫ .

) ﺎﻴﺒﺴﻧ ﺔﻴﺿﺮﻣ ﻂﻐﺿ ﺔﺒﺴﻧ ﱃإ تدا CR

ﻊﻣ ﺔﻧرﺎﻘﳌ5 ( ﻞﻴﺜﻤﺘﻟا نا ﻦﻣ ﻢﻏﺮﻟا ﻰﻠﻋ .ﺔﻴﻟﺎﳊا تﺎﻴﻨﻘﺘﻟا

تﺎﻫﻮﺸﺗ ﻒﻴﻨﺼﺗ و ،دﺪﶈاا ﺖﻗﻮﻟا ﰲ ةرﺎﺷﻻا ﻩﺬﻫ لﺎﺳرإ ﰲ يﺰﻛﺮﻣ رود ﻪﻟ ﺐﻠﻘﻟا ةرﺎﺷﻻ ﻲﺿ[ﺮﻟا .ﻦﻳﺰﺨﺘﻟا ضاﺮﻏﻷ ﺔﺒﺳﺎﻨﻣ ﺖﺴﻴﻟ ﺔﻘﻘﶈا ﻂﻐﻀﻟا ﺐﺴﻧ ﻰﻘﺒﺗ ،( ﺐﻠﻘﻟا ت5ﺮﺿ مﺎﻈﺘﻧا مﺪﻋ ) ﺐﻠﻘﻟا ﻂﻐﺿ تﺎﻄﻄﳐ دﺎﻤﺘﻋا ﻢﺘﻳ ،ﻚﻟﺬﻟ 2D ECG

ﺚﻴﺣ ﺔﻔﻠﺘﺨﳌا تﺎﻗﺪﻟا تاﱰﻓ ىوﺎﺴﺗ نأ ﻲﻐﺒﻨﻳ

تﺎﻴﻨﻘﺘﻟا ﺺﺋﺎﻘﻧ ﻰﻠﻋ ءﻮﻀﻟا ﻂﻴﻠﺴﺗ ﰎ . ةرﻮﺼﻟا ﻂﻐﺿ ﺔﻴﻣزراﻮﺧ ﻖﻴﺒﻄﺗ ﻞﺒﻗ ﺔﻓﻮﻔﺼﻣ ﰲ ﺎﻬﺒﻴﺗﺮﺗ ﰒ ﻦﻣو ﻰﻠﻋ ةردﺎﻗ ﺔﺣﱰﻘﳌا ﺔﻘﻳﺮﻄﻟا .ضﺮﻐﻟا اﺬﻫا ةﺪﻳﺪﺟ ﺔﻘﻳﺮﻃ ﺮﻳﻮﻄﺗ و ﺐﻠﻘﻟا تﺎﻗد تاﱰﻓ ﺔﻳﻮﺴﺘﻟ ﺔﻴﻟﺎﳊا ﻄﺗ ﰎ ﺎﻤﻛ .ةرﺎﺷﻹا ﺺﺋﺎﺼﺧ ﻊﻣ ﻒﻴﻜﺘﻟا ﺔﺳارد ﺖﲤو .ﻞﻳﻮﺤﺘﻟا ﺔﻓﻮﻔﺼﻣ ﺔﻌﺷا ﺪﻴﻟﻮﺘﻟ ﻲﻠﻴﻠﲢ جذﻮﳕ ﺮﻳﻮ

ﰎ ،اﲑﺧأ .ﺔﻘﺑﺎﺴﻟا تﺎﺳارﺪﻟاا ﰲ ةدﺎﻋ ﺔﻣﺪﺨﺘﺴﳌا ىﺮﺧﻷا تﺎﻴﻨﻘﺘﻟا ﻊﻣ ﺔﻧرﺎﻘﳌ5 ﺔﺣﱰﻘﳌا ﺔﻴﻨﻘﺘﻟا [اﺰﻣ ضﻮﻬﻨﻟا ﺔﻴﻌﲨ ﻦﻣ ﺎ‹ ﻰﺻﻮﳌا تﺎﺳرﺎﻤﳌا ﻊﻣ ﻖﻓاﻮﺘﻳ ﺐﻠﻘﻟا ت5ﺮﺿ مﺎﻈﺘﻧا مﺪﻋ ﻒﻴﻨﺼﺘﻟ ﺔﻴﻣزراﻮﺧ ﱘﺪﻘﺗ ا ةﺰﻬﺟﻷا ) ﺔﻴﺒﻄﻟ

