Wavelet Variance Analysis of EEG Based on Window Function

CHINESE J. BIOMED. ENG. VOL.23 NO.2, JUN.2014Wavelet V ariance Analysis of EEG Based on Window FunctionZHENG Yuan-zhuang, YOU Rong-yi .School of Science, Jimei University, Fuyjian Province, X iamen 361021, Fuyjian Province, ChinaAbstract. A new wavelet variance analysis method based on window function is .proposed to investigate the dynamical features of electroencephalogram (EEG).The ex-prienmental results show that the wavelet energy of epileptic EEGs are more discretethan normal EEGs, and the variation of wavelet variance is different between epilepticand normal EEGs with the increase of time-window width. Furthermore, it is found thatthe wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normalEEGs.Key words: wavelet variance; EEG; wavelet subband entropy (WSE); windowfunctionINTRODUCTIONSince non-linear dynamics properties of EEG were generally accepted by many people, non-lineardynamics methods have been widely applied for EEG analysis, such as correlation dimension, thlargest Lyapunov exponent, approximate entropy, etc. In these methods, some non -linear parametersare used to identify diverse EEGs, which can effectively reflect the dynamical features of EEG in thestates of schizophrenia,depression and epilepsy!". However, these methods are only suitable for station-ary signal, which would probably need a great amount of experimental data and computation. There-fore, it is difficult for dynamical analysis of EEG.Generally, the EEG signals are mutational or non -stationary with highly irregular and clusteredfluctuations. People are usually more interested in the exact location of the frequency mutation thanthe amplitude details in the time window as the frequency details can be better to reflect the dynami-cal behavior of EEG; in other words, the characteristics of signal should be expressed in both time do-mian and frequency domain. W avelet transform has the characteristics of multi -resolution analysis andlocalized analysis, which can be used for time -frequency localization. The result of wavelet transformis the decomposition coefficient at each scale, which carries a wealth of detailed information of signals.In recent years, some researchers suggested that both the wavelet variance and wavelet entropy are moresuitalble for reflecting the characteristics of EEGR-4. In the present paper, a new wavelet variance anal-中国煤化工CLC number: R 318.08 Document code:A Article ID: 1004-0552(2014)02- -0054-06Grant sponsor: Natural Science Foundatoin of Fujian Province of China; grant number: 2012J0128.MYHCNMHGCorresponding author: YOU Rong -yi. E- -mail: ryyou@jmu.edu.cnReceived 10 January 2014; revised 16 June 2014-54-Chinese Journal of Biomedical Engineering (English Edition) V olume 23 Number 2, June 2014ysis method based on window function is proposed for studying the dynamical features of EEGs in bothepileptic and normal states.WA VELET VARIANCE AND WAVELET SUBBAND ENTROPY OF EEGThe wavelet varianceIn probability theory and statistics, variance measures how far a set of numbers is spread out.Thewavelet variance is a significantly characteristic index in multi -resolution analysis, which decomposesthe variance of a time series into several components associated with different scales. The waveletvariance can measure the discrete level of signals at different scales.The discrete wavelet transform (DWT) of a signal f(t) ∈L?(R) is defined as Equation (1):c{(k)= | f(),()dt(1)where ψ,()=2° ψ(2j-h) is the wavelet family. According to Parseval's theorem, the wavelet transformon the basis of orthogonal wavelet has the property of energy conservation. Then, the wavelet energy atresolution level j is approximated by the wavelet coefficients as Equation (2):E;=E |()2.The wavelet variance at resolution level j is defined as Equation (3)5-6:V}= vr{c{(k)}(3)so the wavelet variance at resolution level j can be estimated by Equation (4):VF=σ=H 2 lc()(4)The wavelet variance is generally regarded as an effective substitution for the sample varaiance ofstochastic process. From Equation (2) and (4), we can see that the wavelet variance is the average en-ergy at one wavelet scale. Therefore, the wavelet variance measures how far the number betweenwavelet energy and their expected values is spread out.The wavelet subband entropyWith regard to a given signal f(),wavelet coefficients c() at each scale j are squared and normal-ized according to Equation (5)7:C;(n)=-c(m)}2(5)Zc(m}where c; is the cofficient at scale j, is the number of coefficients at scale j. Then the wavelet subbandentropy (WSE) is computed according to Shannon entropy theory as Equation (6): .