J. Biomedical Science and Engineering, 2011, 4, 341351 doi:10.4236/jbise.2011.45043 Published Online May 2011 (http://www.SciRP.org/journal/jbise/ JBiSE ). Published Online May 2011 in SciRes. http://www.scirp.org/journal/JBiSE Comparison of ICA and WT with Stransform based method for removal of ocular artifact from EEG signals Kedarnath Senapati1, Aurobinda Routray2 1Institute of Mathematics and Applications, Bhubaneswar, India; 2Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India. Email: kedar_d2@yahoo.co.in, aroutray@ee.iitkgp.ernet.in Received 11 February 2011; revised 11 March 2011; accepted 7 April 2011. ABSTRACT Ocular artifacts are most unwanted disturbance in electroencephalograph (EEG) signals. These are characterized by high amplitude but have overlap ping frequency band with the useful signal. Hence, it is difficult to remove the ocular artifacts by tradi tional filtering methods. This paper proposes a new approach of artifact removal using Stransform (ST). It provides an instantaneous timefrequency repre sentation of a timevarying signal and generates high magnitude Scoefficients at the instances of abrupt changes in the signal. A threshold function has been defined in Sdomain to detect the artifact zone in the signal. The artifact has been attenuated by a suitable multiplying factor. The major advantage of STfil tering is that the artifacts may be removed within a narrow timewindow, while preserving the frequency information at all other time points. It also preserves the absolutely referenced phase information of the signal after the removal of artifacts. Finally, a com parative study with wavelet transform (WT) and in dependent component analysis (ICA) demonstrates the effectiveness of the pr oposed approach. Keywords: EEG, Ocular Artifact; STransform; Wavelet Transform; Independent Component Analysis 1. INTRODUCTION Electroencephalogram (EEG) is the recorded electric potential from the exposed surface of the brain or from the outer surface of the head. The raw EEG data is con taminated with numerous high and low frequency noise known as artifacts. High frequency noise is a result of atmospheric thermal noise and power frequency noise. Low frequency noise is primarily caused by eye move ments, respiration and heart beats. Such artifacts are characterized by amplitude in the millivolt range (whereas the actual EEG is in microvolt range) in the frequency band of 0  16 Hz [1]. The presence of these artifacts in the raw EEG poses a major problem to researchers. Various methods to re move such artifacts have been proposed in the literature. These methods include Principal Component Analysis (PCA), Independent Component Analysis (ICA) and wavelet based thresholding. Croft and Barry [2] and Kandaswamy et al. [3] reviewed several methods of ar tifact removal. Lagerlund et al. [4] use a Principal Component Analysis (PCA) based filtering of EEG sig nal for artifact removal. Therefore, a major drawback of the PCA method is that it cannot completely separate ocular artifacts from EEG signals, when both waveforms have similar voltage magnitudes. Decomposition into uncorrelated signal components is possible with PCA; however, it is not sufficient to produce independence between the variables, at least when the variables have nonGaussian distributions. The PCA method therefore cannot accommodate higherorder statistical dependen cies. Jung et al. [5], Delorme et al. [6] and LeVan [7] de veloped some artifact removal techniques using ICA which demonstrates the potential not only to decorrelate but also to work with higherorder dependencies. The most significant computational difference between ICA and PCA is that PCA uses only secondorder statistics (such as the variance which is a function of the data squared) while ICA uses higherorder statistics (such as functions of the data raised to the fourth power). Vari ables with a Gaussian distribution have zero statistical moments above secondorder, but most signals do not have a Gaussian distribution and do have higherorder moments. These higherorder statistical properties are put to good use in ICA. While ICA is an extension of PCA method, these componentbased artifact removal procedures are not automated and require tuning of sev eral parameters such as number of sources, permutation of these sources etc. through visual inspection. Krishnaveni et al. [1] recently proposed a wavelet
