NON ADAPTIVE THRESHOLDING METHODS FOR

EEG is an electrical activity of the brain and is a tool which gives an insight into the brain and its abnormalities. The first observation of EEG was reported by Caton [1] and the technique was described in man by a German psychiatrist, Berger [2] in 1929. Generally EEG signals are measured from electrodes positioned on the scalp in an 10-20 arrangement, a placement scheme devised by the International Federation of Societies of EEG [3]. Electrical activity from the brain consists of rhythms and these rhythms are named according to their frequency range as follows: Delta (0.5 - 4 Hz), Theta (4-8 Hz), Alpha (8-13 Hz), Beta (13-30 Hz), Gamma (> 30 Hz). [4] All these waves compose the normal background activity and appear at no precise time location or frequency

EEG can be contaminated by potentials of non-cerebral origins such as heart, muscles, eyes etc., In current data acquisition system, voltage changes generated by eye movements and blinks are dominant over other electrophysiological contaminating signals [5]. Human eye contains an electrical dipole formed by a positive cornea and a negative retina, and there is a potential difference of about 100 mV between these two opposite charges. Hence blinking or moving the eyes produce large electrical potential around the eyes known as ElectroOculoGram (EOG). It is a non-cerebral activity that spreads across the scalp and contaminates the EEG, and these potentials are called Ocular Artifacts (OAs). The shape of the EOG waveform depends on factors such as the mechanism of origin and the direction of eye movements. Vertical, Horizontal and Round eye movements produce square shaped EOG waveforms while blinks produce spikes. OAs act as a major source of noise, making it difficult for the physicians to distinguish normal brain activities from abnormal ones. Hence in order for the EEG to be interpreted properly for clinical use, a control procedure for filtering the OAs from EEG is essential.

Many methods have been proposed by numerous researchers to remove ocular artifacts from EEG. A brief discussion about the existing techniques for correction of OAs in EEG is given below. Eye fixation method in which the subject is asked to close their eyes or fix it on a target is often unrealistic. Another common strategy is to reject all EEG epochs containing artifacts larger than some arbitrarily selected EEG voltage level. When artifacts occur frequently, or when the data is limited, the amount of data lost due to artifact rejection may be unacceptable. Since EEG and EOG occupy the same frequency band, use of analog and digital filters is ineffective. Use of potentiometers to balance out the effect of eye movements, is subjective, since the required adjustments were made manually by observing the EEG [6].

Widely used methods for removing OAs are based on regression in time domain [7,8] or frequency domain [9,10] techniques. All regression methods, whether in time or frequency domain depend on having one or more regressing (EOG) channels. Also both these methods share an inherent weakness, that spread of excitation from eye movements and EEG signal is bidirectional. Therefore regression based artifact removal eliminates the neural potentials common to reference electrodes and to other frontal electrodes. Use of adaptive digital filters for OA removal [11], also requires a suitable EOG reference model for training the filter.

Principal Component Analysis (PCA) [12] has been proposed as a method to remove eye artifacts from EEG [13]. It outperformed the regression based methods; however, this method also required an accurate modeling of propagation paths for the signals involved. Also, PCA cannot completely separate OA from EEG, when both the waveforms have similar voltage magnitudes [14]. It also requires the distribution of the signal sources to be orthogonal and its effectiveness is limited to decorrelating signals and thus it cannot deal with higher-order statistical dependencies.

Independent Component Analysis (ICA) is an extension of PCA which not only decorrelates but can also deal with higher order statistical dependencies [15]. Most popular ICA algorithms that have been used by numerous researchers for denoising EEG are Infomax [16], Extended Infomax [17], JADE [18] and Fast ICA [19]. ICA algorithms are superior to PCA, in removing a wide variety of artifacts from the EEG, even in the case of comparable amplitudes. However, ICA algorithms are not automated, and require visual inspection of the independent components to decide their removal.