AAMI تﻼﺣ ﻒﻴﻨﺼﺗ تﺎﻫﻮﻳرﺎﻨﻴﺳ ﺔﺛﻼﺛ ﺔﺳارﺪﻟا لﻼﺧ ﱪﺘﻋا ﺪﻗو .(

) VEBs ) ﻦﻋ ﻒﺸﻜﻟاو ،(

SVEBs ﺮﻳﻮﻄﺗ ﰎ ﺪﻗو .ت5اﺮﻄﺿﻼﻟ دﺪﻌﺘﳌا ﻒﻴﻨﺼﺘﻟا ﱃا ﺔﻓﺎﺿﻻ5 (

تاﺰﻴﳌا ﻩﺬﻫ ﺔﻳﺬﻐﺗ ﰎو .ﺐﻠﻘﻟا ﻂﻴﻄﲣ ةرﺎﺷﻹ ةﺪﻣﺎﻌﺘﳌا ﻞﻳﻮﺤﺘﻟا ﻖﻴﺒﻄﺗ ﱪﻋ تاﺰﻴﳌا ﻦﻣ ةﺪﻳﺪﺟ ﺔﻋﻮﻤﳎ ﻨﺟ ﱃإ ﺎﺒﻨﺟ ) ﻒﻨﺼﻣ ﰲ ﺎﻬﻣاﺪﺨﺘﺳا ةدﺎﻋ ﺔﻠﻤﻌﺘﺴﳌاا تاﺰﻴﳌا ﺾﻌﺑ ﻊﻣ ﺐ

RLSC .ﻲﻄﳋا ةاﻮﻧ ﻊﻣ (

) لﺪﻌﲟ ةﺪﻴﺟ ﻞﺼﻓ ةرﺪﻘﻟا حﱰﻘﳌا ﻒﻴﻨﺼﺘﻟا ﻂﻄﳐ ﲔﺑ BCR

ﻦﻣ ( 83.9 ﻮﻳرﺎﻨﻴﺴﻟ ٪ multiclass

ﺔﻠﻤﻌﺘﺴﳌا ﺐﻠﻘﻟا ت5ﺮﺿ مﺎﻈﺘﻧا مﺪﻋ ﻒﻴﻨﺼﺘﻟا تﺎﻴﻣزراﻮﺧ ءادﻷ ﻪﺑﺎﺸﻣ ﻮﻫو





The thesis of Hamza Baali has been approved by the followings:

--- Momoh J.E Salami


--- Othman.O.Khalifa

Internal Examiner

--- Nahrul Khair Bin Alang Rashid

Internal Examiner

--- Yussof Mashor

External Examiner

--- Md. Yousuf Ali





I hereby declare that this dissertation is the result of my own investigations, except where otherwise stated. I also declare that it has not been previously or concurrently submitted as a whole for any other degrees at IIUM or other institution.

Hamza Baali

Signature ………...……… Date ………..……





Copyright © 2014 by International Islamic University Malaysia. All rights reserved.


I hereby affirm that the International Islamic University Malaysia (IIUM) holds all rights in the copyright of this Work and henceforth any reproduction or use in any form or by means whatsoever is prohibited without the written consent of IIUM. No parts of this unpublished research may be reproduced, stored in a retrieval system, or transmitted, in any form or by means, electronic, mechanical, photocopying, recording or otherwise without prior written permission of the copyright holder.

Affirmed by: Hamza Baali

--- --- Signature Date




All praise is due unto Allah who has made it possible for one to attain this level of academic pursuit. We praise Him for endowing us with the time, ability and resources for the accomplishment of this goal.

With due respect and a sense of appreciation, I acknowledge the support, contributions and encouragement of my supervisors Prof. Dr. Momoh and Prof. Dr.

Rini towards the completion of my work; and particularly, the financial support of Prof. Dr. Rini is highly appreciated. I pray Allah to reward them abundantly.

May the blessings of Allah continue to shower on my parents Mr. & Mrs. Baali who bear the burden of responsibility for my social and academic wellbeing both in times of ease and adversity. May Allah grant them the opportunity to reap the fruits of their labour. I do also acknowledge the moral support of my brothers and sisters; and other relations of mine who have kindly contributed to the success of this venture.

I offered my unreserved gratitude to my friends who have provided a great deal of moral support and guidance in the course of my studies. May Allah reward them accordingly.

Finally, I pray Allah to reward all those who have contributed in one way or

the other to the successful completion of my programme.