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 342 based thresholding method to remove ocular artifacts from raw EEG data. Kumar et al. [8] developed a similar wavelet based statistical method for removing ocular artifacts. The wavelet based artifact removal techniques are notable for preserving the shape of the waveform of the signal in the artifact free zone compared with other artifact removal methods. But this method is limited by the introduction of noise beyond the specified frequency band when applied to band limited signals. In this paper the authors propose a new method of ocular artifact removal from EEG signal using the Stransform [9,10]. The high amplitude signal compo nents, like the ocular artifacts are filtered out in Sdomain by setting a statistical threshold function. The ST based method is an improvement of the wavelet method since it localizes the power and preserves the absolutely referenced phase information of the original signal. Moreover, integrating the Stransform over time, results in the Fourier transform (FT). This direct relation to the Fourier transform simplifies the task of inverting to the time domain. This property of the Stransform led to the development of Stransform filter, which has been explored in this work to serve the purpose of removing ocular artifacts. The paper has been organized as follows. The meth odology used for signal preprocessing and artifact re moval using ICA, WT and Stransform is described in Section 2. Results and discussions are contained in Sec tion 3 followed by the conclusions in Section 4. 2. METHODOLOGY The methodology involves prefiltering followed by the application of various methods such as ICA, wavelet and Stransform as discussed below. 2.1. Filtering As discussed above the raw EEG data is contaminated with high frequency noises other than ocular artifacts. The signal is passed through a low pass filter with cutoff frequency of 30 Hz followed by normalization. Nor malization ensures removal of any unwanted bias that may have crept into the experimental recordings. These normalized signals have been used further for artifact removal. 2.2. Independent Component Analysis Independent component analysis is a powerful technique which can be used to separate sources from a given lin ear mixture of signals. The brain is supposed to have many independent sources which produce electrical sig nals. The EEG signal that is obtained by various elec trodes actually contains a linear mixture of the signals produced by independent sources in the brain. In a signal having artifacts the linear mixture also contains the sig nals produced by ocular and other visceral sources. If we are able to separate the sources from the signals recorded by the various electrodes we can easily identify the arti fact sources and can separate them from the original EEG sources. Once the independent time courses of dif ferent brain and artifact sources are extracted from the data, “corrected” EEG signals can be derived by elimi nating the contributions of the artifactual sources. The method described here basically tries to separate and eliminate the ocular sources. Subsequently the linear mixture is reconstructed using the artifact free sources. This linear mixture is then called the artifact free signal. The signal obtained from the electrodes can be ex pressed in the following manner . xAs (1) Here 12 ,,, T m kxk xk x 1m 12 is called the observation vector. The observation vector in our case is composed of the signals obtained from the electrodes. The observation vector has () components. The source vector is given by ,,, T n kss 1n k sk ; it gives the different independent sources which results in observation vector after linear mixing. The source vector has ( ) components and they are assumed to be statistically independent; and that they are nonGaussian. A is called the mixing matrix composed of (mn ) constant elements ij . This matrix gives the linear transformation between the source vector and the observation vector. a The independent component analysis problem is for mulated as finding a demixing or separating matrix W from the given observation matrix x, such that . yWx (2) here 12 ,,, T n yk ykyk y is the estimate of original source vector s and the components i are as independent as possible. This can be achieved by maxi mizing some function y , n12 ,, yy mn y that measures independence. The various approaches differ in the spe cific objective function and the optimization method that is used. There are