Tatzana Zikov et.al [20] proposed a wavelet based denoising technique for removal of ocular artifacts in EEG. This method neither relies upon the reference EOG nor visual inspection. However, the threshold limit was estimated from the uncontaminated baseline EEG, which is recorded from the same subject.

This paper discusses various non adaptive thresholding methods using different threshold limit and thresholding function for ocular artifact correction. A more appropriate threshold limit and thresholding function is found, from various combinations which satisfies the following criteria: i) minimization of the magnitude of the Ocular Artifacts, (OAs) ii) preservance of the background EEG activity. A comparison of various methods revealed the fact that the threshold limit calculated from the statistical averages of the noisy signal and hard thresholding function for a two second frame (epoch) satisfies the above said criteria.

WAVELETS FOR ANALYZING EEG SIGNALS:

Wavelet transforms are used to analyze time varying, non-stationary signals, and EEG fall into these category of signals. The ability of wavelet analysis to accurately resolve EEG into specific time and frequency components leads to several analysis applications and one among them is denoising. EEG signals have frequency content that varies as a function of time and recording sites on the scalp. Hence wavelet techniques can optimize the analysis of such signals by providing excellent joint time-frequency resolution, which is not possible with Fourier Transform. In contrast to Short Time Fourier Transform (STFT), wavelet transform adapts the window size according to the frequency. i.e. when wavelet transform is used to decompose a signal, the wavelet acts as its own window at each scale.

In EEG data sets, there may be some specific components or events that may help the clinicians in diagnosis. They may tend to be transient (localized in time), prominent over certain scalp regions (localized in space) and restricted to certain ranges of temporal and spatial frequencies (localized in scale). Wavelet analysis provides flexible control over the resolution with which neuroelectric components and events are localized in time, space, and scale [21].

DENOISING EEG USING WAVELETS:

The wavelet transform of the noisy signal generates the wavelet coefficients which denote the correlation coefficients between the noisy EEG and the wavelet function. Depending on the choice of mother wavelet function (which may resemble the noise component), larger coefficients will be generated corresponding to the noise affected zones. Ironically smaller coefficients will be generated in the areas corresponding to the actual EEG. The larger coefficients will now be an estimate of noise. Appropriate threshold limit is to be found which separates the noise coefficients and the signal coefficients. A proper thresholding function is to be chosen to discard the noise coefficients appropriately. Thresholding functions decide upon which coefficients should be retained and what should be done to them. Hence discarded coefficients would result in the removal of noise, and the retained coefficients represent the wavelet coefficients of the de-noised EEG signal. On taking the inverse wavelet transform, the de-noised signal is obtained. Hence the selection of threshold and thresholding function plays a crucial role in EEG denoising.

PROPOSED METHOD:

Eye activity is one of the main sources of artifacts in EEG recording and occupies the low frequency bands, from (0 up to 6-7 Hz) for eye movement artifacts, and between (8-13 Hz), excluding very low frequencies for the eye blink [22]. Stationary Wavelet Transform (SWT) is used to decompose the recorded EEG into various frequency scales. SWT is chosen since it is time invariant and also it has better sampling rates in the low frequency bands, which produces smoother results. The decomposition level is restricted to five (0-2 Hz, 2-4 Hz, 4-8 Hz, 8-16 Hz, 16-32 Hz and 32-64 Hz), in order to have a reasonable computational complexity. The mother wavelet should be chosen in such a way that it better approximates and captures the artifacts in the noisy EEG signal. Coiflet 3 wavelet has been chosen as the basis function, since it resembles the shape of the eye blink artifact. EEG data for this work is taken from http://www.sccn.ucsd.edu/eeglab/ for testing. Samples from the frontal channels namely FP1, FP2, FPz are taken for the analysis because they are most likely to be affected by ocular artifacts due to the placement of the corresponding frontal electrodes close to the eyes. Analysis is done by taking both one second (128 samples/second) and two second (256 samples/sec) epoch of the noisy EEG signal, since EEG epochs shorter than 12 seconds may be considered stationary [23]. To avoid the boundary effects caused by the convolution of the wavelet filter coefficients with the sampled data, each epoch is extended on both sides with the samples from the previous epoch at the beginning and the flipped samples of the current epoch at the end. On choosing the window size, mother wavelet, length of epoch extensions and the level of decomposition, each epoch is subjected to stationary wavelet transform, and correspondingly, wavelet coefficients will be generated for each scale of decomposition.