Abstract ... ii

Abstract Arabic ... iii

Approval Page ... iv

Declaration ... v

Acknowledgments ... viii

List of Tables ... xi

List of Figures ... xii

List of Abbreviations ... xv

List of Symbols ... xviii


1.1 Overview... 1

1.2Problem Statement and Its Significance ... 3

1.3Research Philosophy ... 6

1.4Research Objectives ... 7

1.5Research Methodology ... 8

1.6Research Scope ... 10

1.7Thesis Organization ... 11


2.1Introduction ... 13

2.2Review On ECG ... 13

2.3ECG Pre-Processing ... 20

2.3.1ECG Filtering ... 20

2.3.2QRS Detection ... 23

2.4Ecg Compression Techniques ... 23

2.4.1Direct Methods for ECG Compression ... 24 Turning Point Method ... 24 Amplitude Zone Time Epoch Coding ... 25 Coordinate Reduction Time Encoding System Algorithm .... 26 Scan Along Polygonal Approximation Algorithm ... 27

2.4.2Transform Based Methods ... 28 KLT Applied to ECG ... 30 Sinusoidal Transforms ... 33 Rectangular Transforms ... 38 Discrete Polynomial Transforms ... 38

2.4.3Parametric Modeling of ECG Signal ... 41 Armax Models ... 42 Gaussian Modeling of ECG Signal ... 44 Multi-Resolution Signal Analysis ... 46 Wavelet Function ... 47 Scaling Function ... 48 Discrete Wavelet Packet Transform ... 52

2.52d Compression Methods ... 52

2.6Arrhythmia Classification ... 57



2.7Summary ... 63


3.1Introduction ... 65

3.2Signal Pre-Processing ... 65

3.3Autoregressive Modeling Of ECG ... 66

3.3.1Matrix Representation Of The LPC Filter ... 69

3.4Parameters Estimation ... 71

3.4.1Prony’s Method ... 72

3.4.2Nonlinear Fitting ... 74

3.5Performance Measurement ... 76

3.6Results and Discussion ... 77

3.7Summary ... 90


4.1Introduction ... 91

4.2Proposed Technique ... 92

4.2.1Proof of Energy Preservation ... 94

4.3Left Singular Vectors ... 96

4.4Experimental Results ... 102

4.5Summary ... 111


5.1Introduction ... 113

5.2ECG Pre-Processing and LPC Analysis ... 114

5.3ECG Features Extraction ... 114

5.3.1RR-Interval Features ... 114

5.3.2Energy Based Features ... 115

5.3.3Transformation Based Features ... 115

5.3.4Higher Order Statistics Features ... 118

5.3.5Feature Normalization ... 119

5.4Regularized Least Squares Classification ... 119

5.4.1Tuning Regularization Parameter ૃ ... 121

5.4.2Multiclass Classification ... 121

5.5Results and Discussion ... 122

5.6Summary ... 128


6.1Conclusion ... 130

6.2Contribution to Knowledge ... 131

6.3Recommendation for Future Work ... 133


Appendix ... 144

List of Publications ... 148

List of Awards ... 150




Table No. Page No.

2.1 Criterion for the determination of the saved points 25 2.2 Comparison between direct ECG compression algorithms 27

2.3 ARMAX models polynomial representations 43

2.4 Summary of 2D ECG compression algorithms 56

2.5 Summary of literatures for ECG modeling and

compression 57

2.6 Grouping of the MIT-BIH arrhythmia database heartbeats

types 62

3.1 Compression ratios of different modeling techniques 82

3.2 PRD of different classes of ECG 87

3.3 Compression ratios of different modeling techniques 88 4.1 Comparison of compression results with other methods 106 5.1 Distribution of the extracted heartbeats in the two datasets 123 5.2 Performance of the proposed classification algorithm 125




Figure No Page No 1.1 Premature Ventricular Contractions (PVCs) with different

shapes 6

1.2 Overall schematic block of the ECG analysis stages 8 2.1 A schematic diagram of the heart anatomical layout 14 2.2 (a)Ventricular action potential; (b) pacemaker action

potential 14

2.3 Significant features of standard (Scalar) electrocardiogram 16

2.4 Standard limb leads 17

2.5 Orientation angles of limb leads 18

2.6 Horizontal plane precordial leads 19

2.7 Magnitude and phase response of a second-order FIR

notch filter 21

2.8 ECG Filtering 22

2.9 Schematic block of the Pan-Tompkins QRS detection

algorithm (pre-processor stage) 23

2.10 KLT based ECG compression 32

2.11 (a) 1st, (b) 2nd, (c)7th , (d)8th basis vectors of the DCT-8 35 2.12 Exemplary Hermite functions plotted as a function of