certain basic assumptions in the prob lem formulation. Firstly the number of observed signals should be equal to the number of independent sources, i.e., . Therefore A represents a full rank square mixing matrix. This is not really a restriction since PCA can always be applied to reduce the dimension of the data set x, to equal that of the source data set s. Another assumption is that source signals must be statistically independent of each other or in practice as independent as possible (including uncorrelatedness). The independ ence condition can be defined by stating that the joint probability density of the source signals is equal to the product of the marginal probability densities of the indi C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 343 kvidual signals, i.e., 1 . n i i ppy y Two categories of ICA algorithm exist. In the first type, source separation can be obtained by optimizing an objective function [11] which can be scalar measure of some distributional property of the output y. More gen eral measures are entropy, mutual independence, diver gence between joint distribution of y and some given mode and higher order decorrelation. The ICA method can be formulated as optimization of a suitable objective function which is also termed as contrast function. The problem in optimization of con trast function is that, they rely on batch computation using the higher order statistics (HOS) of data or lead to complicated adaptive separation. It is often sufficient to use simple HOS such as kurtosis, which is the fourth order cummulant with zero time lags. The kurtosis of the source signal th ii is given by 2 44 2 Cum 3 ii i sEs Es (3) If i is Gaussian, then its kurtosis is zero. Source signals that have negative kurtosis are called subGaus sian and have a probability distribution flatter than usual Gaussian distribution. Source signals having a positive kurtosis are called superGaussian and have a probability distribution with sharp peak and longer tails then the standard Gaussian ones. A contrast function based on kurtosis is given by 2 44 1 11 Cum 3 nn ii ii JyEy Ey y2 i (4) where stands for cummulant. It is maximized by a separating matrix W, if the sign of the kurtosis is same as all the source signals. For prewhitened input vector x and orthogonal separating matrices, Cum 21 i Ey and hence the contrast function 1 Jy reduces to 2 i Ey 3 4 n . Therefore, is maximized when 1 Jy 1 i i Ey is minimized for sources having negative kurtosis and maximized for sources with positive kurtosis. The second category uses neural implementation of ICA algorithms like nonlinear PCA based subspace learning [12,13] for achieving source separation. In this category, there are adaptive algorithms [13] like mini mum mutual information method [14] and maximum entropy method [15] based on stochastic gradient opti mization. An excellent treatment of the various ap proaches, their strengths and weaknesses can be found in Cichicki et al. [16], as well as Hyvärinen et al. [17]. The method that has been used in this study is based on minimization of mutual information between outputs which is equivalent to maximization of their joint en tropy. The details of the algorithm which is known as infomax principle can be found in [18]. In this study we have used 19 electrodes to collect EEG data from a human subject. Hence exactly 19 in dependent components (sources) can be separated out using infomax based ICA, from the observed recordings (mixtures). Out of these 19 sources, the sources contain ing ocular artifacts can be identified and removed and subsequently artifact free signals are obtained recon structing from the rest of the components. 2.3. Artifact Removal Using Wavelet Transform Wavelet transform is a useful tool for time frequency analysis of neurophysiological signals. Wavelets are small wave like oscillating functions that are localized in time as well as in frequency [19,20]. In discrete domain, any finite energy time domain signal can be decomposed and expressed in terms of scaled and shifted versions of a mother wavelet t and a corresponding scaling function t . The scaled and shifted version of the mother wavelet is mathematically represented as /2 ,22, , jj jk ttkj kZ (5) A similar expression holds for , the scaled and shifted version of the scaling function ,jk t t . A signal ht can be expressed mathematically in terms of the above wavelets at level as j ,,jjkj jk kk hta ktdkt (6) where j ak and