Quantitative analysis of EEG signals: Time-frequency methods and ...

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peaks. 7.2.3 Wavelet Transform vs. conventional digital ltering The multiresolution decomposition based on the Wavelet Transform has several advantages over conventional digital ltering based on the Fourier Transform (ideal lters). Moreover, due to the fact that the multiresolution decomposition method is implemented as a ltering scheme, it can be seen as a way to construct lters with an optimal time-frequency resolution. An important pointtobementioned is that the multiresolution decomposition has a powerful mathematical background in fact, it can be seen as a sequence of correlations between the original signal and dilatations and translations of a single \mother function" (and its complementary function, see section x4.2.3). Furthermore, the optimal mother function to be applied to a certain signal can be chosen based on its mathematical properties or just based on visual features that can be more or less suitable for the analysis of a certain signal (see sec. 4.2.4). Since wavelets have a varying window size adapted to each frequency range, the \ltering" of some frequency bands does not aect the morphology of the others. For example, it is well known that when ltering with Fourier based lters the high frequencies of the EEG, the morphology of the low frequencies is also aected (e.g. in the case of a recording of an epileptic seizure, the shape of the spikes can be modied, thus obscuring important details). Moreover, in the case of ERPs, the use of a method based in wavelets avoids unwanted eects as \ringing" (i.e. the spurious appearance of an stimulus related amplitude enhancement previous to stimulation). In general, it can be stated that the Fourier based ltering gives a more smooth signal than the one obtained by using the multiresolution decomposition due to the nearly optimal time-frequency resolution of the Wavelet Transform for every scale. In order to exemplify these advantages, in section 4.5.2 I showed with some selected sweeps how the multiresolution decomposition implemented with B-Spline functions leads to a better resolution of the event-related responses in comparison with an \ideal lter". Another interesting point is that the multiresolution decomposition gives discrete coecients, thus making very easy the design and implementation of statistical tests. Similar type of analysis are more dicult to implement from digitally ltered signals. In this respect, the straightforward implementation of statistical tests plus the high time-frequency resolution of wavelets could be critical for obtaining signicant results as showed for example in the analysis of ERPs (see sec. x4.5 and x4.6). 107
7.2.4 Chaos analysis vs. time-frequency methods (Gabor, Wavelets) Since all the time-frequency methods described in this thesis are linear, due to the very complex non linear nature of EEG signals, a non-linear analysis as the one performed with the methods of Chaos theory could give new information, an alternative way of visualization, or at least a new way ofquantication. Moreover, Chaos analysis can put constraints to the system, thus helping in making models. It can also give a useful way of data reduction, this for example being very useful for calculating cross-correlations between dierent EEG channels. However, since these methods have several prerequisites such as stationarity, small amount of noise, long data recordings, etc., they are very dicult to implement in the case of EEG signals and their results should be taken as relative values. In this respect, the validity of Chaos analysis for discriminating between a random or deterministic nature of EEG signals is subject to several criticisms as I described in section x7.1.3. Up to now, parameters such as the D 2 , 1 , etc., characterized general properties of the EEG, such as the complexity or chaoticity of the brain in dierent states and pathologies. However, the conclusions reached with these methods are still very vague in comparison with more precise conjectures about physiological processes accessed with time-frequency analysis, as described for example in section x7.1.1 in the analysis of epileptic seizures. In this respect, physiological interpretation from results obtained with time-frequency methods is very useful due to the relation of dierent brain oscillations with sources, functions and pathologies of the brain. Moreover, in many cases results reported with Chaos methods are easily visualized in the EEG or with other more simple methods. Then, it is reasonable to check if the results obtained with this approach are in fact new, by comparing them with traditional methods as simple correlations, Fourier analysis or the time-frequency methods described in this thesis. Despite all these diculties, new methods based on Chaos theory should be implemented in the analysis of EEG signals, this approach still being very promising for \visualizing" dynamical properties of the EEG that keep obscure to the linear methods. 7.2.5 Wavelet-entropy vs. frequency analysis Wavelet-entropy gives new information about EEG signals in comparison with the one obtained by using frequency analysis or other standard methods. In fact, I showed that WS is independent of the amplitude or energy of the signal. Instead of giving an amplitude measurement, the WS shows how the energy is distributed in the dierent frequency bands (see section x6.3.2). WS gives a measure of the \order" of the signal, i.e. signals characterized by narrow peaks in the frequency domain are more ordered than 108
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Quantitative analysis of EEG signal
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1. Berichterstatter: Prof. Dr.-Ing.