time: (a) n = 0, (b) n = 1, (c) n = 2, and (d) n = 10 plotted

for the same scale σ 40

2.13 ARMAX input-output model 43

2.14 A standard Gaussian wave, a=c=1; b=0 45

2.15 Multiresolution analysis tree 51

2.16 Zero padding applied to the first 10 min of record N 119 53

2.17 Exemplary waveforms of four types of heartbeats 58



2.18 An annotated ECG from a patient exhibiting normal

rhythm. 61

2.19 An annotated ECG showing a patient transitioning into

ventricular tachycardia 61

3.1 Levinson-Durbin recursion 68

3.2 Analysis filter 69

3.3 Synthesis filter 69

3.4 (a)Original ECG heartbeat , (b) Singular values ECG, (c)

Transformed ECG (θ) 71

3.5 Example of results of nonlinear fitting 75

3.6 Schematic block diagram of the analysis and synthesis of

the signal 78

3.7 Segment of original (a), reconstructed (b) waveforms of a left bundle branch block with ectopic morphology of ECG (ECG with abnormal QRS) taken from lead I of record

109. (PRD1= 3.23 %) 79

3.8 A segment of original (a), reconstructed (b) waveforms exhibiting ventricular bigeminy, taken from lead II of record 119, and (c) represents reconstruction error

(PRD1%= 2.80%) 80

3.9 A segment of original (a), (b) reconstructed (c) waveforms exhibiting a paced rhythm with dissociated P wave. Taken from lead I of record 107. And (c) represents

reconstruction error (PRD1%= 3.5975) 81

3.10 Compression of ECG signals with Het-LaT (Tchiotsop,

2007) 83

3.11 Reconstructed ECG beats (a) N category (b) SVEBs

category (c) VEB category (d) F category 86

3.12 Box plot of PRD for different ECG classes 87

3.13 Result for MIT database records, mean PRD 89

3.14 Result for MIT database records, STD of PRD 90

4.1 Block diagram of the period normalization technique 92



4.2 Period normalization of a normal sinus beat taken from

record 117 in case of shrinking 94

4.3 Graphical representation of energy preservation process 95 4.4 Example of the change of the PRD1 with the number of

truncated coefficients. 96

4.5 Period normalization of an ectopic beat taken from record

119 in case of stretching. 101

4.6 Pre-processing of the first 10 mins of record 119 of the

MIT-BIH ECG database 104

4.7 (a) ECG waveform exhibiting PVC with ventricular bigeminy taken from record 119. (b) Reconstructed waveform and (c) Reconstruction error (CR 16 and PRD=

2.58) 108

4.8 Compression result of a waveform exhibiting morphology of fusion PVCs taken from record 213 (CR 16 and PRD=

4.89) 109

4.9 Compression result of an episode exhibiting left bundle branch block. taken from record 111(CR 16 and PRD=

4.71) 110

4.10 Compression result of an episode exhibiting left bundle branch block with ectopic morphology taken from record

109 (CR 16 and PRD= 2.95) 111

5.1 Pre-RR and Post-RR intervals 115

5.2 Normal sinus beat and transformed ECG 117

5.3 Two -dimensional normal(red ‘+’) and PVC beats (black

‘o’) features 118




ACC Accuracy

AAMI Association Advancement of Medical Instrumentation AZTEC Amplitude Zone Time Epoch Coding

AR Autoregressive

ARX Autoregressive model with Exogeneous Input BCR Balanced Classification Rate

CVD Cardiovascular Disease CELP Code Excited Linear Prediction

CR Compression Ratio

CORTES Coordinate Reduction Time Encoding System

CT Cosine Transform

DC Direct Current

DCT Discrete Cosine Transform

DFT Discrete Fourier Transform

DWPT Discrete Wavelet Packet Transform

DWT Discrete Wavelet Transform

ECG Electrocardiogram

EBR Energy Based Ratio

EDS Exponentially Damped Sinusoids

FIR Finite Impulse Response

F Fusion beats

HBF Hermite Basis Functions

HALF High Amplitude Low Frequency


xvi HOS High Order Statistics

IIR IIR Infinite Impulse Response ICU Intensive Care Units

IDCT Inverse Discrete Cosine Transform

KLT Karhunen-Loève Transform

LM Levenberg-Marquardt

LDA Linear Discriminant Analysis LPCs Linear Prediction Coefficients LAHF Low Amplitude High Frequency