j dk are the approximate and detailed coefficients at level . These coefficients are computed using filter bank approach as proposed by Rioul and Vetterli [21]. j The original signal ht is first passed through a pair of high pass and low pass filters. The low frequency component approximates the signal while the high fre quency components represent residuals between original and approximate signal. The approximate component is further decomposed at successive levels. The output time series is downsampled by two and then fed to next level of input after each stage of filtering. As the wavelet coefficients represent the correlation of signal with the mother wavelet, the signal will generate high amplitude coefficients at places where artifacts are present. These coefficients can be eliminated using a simple thresholding technique. The threshold can be computed as 2 jj TmeanC stdC . j (7) here C is the wavelet coefficient at level of de composition. If the value of any coefficient is greater than the threshold it is reduced to a suitable fraction of th j C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 344 the actual coefficient value [8]. 2.4. STransform The Stransform provides a useful extension to the wavelets by having a frequency dependent progressive resolution as opposed to the arbitrary dilations used in wavelets. The kernel of the Stransform does not trans late with the localizing window function, in contrast to the wavelet counterpart. For that reason the Stransform retains both the amplitude and absolutely referenced phase information [9]. Absolutely referenced phase in formation means that the phase information given by the Stransform is always referenced to time . This is the same meaning of the phase given by the Fourier transform, and is true for each Stransform sample of the timefrequency space. The wavelet transform (WT), in comparison can only localize the amplitude or power spectrum, not the absolute phase. There is, in addition, an easy and direct relation between the Stransform and the natural Fourier transform which cannot be achieved by wavelets. Since its development, the Stransform has been widely used in applications ranging from geophys ics [10], oceanography [22], atmospheric physics [9,23 25], medicine [26,27], hydrogeology [28] and mechani cal engineering [29]. 0t The Stransform of a continuous time signal ht is defined as [30,31] 2π ,, ift Sfhtw tft ed. (8) The window function w, is generally chosen to be positive and normalized Gaussian [25] 22 2 ,e 2π tf f wtf (9) where f represents the frequency, t is the time and is the delay. It is worth emphasizing that in order to have an inverse Stransform, the window must be normalized ,d1wtf t . (10) The Stransform can also be written as the convolution of two functions over the variable t ,,, ,, Sfptfw tf pfwf dt (11) where 2π ,e if pfh (12) and 22 2 ,e 2π f wf (13) Let ,Bf be the Fourier transform (from to ) of the Stransform . By the convolution theorem the convolution in the ,Sf (time) domain be comes a multiplication in the (frequency) domain: ,,,BfPfWf . (14) Here ,Pf and ,Wf are the Fourier trans forms of ,pf and ,wf respectively. Equation (14) can also be written as 22 2 2π ,f BfH fe (15) where f is the Fourier transform of (12) and the exponential term is the Fourier transform of the Gaussian function (13). Thus the Stransform can be retrieved by applying the inverse Fourier transform ( to ) to the above equation for , 0f 22 2 1 2π 2π ,, eed f SfHfW f Hf . (16) One of the important characteristics of the Stransform is that summing ,Sf over yields the Fourier spectrum of the signal h. Using the definition (8) of Stransform we obtain 2π ,e dd ft fhtwtft (17) where f is the Fourier transform of ht . If Hf , applying Fubini’s theorem and taking into account the normalization condition (10), the above equation reduces to a simple Fourier transform ,dHfS f. (18) This spectral property enables the definition of an in verse Stransform through the inverse Fourier transform. Thus 2π ,ded. ift htS ff (19) This is clearly different from the concept of wavelet transform. The Stransform can be written as operations on the Fourier spectrum f of ht. 22 2 2π 2π ,eed i f SfH ff 0. (20) The discrete analog of (20) is used to compute the C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 345 discrete Stransform by taking advantage of the Fast Fourier Transform (FFT) and the convolution theorem. Using (13), the Stransform of a