Biomedical Signal Analysis

Artifacts 91 3.1 Problem Statement 91 3.2 Random, Structured, and Physiological Noise 92 3.2.1 Random noise 92 3.2.2 Structured noise 98 3.2.3 Physiological interference 98 3.2.4 Stationary, nonstationary, and cyclostationary processes 99 3.3 Illustration of the Problem with Case Studies 101 3.3.1 Noise in event-related potentials 102 3.3.2 High-frequency noise in the ECG 102 3.3.3 Motion artifact in the ECG 102 3.3.4 Power-line interference in ECG signals 103 3.3.5 Maternal ECG interference in fetal ECG 105 3.3.6 Muscle-contraction interference in VAG signals 105 3.3.7 Potential solutions to the problem 106 3.4 Fundamental Concepts of Filtering 106 3.4.1 Linear shift-invariant filters and convolution 107 3.4.2 Transform-domain analysis of signals and systems 117 3.4.3 The pole-zero plot 123 3.4.4 The Fourier transform 125 3.4.5 The discrete Fourier transform 126 3.4.6 Convolution using the DFT 131 3.4.7 Properties of the Fourier transform 133 3.5 Synchronized Averaging 135 3.6 Time-domain Filters 139 3.6.1 Moving-average filters 139 3.6.2 Derivative-based operators to remove low-frequency artifacts 145 3.6.3 Various specifications of a filter 152 3.7 Frequency-domain Filters 153 3.7.1 Removal of high-frequency noise: Butterworth lowpass filters 154 3.7.2 Removal of low-frequency noise: Butterworth highpass filters 161 3.7.3 Removal of periodic artifacts: Notch and comb filters 162 3.8 Order-statistic Filters 169 3.9 The Wiener Filter 171 3.10 Adaptive Filters for Removal of Interference 180 3.10.1 The adaptive noise canceler 181 3.10.2 The least-mean-squares adaptive filter 184 3.10.3 The RLS adaptive filter 185 3.11 Selecting an Appropriate Filter 190 3.12 Application: Removal of Artifacts in ERP Signals 193 3.13 Application: Removal of Artifacts in the ECG 196 3.14 Application: Maternal-Fetal ECG 197 3.15 Application: Muscle-contraction Interference 199 3.16 Remarks 202 3.17 Study Questions and Problems 202 3.18 Laboratory Exercises and Projects 208 References 209 4 Detection of Events 213 4.1 Problem Statement 213 4.2 Illustration of the Problem with Case Studies 214 4.2.1 The P, QRS, and T waves in the ECG 214 4.2.2 The first and second heart sounds 215 4.2.3 The dicrotic notch in the carotid pulse 215 4.2.4 EEG rhythms, waves, and transients 215 4.3 Detection of Events and Waves 218 4.3.1 Derivative-based methods for QRS detection 218 4.3.2 The Pan-Tompkins algorithm for QRS detection 220 4.3.3 Detection of the P wave in the ECG 224 4.3.4 Detection of the T wave in the ECG 226 4.3.5 Detection of the dicrotic notch 228 4.4 Correlation Analysis of EEG Rhythms 228 4.4.1 Detection of EEG rhythms 228 4.4.2 Template matching for EEG spike-and-wave detection 231 4.4.3 Detection of EEG rhythms related to seizure 234 4.5 Cross-spectral Techniques 235 4.5.1 Coherence analysis of EEG channels 235 4.6 The Matched Filter 237 4.6.1 Derivation of the transfer function of the matched filter 237 4.6.2 Detection of EEG spike-and-wave complexes 241 4.7 Homomorphic Filtering 242 4.7.1 Generalized linear filtering 244 4.7.2 Homomorphic deconvolution 244 4.7.3 Extraction of the vocal-tract response 245 4.8 Application: ECG Rhythm Analysis 253 4.9 Application: Identification of Heart Sounds 254 4.10 Application: Detection of the Aortic Component of S 2 256 4.11 Remarks 259 4.12 Study Questions and Problems 259 4.13 Laboratory Exercises and Projects 261 References 262 5 Analysis of Waveshape and Waveform Complexity 267 5.1 Problem Statement 267 5.2 Illustration of the Problem with Case Studies 268 5.2.1 The QRS complex in the case of bundle-branch block 268 5.2.2 The effect of myocardial ischemia on QRS waveshape 268 5.2.3 Ectopic beats 268 5.2.4 Complexity of the EMG interference pattern 268 5.2.5 PCG intensity patterns 269 5.3 Analysis of ERPs 269 5.4 Morphological Analysis of ECG Waves 269 5.4.1 Correlation coefficient 270 5.4.2 The minimum-phase correspondent and signal length 270 5.4.3 ECG waveform analysis 274 5.5 Envelope Extraction and Analysis 277 5.5.1 Amplitude demodulation 278 5.5.2 Synchronized averaging of PCG envelopes 280 5.5.3 The envelogram 