ML Machine Learning

MSE Mean Squared Error

MA Moving Average

ARMAX Moving Average with Exogenous Variable MRA Multi-Resolution Analysis

N Normal beats

NN Neural Networks

OVA One-Versus-All

PDWT Packet Discrete Wavelet Transform PRD Percent Root mean square Difference

+P Positive Predictivity

PVC Premature Ventricular Contraction RLS Regularized Least Squares

RLSC Regularized Least Squares Classifier

SRC Sampling Rate Conversion

SAPA Scan Along Polygonal Approximation



Se Sensitivity

SA Sinoatrial

SA node Sinoatrial node

SNR SNR Signal to Noise Ratio

SVEBs Supraventricular Ectopic Beats

Sp Specificity

SVM Support Vector Machine

TP Turning Point

2D Two-Dimensional

VEBs Ventricular Ectopic Beats

VE Ventricular Escape

WT Walsh Transform

WHO World Health Organization 2D DCT 2D Discrete Cosine Transform




V1,VII, VIII Lead voltages

ɸL Potential of the left arm

ɸR Potential of the right arm

ɸF Potential of the left foot

aVL, aVR and aVF Unipolar leads

fs Sampling frequency

f0 Fundamental frequency

b0 Gain

r Notch filter width

ω0 Oscillation frequency

zn Complex exponential sequence

y(n) ECG signal (zero state response) ε Threshold

s(n) ECG signal (Full response)

μ(n) Zero input response

w Transform ECG vector using KLT

φk Basisvector

ɸ KLT matrix

N ECG heartbeat length

ෝ Approximated ECG

C Covariance matrix λk Kth eigenvalue



Λ Eigenvalues matrix

Jm Mean square error

u Vector of mean value

U Left singular values matrix V Right singular values matrix D Singular values matrix σi ith singular values

߰κ Hermite basis function

Hl Hermite polynomials

clm Expansion coefficient

E Sum of squared error

H Filter transfer function

q Shift operator

߰௝ǡ௞ Wavelet function

߮௝ǡ௞ Scaling function dj,k Wavelet coefficient

ܽ Approximation coefficient

Ժ Complex numbers space

Թ Real numbers

L2(Թ) Hilbert space

Vj Approximation space

Wj Wavelet space

ai ith LPC coefficient

E Sum of squared error R Correlation


xx e Residual error

A(z) Analysis filter

H(z) Synthesis filter Y ECG vector H Impulse response matrix e Residual error vector

θ Transformed ECG vector

ࣀ Transformed Residual error vector

ߠ෠(n) Estimated ECG

ܣAmplitude of the complex exponential

ߪDamping factor in seconds-1

݂Oscillation frequency in hertz

߮Initial phase in radians

ܶSampling time in seconds

F(z) Auxiliary polynomial

θnz Normalized transformed ECG

Ynz Normalized ECG vector

N* Normalization period

Hnz Normalized impulse response matrix

Unz Normalization Left singular vector matrix

B Inverse of H

Ere Residual error energy

skew Third order central moment Kurt Fourth order central moment xi ith feature element


xxi ݔො Normalized ith feature element V loss function

K Kernel function

f* Regularization solution ԡ݂ԡ Norm in the Hilbert space I Identity Matrix

c Closed form solution xt Testing point





Cardiovascular Diseases (CVDs) are the leading causes of death in the world, where more than 80% of these cases are found in developing countries (Goldberger et al., 2000). This leading position will last for the next thirty years as forecasted by the World Health Organization (WHO) (Organization, 2012). In terms of numbers, CVDs claimed the lives of about 17.3 million of the world population (i.e., 30% of the global deaths) in 2008. In addition, the estimated economical cost of heart related diseases in the United States only was about 316.4 us $ billion in 2010. This cost covers health care services, medications and decrease in productivity (Frieden, 2010). For accurate and early-on assessing of different cardiac diseases Electrocardiogram (ECG) is a crucial non-invasive diagnostic tool. Abnormalities in both electrical generation and conduction at different levels in the heart are reflected on the surface ECG as deviations from the normal heart rhythm. The term arrhythmia is used to refer to these deviations (Cliffordet al., 2006).