discrete time series is given by (letting hkT nNT and jT ) 22 2 2π2π 1 0 ,ee mimj NnN m nmn SjT Hn NT NT 0 (21) and for it is equal to the constant defined as 0,n 1 0 1 ,0 N m m SjTh NNT (22) where and The discrete in verse of Stransform [9] is given by ,jm0,1, ,1.nN 2π 11 00 1,e ink NN N nj n hkTS jT NNT . (23) The amplitude of the Stransform has the same mean ing as the amplitude of the Fourier transform. This pro vides a frequency invariant amplitude response in con trast to the wavelet approach [31]. The term “frequency invariant amplitude response” means that for a sinusoi dal signal with amplitude 00 cos 2π ht Aft 0 , the Stransform returns amplitude regardless of the frequency f. 2.5. Artifact Removal Using STransform When only single channel signal is available, component based methods like PCA and ICA cannot be applied. In such case, the use of Stransform has been demonstrated to be an important tool to remove ocular artifacts from EEG signals, since it not only solves the task efficiently but also retains the local phase information of the origi nal signal even after denoising. The following is a sum mary of the proposed algorithm. 1) Decompose the entire EEG signal using Strans form. 2) Select the frequency band 0, 1 6 z, where, gen erally the ocular artifacts lie. 3) Determine the mean and standard deviation of the absolute values of Stransform coefficients ,Sij in the selected frequency band. 4) Set the threshold function as: mean,2*std,,TSij Si jwhere ,Sij is the absolute value of . ,Sij 5) Set the multiplying factor . 01mf 6) If ,Sij T, then, , else . ,Sij Si ,*j mf ,,Sij Sij 7) Reconstruct the signal using the modified Strans form coefficients. High amplitude Stransform coefficients are generated at the places where artifacts are present. These coeffi cients are eliminated by using the above threshold tech nique. The time average of the local spectral representa tion (i.e., the Stransform) is the complexvalued global Fourier spectrum as in (18). As a result, the ST can be interpreted as a generalization of Fourier transform to a nonstationary signal. Since the EEG signal is highly nonstationary, the Stransform is the ideal method for representing its timefrequency distribution. It is also customary in Fourier spectra to show only the positive frequency part of the spectrum, because the amplitude spectrum is symmetric, and the phase spectrum is anti symmetric. However, any operation (here, thresholding) in the Sdomain must be applied to both the positive and negative frequency parts of the spectrum. Otherwise, the summed ST will not collapse to FT. When any operation is applied to the positive or negative part of the spectrum only, the inverse FT leads to a complex (not real) time series, and would be in error. Here, signal reconstruction performance is measured by the signaltonoise ratio (SNR) and is defined by 2 2 10 20log l rec l h SNR hh (24) where h and rec h represent the original and recon structed signal respectively. 3. RESULT AND DISCUSSIONS In this paper we have evaluated the performance of the proposed denoising method using Stransform to remove ocular artifacts from EEG signal with respect to the ICA and wavelet based method discussed in Section II. The Figures related to ICA presented in this paper are pro duced using the EEGLAB software package which op erates in the MATLAB environment and available at http://sccn.ucsd.edu/eeglab. In Figure 1, the removal of ocular artifacts from EEG signals collected from multiple sensors is demonstrated. A fivesecond epoch of raw EEG time series containing prominent artifact due to eye movement is shown in Figure 1(a). First, the raw 19channel EEG data are de composed into nineteen independent components using ICA based on infomax principle (Figure 1(b)). As ex pected, correlation between ICA traces are close to zero. The 2D scalp component map of all nineteen ICs is illustrated in Figure 1(c). Since the EEG spectrum of eye artifacts decreases smoothly, their scalp topogra phies look like component 1. This artifactual component is also relatively easy to identify by visual inspection of component time course (Figure 1(b)). Since this com ponent accounts for eye activity, we may wish to sub tract it from the data. After removing component 1 we reconstruct the data using the rest 18 components in or der to get ocular artifacts free EEG signals which is shown in Figure 1(d). C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 Copyright © 2011 SciRes. 