P.J. Durka Matching Pursuit and Unification in EEG Analysis Table of Contents

Foreword	ix
Preface	xi
I Some Basic Notions	1
Chapter 1 Signal: Going Digital	3
1.1 Sampling	4
1.2 Drawback: Aliasing	5
1.3 Advantage: Checksums	8
Chapter 2 Analysis	11
2.1 Inner Product—A Measure of Fit	15
2.2 Orthogonality	15
2.3 Frequency and Phase	16
Chapter 3 Spectrum	19
3.1 Example Calculations	21
3.2 Uncertainty Principle and Resolution	25
3.3 Real-World Spectra	26
Chapter 4 Between Time and Frequency	29
4.1 Spectrogram	29
4.2 Interpretation of the Spectrogram	32
4.3 Wavelets	33
4.4 Wigner Transform and Cross-Terms	35
References	38
Chapter 5 Choosing the Representation	39
5.1 Gabor Dictionary	39
5.2 Adaptive Approximation	41
5.3 Matching Pursuit	43
5.4 Time-Frequency Energy Density	44
References	46
Chapter 6 Advantages of Adaptive Approximations	47
6.1 Explicit Parameterization of Transients	47
6.2 Automatic Negotiation of Time-Frequency Tradeoff	50
6.3 Freedom from Arbitrary Settings	52
6.4 A Unified Framework	53
Chapter 7 Caveats and Practical Issues	55
7.1 Dictionary Density	55
7.2 Number of Waveforms in the Expansion	57
7.3 Statistical Bias	58
7.4 Limitations of Gabor Dictionaries	59
References	60
II EEG Analysis	61
Chapter 8 Parameterization of EEG Transients	63
8.1 Selecting Relevant Structures	66
8.2 Sleep Spindles and Slow Waves	68
8.3 Real-World Problems	72
8.4 Hypnogram and Continuous Description of Sleep	75
8.5 Sensitivity to Phase and Frequency	77
8.6 Nonoscillating Structures	79
8.7 Epileptic EEG Spikes	82
References
Chapter 9 Epileptic Seizures	87
9.1 Series of Spikes	88
9.2 Periodicity and Greedy Algorithms	89
9.3 Evolution of Seizures
9.4 Gabor Atom Density	95
References	99
Chapter 10 Event-Related Desynchronization and Synchronization	101
10.1 Conventional ERD/ERS Quantification	102
10.2 A Complete Time-Frequency Picture	104
10.3 ERD/ERS in the Time-Frequency Plane	105
10.4 Other Estimates of Signal’s Energy Density	108
References	112
Chapter 11 Selective Estimates of Energy	115
11.1 ERD/ERS Enhancement	117
11.2 Pharmaco EEG	117
References	129
Chapter 12 Spatial Localization of Cerebral Sources	131
12.1 EEG Inverse Solutions	132
12.2 Is It a Tomography?	133
12.3 Selection of Structures for Localization	134
12.4 Localization of Sleep Spindles	137
References	139
III Equations and Technical Details	141
Chapter 13 Adaptive Approximations and Matching Pursuit	143
13.1 Notation	143
13.2 Linear Expansions	144
13.3 Time-Frequency Distributions	145
13.4 Adaptive Time-Frequency Approximations	146
13.5 Matching Pursuit Algorithm	147
13.6 Orthogonalization	148
13.7 Stopping Criteria	149
13.8 Matching Pursuit with Gabor Dictionaries	151
13.9 Statistical Bias	153
13.10 MP-Based Estimate of Signal’s Energy Density	155
13.11 An Interesting Failure of the Greedy Algorithm	157
13.12 Multichannel Matching Pursuit	158
References	163
Chapter 14 Implementation: Details and Tricks	167
14.1 Optimal Phase of a Gabor Function	168
14.2 Product Update Formula	170
14.3 Sin, Cos, and Exp: Fast Calculations and Tables	170
References	172
Chapter 15 Statistical Significance of Changes in the Time-Frequency Plane	173
15.1 Reference Epoch	173
15.2 Resolution Elements	174
15.3 Statistics	175
15.4 Resampling	176
15.5 Parametric Tests	177
15.6 Correction for Multiple Comparisons	177
References	179
About the Author	181
Index	183