Semi-Blind Source Separation for fetal ECG extraction

Contents 
 
VI 
 
CONTENTS 
Acknowledgments --------------------------------------------------------------------------------------- I 
Sommario -------------------------------------------------------------------------------------------------- II 
Abstract---------------------------------------------------------------------------------------------------- V 
Contents --------------------------------------------------------------------------------------------------- VI 
List of Figures -------------------------------------------------------------------------------------------- IX 
Glossary -------------------------------------------------------------------------------------------------- XII 
1 Introduction ----------------------------------------------------------------------------------------- 1 
2 Fetal Monitoring ----------------------------------------------------------------------------------- 3 
2.1 A Brief History ------------------------------------------------------------------------------------------ 3 
2.2 Monitoring Techniques ------------------------------------------------------------------------------ 4 
2.3 Fetal Electrocardiography --------------------------------------------------------------------------- 6 
2.3.1 Electrocardiogram---------------------------------------------------------------------------------------------- 6 
2.3.1.1 ST Segment: Oxygen deficiency -------------------------------------------------------------------- 8 
2.3.2 The most important Invasive and Noninvasive Techniques --------------------------------------- 12 
2.3.2.1 Invasive: Internal Monitoring ---------------------------------------------------------------------- 12 
2.3.2.2 Noninvasive: External Monitoring (AECG) ------------------------------------------------------ 12 
2.3.3 Interfaces and Noise affecting the fECG Signal -------------------------------------------------------- 13 
2.3.4 Electrode position --------------------------------------------------------------------------------------------- 16 
3 Comparison of fECG Extraction Methods -------------------------------------------------- 22 
3.1 Past research ----------------------------------------------------------------------------------------- 22 
3.2 Adaptive filtering ------------------------------------------------------------------------------------ 23 
3.2.1 Least Mean Squares (LMS) adaptive filter -------------------------------------------------------------- 25 
3.2.2 Artificial Intelligence (AI) ------------------------------------------------------------------------------------ 26 
3.2.2.1 FIR Neural Network ----------------------------------------------------------------------------------- 27 
3.2.2.2 Dynamic neural network ---------------------------------------------------------------------------- 27 
3.3 Orthogonal basis function------------------------------------------------------------------------- 29 
3.4 Subtraction of an average pattern -------------------------------------------------------------- 30

Contents 
 
VII 
 
3.5 State space projection ----------------------------------------------------------------------------- 34 
3.6 Wavelet Transform (WT) -------------------------------------------------------------------------- 37 
3.7 Temporal structure --------------------------------------------------------------------------------- 40 
3.8 Polynomial networks ------------------------------------------------------------------------------- 42 
3.9 Independent Component Analysis (ICA) ------------------------------------------------------ 44 
4 Independent Component Analysis for Extraction of fECG ----------------------------- 52 
4.1 Cocktail party problem ----------------------------------------------------------------------------- 52 
4.2 Principal Component Analysis (PCA): Second-order approach -------------------------- 55 
4.2.1 PCA by variance maximization ----------------------------------------------------------------------------- 55 
4.2.2 Singular Value Decomposition (SVD) --------------------------------------------------------------------- 58 
4.3 Independent Component Analysis (ICA): High-order approach ------------------------ 60 
4.3.1 Restrictions in ICA --------------------------------------------------------------------------------------------- 60 
4.3.2 Ambiguities of ICA --------------------------------------------------------------------------------------------- 62 
4.3.3 Preprocessing for ICA ---------------------------------------------------------------------------------------- 63 
4.3.3.1 Centering the variables ------------------------------------------------------------------------------ 63 
4.3.3.2 Uncorrelatedness and Whitening ----------------------------------------------------------------- 63 
4.3.4 Gaussian variables are forbidden ------------------------------------------------------------------------- 65 
4.3.5 Measuring of nongaussianity ------------------------------------------------------------------------------ 66 
4.3.5.1 Kurtosis --------------------------------------------------------------------------------------------------- 68 
4.3.5.2 Negentropy --------------------------------------------------------------------------------------------- 69 
4.3.6 ICA Algorithms ------------------------------------------------------------------------------------------------- 71 
4.3.6.1 Comon’s -------------------------------------------------------------------------------------------------- 71 
4.3.6.2 Joint Approximate Diagonalization of Eigenmatrices (JADE) ------------------------------ 72 
4.3.6.3 Information maximization (Infomax) ------------------------------------------------------------ 73 
4.3.6.4 Fixed Point ICA (FastICA) ---------------------------------------------------------------------------- 74 
4.3.6.5 Cumulant Based Independent Component Analysis (CuBICA) ---------------------------- 75 
4.3.6.6 Minimum Renyi’s Mutual Information (MeRMaId) ------------------------------------------ 76 
5 Semi-Blind Source Separation Approach -------------------------------------------------- 78 
5.1 Problem description -------------------------------------------------------------------------------- 78 
5.2 ICA algorithms ---------------------------------------------------------------------------------------- 79 
5.2.1 FastICA algorithm implementation ----------------------------------------------------------------------- 79 
5.2.2 JADE algorithm implementation -------------------------------------------------------------------------- 79

Contents 
 
VIII 
 
5.3 ICA without pre-filtering --------------------------------------------------------------------------- 80 
5.3.1 First case: 39
th
 week ------------------------------------------------------------------------------------------ 81 
5.4 ICA with pre-filtering ------------------------------------------------------------------------------- 85 
5.4.1 Filtering ---------------------------------------------------------------------------------------------------------- 85 
5.4.1.1 Notch Filter --------------------------------------------------------------------------------------------- 86 
5.4.1.2 Low Pass Filter ----------------------------------------------------------------------------------------- 94 
5.4.1.3 Baseline Wander Removal -------------------------------------------------------------------------- 95 
5.4.1.4 Maternal ECG suppression ------------------------------------------------------------------------ 100 
5.4.2 First case: 39
th
 week ---------------------------------------------------------------------------------------- 101 
5.4.3 Second case: 25
th
 week ------------------------------------------------------------------------------------ 108 
5.4.4 Third case: 30
th
 week --------------------------------------------------------------------------------------- 115 
5.5 Averaged fECG -------------------------------------------------------------------------------------- 118 
6 Conclusions and Future Works ------------------------------------------------------------- 122 
References --------------------------------------------------------------------------------------------- 125