346 (a) (b) (c) (d) Figure 1. Demonstration of ocular artifact removal using ICA in EEG signals. (a) A fivesecond epoch of a nineteenchannel EEG time series containing prominent arti fact due to eye movement; (b) Corresponding ICA component activations and (c) scalp map of all the nineteen ICs; (d) Ocular artifactfree EEG signals by removing component 1 in (b). JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 347 ICA decomposition is possible only for multi channel data and hence cannot be applied when the data is avail able in single channel. Therefore the proposed Strans form technique is effectively applied in order to remove artifacts from single channel signal. A raw EEG signal of 8 sec duration sampled at 256 Hz and its Stransform is shown in Figure 2(a). Using infomax based ICA method, ocular artifacts are removed from all the nineteen channel EEG signals and the exact segment of the signal (Figure 2(b)) that has been used for WT and ST study also is taken for comparison. It can be observed in Figure 2(b), that the high amplitude ocular artifacts are significantly reduced in the reconstructed signal but its Stransform plot reveals that the timefrequency distribution as com pared to the original signal is massively disturbed which implies substantial loss in data in the useful signal outside the artifact range. In Figure 2(d), the time frequency plot after thresholding the Scoefficients and the correspond ing reconstructed signal are illustrated. The Scoefficients in the range of 0.5  16 Hz have been subjected to thresh olding since most artifacts lie within this band of signal. It can be observed in the Figure 2(d), that the high am plitude ocular artifacts in the specified band are signifi cantly reduced in the reconstructed signal. In addition, the reconstructed signal retains all other amplitudes and frequencies as well, of the signals. This is also apparent in the corresponding ST plot and can be explained by the “frequency invariant amplitude response” property of Stransform. The artifact removed signal using wavelet transform and its corresponding time frequency repre sentation using Stransform is demonstrated in Figure 2(c). This timefrequency plot contains some unwanted frequency components beyond the actual frequency range of the signal. A comparison of the power spectral density (PSD) of the raw signal and the reconstructed signal is shown in Figure 3. The PSD of Stransform based reconstructed signal almost replicates the PSD of the raw signal be Figure 2. (a) Normalized raw EEG signal; (b) Artifact free EEG signal using ICA; (c) Artifact free EEG signal using wavelet trans form; (d) Artifact free EEG signal using Stransform. The figures in the right side are the corresponding timefrequency plot using Stransform, of the signals in the left. C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 348 Figure 3. Comparison of artifacts free signals using ICA, WT, ST in time domain and their PSD. yond the artifact range ([0,16] Hz). It can be seen that the PSD is least affected due to the removal of artifacts within the range (below 16 Hz). With the wavelet based reconstructed signal the PSD has a good correlation with that of the raw EEG, but beyond the specified band it has wide variations. When thresholding is applied to any frequency band of the wavelet transformed signal, the sample values in the time domain are replaced. Replac ing sample values in the time domain introduces a step discontinuity after the threshold replacement. A series of such replacements in the time domain at arbitrary time locations will give rise to high frequency noise in the frequency domain which is portrayed in Figure 2(c). Figure 4(b) shows the comparison of PSD of artifact removed signals for various multiplying factors mf . In this example, reducing the multiplying factor of the wavelet coefficients, results in a distortion of the smooth profile of the signal, which introduces sharp changes in the artifact zone (Figure 4(a)). This is also observed in the timefrequency plot (Figure 2(c)) of the WT based artifact free signal. The variation of multiplying factor for ST does not affect the PSD in the nonartifact zone within the specified band (16  30 Hz). The signal to noise ratio in the reconstructed signals for all the three methods is also compared and observed that, it is more in the case of ST based reconstructed signal (2.33 dB) as compared to the WT (1.81 dB) and ICA (0.98 dB) based methods. The proposed method is applied to ten epochs of an EEG signal of duration of four seconds and com pared with the method based on wavelet transform. As shown in Figure 5, in each epoch the reduction of ocular artifacts is improved in the case of the proposed method with minimal impact to the other part of signal. 