In general, the main challenge in developing countries is due to an inadequate number of physicians who are able to read and analyze ECG signal particularly in rural areas. In developed countries, on the other hand, the increasing number of patients in Intensive Care Units (ICU) and the large amount of data recorded by the Holter monitors make it almost unfeasible for the physicians to manually analyze all the acquired data (Goldberger et al., 2000). One of the engineering solutions for the mentioned problem is applying machine learning techniques.



Machine Learning (ML), provides an automatic and low cost analysis of ECG data, which can assist the human being. Such analysis can reveal hidden information that is crucial for final decision. The fast development in ML algorithms and the possibility of extraction of discriminative and stable features using signal processing techniques give rooms to improve on the current state-of-the-art. Consequently, the possibility to save many lives if heart abnormalities are detected early-on and accurately is garanteed.

Generally, learning algorithms can be grouped into two main categories. In the first, supervised learning, it is assumed that a set of training data is available, and the classifier is designed by exploiting this apriori known information (Chazal et al., 2004; Cliffordet al., 2006; Kampouraki et al., 2009; Minamiet al., 1999; Osowskiet al., 2004). In the second category, training data of known class labels is not available.

In this type of problems, a set of feature vectors is given and the goal is to unravel the underlying similarities and cluster (group) “similar” vectors together. This is known as

unsupervised pattern recognition, unsupervised learning or clustering (Franciscoet al., 2007; Khawaja, 2006; Sotelo, 2010). With the increase of the number of abnormalities the clustering task becomes more challenging with unsupervised learning methods.

One of the most promising algorithms for supervised learning is the Regularized Least Squares Classifier (RLSC). This algorithm has shown to perform as accurately as Support Vector Machine (SVM) with some advantages in terms of reduced computational complexity and memory requirements when applied with linear kernel (Rifkin, 2002).

Parametric modeling of the ECG signal serves to reduce the size of the data for real-time transmission and to provide features for signals classification. However, by applying parametric modeling techniques only intersamples (intrabeat) redundancy is



exploited. Interbeats redundancy manifested by the quasi-periodicity of the ECG signal can be exploited by adopting Two-Dimensional (2D) image compression algorithms which are more suitable for storage purposes.


Usually a large amount of ECG data is recorded from each patient (about 100,000 heartbeats daily), hence there is a need to store and retrieve these data efficiently for further consultation. Furthermore, some special applications of telemedicine, where consultation between medical specialists in different locations is conducted in real- time, need a compact representation of the ECG signal. This compact representation of the signal helps to reduce the time and the cost of transmission through telecommunication networks. Examples of these applications include transmissions initiated from an ambulance or a patient's home to the hospital for early diagnosis.

The ability of signal processing techniques to detect and classify automatically and rapidly the large amount of data generated by the Holter monitor at low cost when compared to manual analysis has brought the interest of many researchers in the last decades to develop new algorithms for automatic ECG monitoring.

Each of these research problems are discussed more specifically as follows:

a) Lack of efficient modeling techniques for ECG signals. Existing techniques fail to bring acceptable signal reconstruction for clinical evaluation in many cases due to the fact that they are based on symmetry assumptions or due to the large variety in the morphology of the ECG within and across patients (Osowski and Linh, 2001). The assumptions of the symmetry of the ECG waves are suitable to model normal and some



pathological rhythms but they do not hold for abnormal rhythms which are clinically more important.

b) The best way for ECG period normalization still posses some challenges.

Due to the capability of 2D ECG compression algorithms to exploit further the redundancy in the signal when compared to 1D compression algorithms and to yield better compression ratios, an extensive research effort has been devoted to their development in recent years. In 2D ECG compression, the beats of differing periods should be equalized to the same period length using different techniques. These techniques can be classified into two main categories, namely signal extension and period normalization techniques. Unlike signal extension, period normalization techniques are lossy. However, the latter produce a lower Percent Root mean square Difference (PRD) as compared to the former when used with 2D ECG coder (Chou et al., 2006). This outperformance is justified by the fact that period normalization provides higher inter-beat correlations compared to signal extension. The main problem of the widely used period normalization technique for ECG signals introduced by Wei et al is that it cannot process extremely irregular ECG very well (Wei et al., 2001). This problem has been observed and documented by (Chou et al., 2006).

Sampling Rate Conversion (SRC) in the frequency domain using sinusoidal transforms (Discrete Fourier Transform (DFT) or Discrete Cosine Transform (DCT)), has not received sufficient attention from the research community in the past and have not been considered for ECG signals period normalization. However, recently Bi and Mitra have shown the merits of this approach in terms of lower computational complexity



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