281 5.6 Analysis of Activity 283 5.6.1 The RMS value 283 5.6.2 Zero-crossing rate 285 5.6.3 Turns count 285 5.6.4 Form factor 286 5.7 Application: Normal and Ectopic ECG Beats 287 5.8 Application: Analysis of Exercise ECG 288 5.9 Application: Analysis of the EMG in Relation to Force 290 5.10 Application: Analysis of Respiration 292 5.11 Application: Correlates of Muscular Contraction 294 5.12 Application: Statistical Analysis of VAG Signals 295 5.12.1 Acquisition of knee-joint VAG signals 297 5.12.2 Estimation of the PDFs of VAG signals 297 5.12.3 Screening of VAG signals using statistical parameters 299 5.13 Application: Fractal Analysis of the EMG in Relation to Force 302 5.13.1 Fractals in nature 302 5.13.2 Fractal dimension 303 5.13.3 Fractal analysis of physiological signals 304 5.13.4 Fractal analysis of EMG signals 305 5.14 Remarks 306 5.15 Study Questions and Problems 307 5.16 Laboratory Exercises and Projects 309 References 310 6 Frequency-domain Characterization of Signals and Systems 317 6.1 Problem Statement 318 6.2 Illustration of the Problem with Case Studies 318 6.2.1 The effect of myocardial elasticity on heart sound spectra 318 6.2.2 Frequency analysis of murmurs to diagnose valvular defects 319 6.3 Estimation of the PSD 321 6.3.1 Considerations in the computation of the ACF 321 6.3.2 The periodogram 323 6.3.3 The need for averaging PSDs 325 6.3.4 The use of windows: spectral resolution and leakage 326 6.3.5 Estimation of the ACF from the PSD 330 6.3.6 Synchronized averaging of PCG spectra 331 6.4 Measures Derived from PSDs 333 6.4.1 Moments of PSD functions 334 6.4.2 Spectral power ratios 337 6.5 Application: Evaluation of Prosthetic Heart Valves 337 6.6 Application: Fractal Analysis of VAG Signals 339 6.6.1 Fractals and the 1/f model 339 6.6.2 F D via power spectral analysis 341 6.6.3 Examples of synthesized fractal signals 341 6.6.4 Fractal analysis of segments of VAG signals 342 6.7 Application: Spectral Analysis of EEG Signals 345 6.8 Remarks 349 6.9 Study Questions and Problems 350 6.10 Laboratory Exercises and Projects 351 References 353 7 Modeling of Biomedical Signal-generating Processes and Systems 357 7.1 Problem Statement 357 7.2 Illustration of the Problem 358 7.2.1 Motor-unit firing patterns 358 7.2.2 Cardiac rhythm 358 7.2.3 Formants and pitch in speech 359 7.2.4 Patellofemoral crepitus 360 7.3 Point Processes 360 7.4 Parametric System Modeling 365 7.5 Autoregressive or All-pole Modeling 369 7.5.1 Spectral matching and parameterization 374 7.5.2 Optimal model order 377 7.5.3 AR and cepstral coefficients 384 7.6 Pole-Zero Modeling 384 7.6.1 Sequential estimation of poles and zeros 387 7.6.2 Iterative system identification 389 7.6.3 Homomorphic prediction and modeling 393 7.7 Electromechanical Models of Signal Generation 395 7.7.1 Modeling of respiratory sounds 396 7.7.2 Modeling sound generation in coronary arteries 400 7.7.3 Modeling sound generation in knee joints 402 7.8 Electrophysiological Models of the Heart 404 7.8.1 Electrophysiological modeling at the cellular level 405 7.8.2 Electrophysiological modeling at the tissue and organ levels 410 7.8.3 Extensions to the models of the heart 412 7.8.4 Challenges and future considerations in modeling the heart 414 7.9 Application: Heart-rate Variability 416 7.10 Application: Spectral Modeling and Analysis of PCG Signals 418 7.11 Application: Coronary Artery Disease 421 7.12 Remarks 423 7.13 Study Questions and Problems 424 7.14 Laboratory Exercises and Projects 425 References 426 8 Adaptive Analysis of Nonstationary Signals 431 8.1 Problem Statement 432 8.2 Illustration of the Problem with Case Studies 432 8.2.1 Heart sounds and murmurs 432 8.2.2 EEG rhythms and waves 433 8.2.3 Articular cartilage damage and knee-joint vibration 433 8.3 Time-variant Systems 435 8.3.1 Characterization of nonstationary signals and dynamic systems 436 8.4 Fixed Segmentation 438 8.4.1 The short-time Fourier transform 438 8.4.2 Considerations in short-time analysis 441 8.5 Adaptive Segmentation 445 8.5.1 Spectral error measure 445 8.5.2 ACF distance 450 8.5.3 The generalized likelihood ratio 450 8.5.4 