4. CONCLUSIONS This paper demonstrates the effectiveness of the S transform based approach in removing the ocular arti facts from the EEG signal. It outperforms some of the recently proposed methods based on wavelet transform and ICA. The wavelet transform only localizes the power spectrum as a function of time. It does not retain the absolutely referenced phase information that the Stransform contains and is therefore not directly invert ible to the Fourier transform spectrum. Additionally, we have also demonstrated that the PSD of the raw EEG is not affected by the proposed method, which implies the preservation of the information content is better than the other method based on wavelets and ICA. In conclusion, the Stransform method can be used as a very effective tool for removing ocular artifacts from EEG signals. Additional research in this field will refine our techniques and lead to improved methodology for filtering noise from EEG signals. Table 1. Comparison of signaltonoise ratio. METHOD SNR (dB) ST 2.33 WT 1.81 ICA 0.98 C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 349 (a) (b) (c) Figure 4. (a) An artifact zone of the signal and its removal using WT and ST for three different multiplying factors (mf = 0.9, 0.7 and 0.4) and (b) corresponding PSDs; (c) An artifact zone of the signal and its removal using ICA, WT and ST. C opyright © 2011 SciRes. JBiSE
K. Senapati et al. / J. Biomedical Science and Engineering 4 (2011) 341351 350 Figure 5. Comparison of artifact removal using ST and WT for ten 4second EEG segments. 5. ACKNOWLEDGEMENTS The authors would like to thank Prof. L. Mansinha, Department of Earth Sciences, The University of Western Ontario, London, Ontario, Canada, for his useful comments and support. The authors also thank Ms. Marilyn CarrHarris for her careful review of the English Usage. REFERENCES [1] Krishnaveni, V., Jayaraman, S., Aravind, S., Hariharasud han, V. and Ramadoss, K. (2006) Automatic identifica tion and removal of ocular artifacts from EEG using wavelet transform. Measurement Science Review, 6, 4557. [2] Croft, R.J. and Barry, R.J. (2000) Removal of ocular artifact from the EEG: A review. Clinical Neurophysiology, 30, 519. doi:10.1016/S09877053(00)000551 [3] Kandaswamy, A., Krishnaveni, V., Jayaraman, S., Mal murugan, N. and Ramadoss, K. (2005) Removal of ocu lar artifacts from EEG—A Survey. IETE Journal of Re search, 52, 112130. [4] Lagerlund, T.D., Sharbrough, F.W. and Busacker, N.E. (1997) Spatial filtering of multichannel electroencepha lographic recordings through principal component analy sis by singular value decomposition. Clinical Neuro physiology, 14, 7382. doi:10.1097/0000469119970100000007 [5] Jung, T., Makeig, S., Humphries, C., Lee, T., Mckeown, M.J., Iragui, V. and Sejnowski, T.J. (1998) Extended ICA removes artifacts from electroencephalographic record ings. Advances in Neural Information Processing Sys tems 10, MIT Press, Cambridge, 894900. [6] Delorme, A., Makeig, S. and Sejnowski, T. (2001) Auto matic artifact rejection for EEG data using highorder statistics and independent component analysis. Proceed ings of the 3rd International ICA Conference, San Diego, December 913. [7] LeV an, P., Urrestarrazu E. and Gotman, J. (2006) A sys tem for automatic artifact removal in ictal scalp EEG based on independent component analysis and Bayesian classification. Clinical Neurophysiology, 117 , 912927. doi:10.1016/j.clinph.2005.12.013 [8] Kumar, P.S., Arumuganathan, R., Sivakumar, K. and Vimal, C.A. (2008) Wavelet based statistical method for denoising of ocular artifacts in EEG signals. Interna tional Journal of Computer Science and Network Secu rity, 8, 8792. [9] Stockwell, R.G., Mansinha, L. and Lowe, R.P. (1996) Localization of the complex spectrum: The Stransform. IEEE Transactions on Signal Processing, 44, 9981001. doi:10.1109/78.492555 [10] Mansinha, L., Stockwell, R.G., Lowe, R.P., Eramian, M. and Schincariol, R.A. (1997) Local Sspectrum analysis of 1D and 2D data. Physics of the Earth and Planetary Interiors, 103, 329336. C opyright © 2011 SciRes. JBiSE
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