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an okzipitalen Positionen und (c) d
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To my family: Mama, Consuelo, Hugui
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Preface In this work, I will descri
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I would certainly like to remember
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Contents Zusammenfassung Preface Ac
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5.2.6 Calculating Lyapunov Exponent
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Summary Since the rsts recordings i
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1 Outline of Neurophysiology: Brain
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Figure 2: Normal 20 channels (10-20
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1.1.2 EEG in Epilepsy One important
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Figure 3: Scalp EEG of 18 channels
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Figure 4: Averaged responses upon N
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2 Fourier Transform 2.1 Introductio
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I xx (k) =jX(k)j 2 = X(k) X (k) (
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17 Figure 5: Topographical mapping
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1987) is that coherence gives the c
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3 Gabor Transform (Short Time Fouri
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where k g D k= R 1 ;1 jg D(t 0 )j 2
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and the band maximum peak frequency
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Figure 7: Intracraneal seizure reco
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Figure 10: Mean (soft line) and max
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EEG as the one with least amount of
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Figure 11: Scalp EEG of the right c
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3.5 Conclusion In this chapter I de
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Original signal FOURIER TRANSFORM G
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4.2.3 Multiresolution Analysis Cont
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Original signal -15 0 15 -1sec 0 1s
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4.2.5 Wavelet Packets In the approa
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marked decrease in computational ti
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ain activity during an epileptic se
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3 2 3 3 3 3.2 Hz 3.6 Hz 4.0 Hz 4.4
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Silva et al.,1973a,1973b Lopes da S
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sweep #1 sweep #2 sweep #3 sweep #4
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VEP non-target target F3 F4 F3 F4 F
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Page 76 and 77: Electrode F3 F4 Cz P3 P4 O1 O2 Dela
Page 78 and 79: In conclusion, our results point to
Page 80 and 81: 63 Figure 22: Gamma responses for a
Page 82 and 83: Figure 24: T-test comparison of the
Page 84 and 85: wavelet coecients allowed an easy d
Page 86 and 87: the position vs. the linear momentu
Page 88 and 89: unknown topology it is necessary to
Page 90 and 91: the sum of the positive exponents (
Page 92 and 93: performed. On one hand, must be lar
Page 94 and 95: Duke (1992) and Elbert et al. (1994
Page 96 and 97: agation time. They applied this pro
Page 98 and 99: Figure 28: Histogram for the EEG da
Page 100 and 101: Figure 29: Attractors corresponding
Page 102 and 103: able for automatic detection proces
Page 104 and 105: ENTROPY Thermodynamics Signal analy
Page 106 and 107: 6.3 Application to visual event-rel
Page 108 and 109: VEP Non Target Target F3 -20 -10 0
Page 110 and 111: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 112 and 113: 1 VEP NON-TARGET TARGET 1 1 F3 F3 0
Page 114 and 115: and the Lorenz equations (a model o
Page 116 and 117: P300 deection. Due to the relation
Page 118 and 119: 7 General Discussion In this chapte
Page 120 and 121: Wavelet analysis was also applied t
Page 122 and 123: aect the whole spectrum and for thi
Page 126 and 127: the ones having wide peaks (being t
Page 128 and 129: A Time-frequency resolution and the
Page 130 and 131: Z 1 ;1 tx(t) d dt x(t) dt = 1 2 Z 1
Page 132 and 133: Figure 37: Time-frequency resolutio
Page 134 and 135: References Abarbanel HDI, Brown R,
Page 136 and 137: Berger, H. Uber das Elektrenkephalo
Page 138 and 139: Gastaut H and Broughton R. Epilepti
Page 140 and 141: Lopes da Silva FH, van Lierop THMT,
Page 142 and 143: Pradhan N, Sadasivan P, Chatterji S
Page 144 and 145: Serrano E, Ph.D. Thesis, Department
Page 146: Biographical sketch 21.03.1967 born
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