Comparative analysis of the ACF, SEM, and GLR methods 452 8.6 Use of Adaptive Filters for Segmentation 452 8.6.1 Monitoring the RLS filter 453 8.6.2 The RLS lattice filter 456 8.7 The Kalman Filter 463 8.8 Wavelet Analysis 474 8.8.1 Approximation of a signal using wavelets 474 8.9 Bilinear TFDs 479 8.10 Application: Adaptive Segmentation of EEG Signals 485 8.11 Application: Adaptive Segmentation of PCG Signals 489 8.12 Application: Time-varying Analysis of HRV 490 8.13 Application: Analysis of Crying Sounds of Infants 493 8.14 Application: Wavelet Denoising of PPG Signals 493 8.15 Application: Wavelet Analysis for CPR Studies 494 8.16 Application: Detection of Ventricular Fibrillation in ECG Signals 499 8.17 Application: Detection of Epileptic Seizures in EEG Signals 503 8.18 Application: Neural Decoding for Control of Prostheses 505 8.19 Remarks 506 8.20 Study Questions and Problems 507 8.21 Laboratory Exercises and Projects 507 References 508 9 Signal Analysis via Adaptive Decomposition 515 9.1 Problem Statement 517 9.2 Illustration of the Problem with Case Studies 517 9.2.1 Separation of the fetal ECG from a single-channel abdominal Ecg 517 9.2.2 Patient-specific EEG channel selection for BCI applications 518 9.2.3 Detection of microvolt T-wave alternans in long-term ECG recordings 518 9.3 Matching Pursuit 518 9.4 Empirical Mode Decomposition 520 9.4.1 Variants of empirical mode decomposition 521 9.5 Dictionary Learning 523 9.6 Decomposition-based Adaptive TFD 525 9.7 Separation of Mixtures of Signals 531 9.7.1 Principal component analysis 533 9.7.2 Independent component analysis 539 9.7.3 Nonnegative matrix factorization 542 9.7.4 Comparison of PCA, ICA, and NMF 546 9.8 Application: Detection of Epileptic Seizures Using Dictionary Learning Methods 553 9.9 Application: Adaptive Time-Frequency Analysis of VAG Signals 560 9.10 Application: Detection of T-wave Alternans in ECG Signals 568 9.11 Application: Extraction of the Fetal ECG from Single-channel Maternal ECG 572 9.12 Application: EEG Analysis for Brain-Computer Interfaces 577 9.12.1 NMF-based channel selection 579 9.12.2 Feature extraction 579 9.13 Remarks 586 9.14 Study Questions and Problems 586 9.15 Laboratory Exercises and Projects 586 References 587 10 Computer-aided Diagnosis and Healthcare 595 10.1 Problem Statement 596 10.2 Illustration of the Problem with Case Studies 596 10.2.1 Diagnosis of bundle-branch block 596 10.2.2 Normal or ectopic ECG beat? 597 10.2.3 Is there an alpha rhythm? 598 10.2.4 Is a murmur present? 598 10.2.5 Detection of sleep apnea using multimodal biomedical signals 598 10.3 Pattern Classification 599 10.4 Supervised Pattern Classification 600 10.4.1 Discriminant and decision functions 600 10.4.2 Fisher linear discriminant analysis 601 10.4.3 Distance functions 605 10.4.4 The nearest-neighbor rule 605 10.4.5 The support vector machine 606 10.5 Unsupervised Pattern Classification 607 10.5.1 Cluster-seeking methods 607 10.6 Probabilistic Models and Statistical Decision 611 10.6.1 Likelihood functions and statistical decision 611 10.6.2 Bayes classifier for normal patterns 613 10.7 Logistic Regression Analysis 614 10.8 Neural Networks 615 10.8.1 ANNs with radial basis functions 617 10.8.2 Deep learning 620 10.9 Measures of Diagnostic Accuracy and Cost 620 10.9.1 Receiver operating characteristics 623 10.9.2 McNemar's test of symmetry 625 10.10 Reliability of Features, Classifiers, and Decisions 627 10.10.1 Separability of features 628 10.10.2 Feature selection 630 10.10.3 The training and test steps 631 10.11 Application: Normal versus Ectopic ECG Beats 633 10.11.1 Classification with a linear discriminant function 633 10.11.2 Application of the Bayes classifier 637 10.11.3 Classification using the K-means method 637 10.12 Application: Detection of Knee-joint Cartilage Pathology 637 10.13 Application: Detection of Sleep Apnea 644 10.14 Application: Monitoring Parkinson's Disease Using Multimodal Signal Analysis 647 10.15 Strengths and Limitations of CAD 650 10.16 Remarks 656 10.17 Study Questions and Problems 657 10.18 Laboratory Exercises and Projects 658 References 659 Index 665