中国煤化工WSE:log(N)MHCNMHG(6)-55一CHINESE J. BIOMED. ENG. VOL.23 NO.2, JUN.2014Equation (5) enhances the contribution of high-amplitude signal values in relation to lower-amplitudesignal values, so that the WSE is more sensitive to the characteristics of brain activity.ANALYSIS OF EEG BASED ON WINDOW FUNCTIONIn light of the definition of wavelet variance and WSE, the calculation of wavelet variance and theWSE are based on the energy distribution in wavelet sub-bands, so that the estimation of wavelet en-ergy distribution plays an important role in the calculation. In essence, the calculation of the waveletenergy distribution is similar to the W elch approach, which is usually used to calculate spectrum inthe frequency domain by FFTB8-91. For Welch spectrum estimation, a signal is usually segmented andwindowed with some functions such as Hamming, Blackman, etc. Then all individual segment's spectraare averaged to obtain a more reliable and smooth spectrum estimation. However, without a windowsmoothing strategy, so this estimation will be easily affected by noise, artifacts, eventually leading to anunstable calculation of wavelet variance spectrum and WSE. Furthermore, EEG data is almost alwayscontaminated by some artifacts which is not only generated by the body (such as eye-induced artifacts,ECG artifacts, EMG- -induced artifacts,etc),but also originated from outside the body (such as movementby the patient,or even just settling the electrodes,ect)l.Therefore, such a procedure can be improvedby adding to an additional windowing and smoothing technique to calculate the wavelet energy distri-bution. The window wavelet variance and the wavelet subband approach can be realized as follows:1) Initialization. Define the window W (t), set i=0, M=1; the window size N; overlapping ratio be-tween two adjacent windows to be r(r<1.0).2) Apply window function to EEGs f(t) included in the current window. Fr(t)=f(t) xW(t), i≤t≤i+N-1, where the Hamming window is used in the calculation.3) Decompose curent windowed segment Fw(t), i≤t≤i+N-1, where the wavelet decompositionlevel to be J, and use Equation(4) (5) (6) to calculate the corresponding wavelet variance at each scaleW(M)={V,V2,*,V} and the corresponding WSE at each scale respectively.4) Get smoothed and reliable wavelet variance, move window and update i=i+(1-r)xN, if i≤L,M=M+1 and repeat procedure 2) and 3).EXPERIMENTAL RESULTSIn the present paper, a total of 100 samples of EEG time series are recorded from epileptic sub-jects and healthy subjects by the international 10- -20 system with the sampling frequency of 173.6 Hz,12 bits A/D transformation and 0.53-40 Hz band-pass filtering.The epileptic EEGs are recorded fromthe scalp of those patients who are suffered from partial epilepsy or focal epilepsy. Fig.1 shows thetime series of a typical epileptic EEG (a) and a normal EEG (b) repectively, and Fig.2 shows the cor-responding variations of wavelet variance with the change of the time window.中国煤化工MYHCNMHG-56-Chinese Journal of Biomedical Engineering (English Edition) V olume 23 Number 2, June 2014200间)μVo-2000100200 300 400 500600700 800 900 1000100wWWWWWWW-100100 200 300 400 500 600 700 800 900 1000Fig.1 The epileptic EEG (a) and the normal EEG (b)From Fig.2， we can see that the wavelet variances of normal EEG at wavelet scale j=3,4 are fargreater than the other scales. However the wavelet variances of epileptic EEG are more uniform aeach scales, this is to say that the wavelet energy of epileptic EEG is less concentrated than normalEEG. On the other hand, at each scale, the wavelet variance of epileptic EEG oscillates much fasterthan normal EEG with time evolution, and this difference is more obvious at scale j=3,4.j-2400j-3204608(100 02080Fig.2 Wavelet variance of epileptic EEGs (a) and normal EEGs (b)( corresponding to Fig.1)The wavelet subband entropy (WSE) at scale j=3,4 are computed for further analysis. Fig.3 showsthe WSE of epileptic EEG (a) and normal EEG (b) at scale j=3,4, which is corresponding to Fig.1. FromFig.3, the mean values of WSE at scale j=3,4 are 0.6931 and 0.7297 respectively for epileptic EEG,which is lower than the mean values of WSE of normal EEG (0.