In the proposed scheme, the following thresholds were used for calculating the threshold limits and the most optimum one is found:

i) Modified Donoho’s Universal Threshold:

Donoho’s Universal Threshold [24] is given by T = sigma * sqrt (2 log (N))

where sigma = Estimation of noise variance.

N = frame length (number of samples taken at a time

for denoising)

Since no noise model has been imposed on the EEG signal, the threshold has been modified to use the signal variance rather than the noise variance.

ii) Thresholds based on statistics of the signal:

a) T_k = mean (H_k) + 2.std (H_k)

where H_k denotes the wavelet coefficients of each band k of decomposition. This threshold is the modified version of the threshold proposed by Tatjana Zikov et. al. [20]. Here H_kwas taken to be the maximum absolute value of wavelet coefficients for each band k of decomposition.

b) T_k = 1.5 * std (H_k)

where H_k denotes the wavelet coefficients of each band k of decomposition. This threshold is newly proposed in this paper and has been empirically chosen for ocular artifact correction.

Various thresholding functions used in this work are as follows:

i) Hard thresholding

Hard thresholding sets any coefficient ‘coef’ greater than the threshold ‘thresh’ to zero (if (coef[i] > thresh) then coef[i] = 0.0) [25].

ii) Soft thresholding

In the soft thresholding method, the threshold is subtracted from any coefficient that is greater than the threshold value if (coef[i] > thresh) then coef[i] = coef[i] – thresh). . This moves the time series toward zero [25].

iii) Qian thresholding

Qian thresholding is between hard and soft thresholding.

if (coef[i] > thresh) then coef[i] =coef[i] *{coef[i]^{^}q - thresh^{^}q} /coef[i]^{^}q;

When ‘q’ = 1, it is equivalent to soft thresholding. When ‘q’ = infinity, it is equivalent to hard thresholding. With the careful tuning of the parameter ‘q’ for a particular signal, one can achieve best de-noising effect within the thresholding framework [26].

RESULTS:

The de-noising of EEG signal is carried out by using different combinations of threshold limit, thresholding function and window sizes. Choice of threshold limit and thresholding function is a crucial step in the denoising procedure, as it should not remove the original signal coefficients leading to loss of critical information in the analyzed data. Fig 1 to Fig 5 shows the time domain plots of the noisy EEG and denoised EEG signals obtained using different threshold limit and thresholding functions.

Fig 1 Fig 2

Donoho’s Modified Threshold, Hard, Donoho’s Modified Threshold, Soft

Frame Length= 1 sec & 2 sec Qian, Frame Length= 1 sec & 2 sec

Fig 3 Fig 4

mean + 2 std Statistical Threshold, mean + 2 std Statistical Threshold,

Hard, Frame Length= 1 sec & 2 sec Soft, Qian, Frame Length= 1 sec & 2 sec

Fig 5

1.5 std Statistical Threshold, Hard,

Frame Length= 1 sec & 2 sec

In addition to the time domain plots, certain validation methods such as cross correlation and power spectral density are used to study the performance of the proposed method.

The EEG signal recorded from the frontal channels are distorted by the ocular artifacts and is recorded in the reference EOG channel in the dataset. The cross correlation between the noisy EEG and EOG is taken (Fig 6). This shows how close both the signals are in terms of the shape. The cross correlation is then taken between the de-noised EEG signal (using different threshold limits, thresholding functions, window size) and the EOG reference. Naturally, the correlation should have been reduced due to the reduction in the noise amplitude in the de-noised signal. But a highly minimum cross correlation would be obtained if the background EEG has also been removed in addition to the ocular artifacts. So the time domain plots have to be considered along with the cross correlation plots to check for the retainment of the background activity.