中国煤化工ively, whichsuggests that the epileptic EEG may be less complex than the normMHCNMHGCHINESE J. BIOMED. ENG. VOL.23 NO.2, JUN.2014average line09j=30.80.7204060100800HpwfAA~100080100Fig.3 Wavelet subband entropy (WSE) of epileptic EEGs (a) and normal EEGs (b)Clinically, the EEG activity can be divided into four frequency bands (i.e. Delta=1-4 Hz, Theta=4-8 Hz, Alpha=8-13 Hz and Beta=13-20 Hz). The normal EEGs are mainly in the Alpha and Betabands, their amplitudes usually range from 5 to 50 μV. But epileptic EEGs such as spike wave, sharpwave, spike -and -slow wave overlapping above the background activity, and their amplitudes arerelatively higher than normal EEGs, and their periods range from 20-200 ms. As shown in Fig.3, WSEof the epileptic EEG exihibits an obvious periodicity with temporal evolution, its WSE oscillatesaround its mean value, however, the normal EEGs have not these characteristics.CONCLUSION. In this paper, a new wavelet variance analysis method based on window function is proposed. Bythe original EEGs windowed with function such as Hamming, Blackman, etc, the reliable and smoothresults are obtained, and the effect of noise and artifacts are reduced. The experimental results showthat this method can distinguish the characteristics very well between epileptic EEG and normal EEG.In addition, by calculating the WSE, these characteristics are further analyzed, and the time evolutionof WSE can identify the localizations of abnormal dynamic behavior of brain activity, these conclusionsare helpful to clinical analysis of EEG.REFERENCES[1] Li Yinjie,Qiu Yihong,Zhu Yisheng. EEG analysis methods and application[M].Beijing:Science Press,2009.2] Rosso OA, Blanco S, YordanovaJ, et al. Wavelet entropy: a new tool for analysis of short duration brain electricalsignals[]. Journal of Neuroscience Methods, 2001, 105(1): 65-75.[3] Yan Shiyu, Liu Chong, W ang Hong, et al. ECoG lasification based on wavelet variancel[J]. Journal of BiomedicalEngineering, 2013, 3: 3.4] Mirzaei A, Ayatollahi A, Gifani P, et al. EEG analysis based on wavelet-spectral entropy for epileptic seizuresdetection[C]. 2010 3rd International Conference on IEEE Biomedical Engineering and Informatics (BMEI), 2010, 2:878- -882.中国煤化工[5] Pereival DB, Walden AT. Wavelet methods for time series analysis[M]. Car.MHCNMH C06.[6] LI J, KE X, GUO H. The application of wavelet variance and wavelet entropy n signal feature extraction [J]. JournalChinese Journal of Biomedical Engineering (English Edition) V olume 23 Number 2, June 2014of Xi'an University of Technology, 2007, 4: 6.[7] Sarkela MOK, Ermes MJ, van Gils MJ, et al. Quantification of epileptiform electroencephalographic activity duringsevoflurane mask induction[J]. Anesthesiology, 2007, 107(6): 928 -938.[8] Naidu PS. Modern spectrum analysis of time series[M]. CRC Press, 1996.[9] Xu P, Hu X, Yao D. Improved wavelet entropy calculation with window functions and its preliminary application tostudy intracranial pressure[J]-. Computers in biology and medicine, 2013, 43(5): 425-433.[10] Okuma T. Clinical electroencephalography[M]. Bejjing: Tsinghua University Press, 2005.NEWS●Antibodies that Better Handle HIV Could Lead to More Effective VaccinesAntibodies, also known as immunoglobulins, are incredibly specific and very good at sticking tomolecules. They are able to discriminate between molecules that vary by as little as a single atom andflag foreign or harmful ones for attack or removal by the immune system. Essentially, they serve as thebackbone of the humoral immune system. This " exquisite specificity" is important to prevent the im-mune system from mistaking healthy, human proteins and molecules from invading ones. However,when dealing with viruses and other rapidly mutating and adapting pathogens, the specificity can ren-der the immune response useless. 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