Fig 7 shows the power spectra of the contaminated EEG and the corrected EEG. From this figure it is shown that, power of the spectral components belonging to the low frequency range (EOG), has been reduced, while reasonably retaining the high frequency content of the signal, for the proposed combination.

Fig 6 Fig 7

Cross correlation plot Power Spectral Density

The most important criteria for determining the optimum method for ocular artifact correction in the EOG signal are: i) The extent to which the amplitude of the ocular artifact has been reduced. ii) The extent to which the background EEG activity has been retained Using the above two criteria and by the visual inspection of the time domain plots by a domain expert (Neurophysician) it is concluded that the following combination produces better de-noised results than the other methods taken into consideration.

Threshold: T_k = 1.5 * std (H_k)

Thresholding Function : Hard

Window/Frame Length : 2 seconds

The threshold limit is calculated from the uncontaminated baseline EEG recorded from the same subject, in the method proposed in [20]. In contrast to this, the algorithm discussed in this paper, calculates the threshold limit, based on the statistical averages calculated from the contaminated EEG data itself. This shows that the algorithm is data independent. Table 1 shows a qualitative comparison of various non adaptive thresholding schemes for different combinations.

CONCLUSION:

Different techniques for correcting ocular artifacts have been proposed by numerous researchers and are reviewed in [27]. Each technique has its own merits and demerits and there is no general consensus of which of them offers the best solution for correcting ocular artifacts in EEG. In this work, a method to correct ocular artifacts using various non adaptive thresholding schemes is devised and tested for various combinations. De-noising using the proposed algorithm yields better results, in terms of ocular artifact amplitude reduction and the retainment of the background EEG activity.

However, selection of threshold limit and the thresholding function is still a critical issue, and need to be further investigated. Certain abnormalities like spikes, resemble the eyeblink, and the database which consists of such abnormalities need to be tested. In addition to this, proper performance metrics for validating the de-noised EEG signals need to be devised.

Table 1 Qualitative comparison of different non adaptive

thresholding schemes for EEG Denoising

S.No.	Threshold	Thresholding Function	Window size (seconds)	Frequency band thresholded	Comments
1.	Modified Donoho’s threshold	Hard	One	0 - 16Hz	Retains background EEG reasonably; spikes introduced near the artifact zone
2.	Modified Donoho’s threshold	Hard	Two	0 - 16Hz	Retains background EEG reasonably; spikes introduced near the artifact zone
3.	Modified Donoho’s threshold	Qian	Two	0 - 16Hz	Retains background EEG; artifact amplitude highly reduced; but spikes introduced near the artifact zone
4.	Modified Donoho’s threshold	Soft	Two	0 - 16Hz	Retains background EEG; artifact amplitude is still high
5.	mean+2*std	Hard	One	0 - 16Hz	Retains background EEG; artifact amplitude is still high
6.	mean+2*std	Hard	Two	0 - 16Hz	Retains background EEG; artifact amplitude highly reduced; spikes introduced near the artifact zone
7.	mean+2*std	Qian	Two	0 - 16Hz	Retains background EEG; spikes introduced near the artifact zone
8.	mean+2*std	Soft	Two	0 - 16Hz	Retains background EEG; artifact amplitude is still high
9.	1.5*std	Hard	One	0 - 64Hz	Smoothens the EEG background activities
10	*1.5std**	Hard	Two	0 - 64Hz	Retains background EEG; no spikes are introduced; artifact amplitude greatly reduced

ACKNOWLEDGEMENTS

The authors are grateful for the support extended by the Network Project funded by Swiss Development Cooperation (SDC) towards the completion of this project and Arnaud Delorme and Scott Makeig of a Center of the Institute for Neural Computation, the University of California San Diego for providing data and EEGLAB Toolbox.

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Technical College - Bourgas,