EEG signal co-channel interference suppression based on image dimensionality reduction and permutation entropy

Signal Processing 134 (2017) 113–122

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Signal Processing journal homepage: www.elsevier.com/locate/sigpro

EEG signal co-channel interference suppression based on image dimensionality reduction and permutation entropy

crossmark

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Yi Wanga, Guanghua Xua,b, , Sicong Zhanga, Ailing Luoa, Min Lia, Chengcheng Hana a b

School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China State Key Laboratory for Manufacturing Systems Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China

A R T I C L E I N F O

A BS T RAC T

Keywords: Brain-computer interface (BCI) Electroencephalogram (EEG) Co-channel interference suppression Image dimensionality reduction Permutation entropy

It is well known that electroencephalogram (EEG) signals collected from scalps are highly contaminated by various types of artifacts and background noise. The perturbations induced by artifacts and random noise are particularly difficult to correct because of their high amplitude, wide spectral distribution, and variable topographical distribution. Therefore, de-noising of EEG is a very challenging pre-processing step prior to qualitative or quantitative EEG signal analysis. To address this issue, some de-noising approaches have been proposed for noise suppression. However, most of these methods are only available for multi-electrode EEG signal processing, besides, the co-channel interference are always left unprocessed. Aiming at the obstacles encountered by the conventional approaches in single electrode EEG signal co-channel interference suppression, a method based on time-frequency image dimensionality reduction is proposed in this paper. The innovative idea of the proposed method is that it is applicable for single electrode EEG signal enhancement and the background noise can be suppressed in entire time-frequency space. The proposed method is experimentally validated by a group of real EEG data. The experimental results indicate that the proposed method is effective in EEG single electrode co-channel interference suppression.

1. Introduction Brain-computer interfaces (BCIs) provide humans with a new communication approach between their brains and external devices [1–3], especially for the disabled people. By translating brain electrical activities typically measured by electroencephalogram (EEG) into computer commands, the communicative and environmental control abilities for severely disabled people can be reconstructed [4–9]. Recently, steady-state visual evoked potentials (SSVEPs)-based BCIs, which show advantages of little user training and high information transfer rate (ITR), have received increasing attentions [10,11]. In SSVEP-based BCIs, users gaze at one of multiple visual flickers tagged by frequencies, then SSVEP is elicited at the same frequency as the target stimulus and also its harmonics over occipital scalp areas [12,13]. Therefore, the basic idea of SSVEP-based BCI is to detect the desired commands through identifying the SSVEP target frequency in EEG. Although original SSVEP responses present relatively stable spectrums over time, they are likely to be contaminated by various sources of artifacts and other background noises. Some of these artifacts are externally generated, such as power line noise and instrumentation noise. Additionally, there is noise that is generated

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by physiological sources, external to the brain, such as eye movements, muscle activity and heart pulse. Due to the heavy artifacts and background noise, the EEG signal will be corrupted and the accuracy of the recognition of the SSVEP frequency will be influenced. Therefore, de-noising is a very important and challenging pre-processing stage for development of SSVEP-based BCI with high performance. In recent years, EEG signal de-noising has received increasing attentions. Different de-noising methods have been proposed and tested to extract noise free SSVEP responses, such as wavelets [14– 20], independent component analysis (ICA) [21–27], and adaptive filters [28–31]. To reduce the instrumentation complexity, many ambulatory systems operate using single-electrode EEG signal only [32]. In the case of single source, it is of significance importance to extract as much useful information as possible by corrupting artefact suppression or removal techniques. Therefore, the ICA methods based on multi-electrode EEG signals are not applicable in this circumstance. Besides, the adaptive filtering, due to its requirements of additional electrodes for reference purpose, is also ineffective for single-electrode EEG signal processing. Furthermore, since artifacts and other background noises span within a wide frequency range, the wavelet

Corresponding author at: School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China. E-mail address: [email protected] (G. Xu).

http://dx.doi.org/10.1016/j.sigpro.2016.11.015 Received 22 September 2016; Accepted 21 November 2016 Available online 22 November 2016 0165-1684/ © 2016 Elsevier B.V. All rights reserved.

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methods based on bandpass filtering can just suppress the noise outside the filtering frequency band while the co-channel interferences are left unprocessed. Especially for the multi-target SSVEP-based BCIs, the SSVEP target frequencies in EEG signals always vary within a relative large frequency range to represent different commands, therefore, the traditional bandpass filtering with fixed passband cannot effectively and adaptively extract the SSVEP response. To tackle the difficult problems occurred in the traditional singleelectrode EEG signal processing methods, a method which can adaptively wipe off the interference in the whole frequency band is necessary. Motivated by the concept of noise suppression based on image dimensionality reduction [33], this paper proposes a novel SSVEP response extraction method by T-F image dimensionality reduction. As time-frequency distribution (TFD) image can reveal intrinsic feature of non-stationary EEG signals, and the degrees of freedom or possible independent pixel values in the T-F image refer to image dimensionality. Thus we intend to use the dimensionality reduction method based on singular value decomposition (SVD) to suppress the background noise in raw T-F image. In the proposed method, SVD is used to transform the original T-F image, defined in a high dimensional space, to another space with fewer dimensions by subtracting the redundant or irrelevant pixel values related to background noise, without loss of valuable information of periodic SSVEP response. The minimum permutation entropy criterion is employed to optimize the selection of intrinsic dimension of the T-F matrix. The proposed method is experimentally validated by a group of real EEG data. The results indicate that the proposed method is effective in EEG co-channel interference suppression and outperforms the traditional methods. The outline of this paper is as follows. The following section presents the proposed image dimensionality reduction based T-F image noise suppression method in detail. In ‘Experimental validation’ section, the effectiveness of the proposed method is experimentally validated. Finally, conclusions are drawn in the last section.

The columns of U and V will be denoted respectively as uk ,vk , and are called left and right singular vectors of A. The singular values, δkk are real and positive valued. The rank, in other words the dimensionality of A, is directly related to the matrix ∑. The singular values (δkk ) denotes the importance of individual singular vectors in the composition of the T-F matrix. In this sense, singular vectors corresponding to the larger singular values are considered more informative and representative in the composed T-F image. The rank of A, we denote as r , is the number of non-zero values in matrix ∑. The T-F image can be rewritten taking considering the SVD factorization as, r

A=

∑ uk δk vkT

Eq. (3) indicates that the EEG signal T-F image can be decomposed in terms of a summation of sub-images as, r

A=

∑ Ak

As different sub-images Ak are orthogonal so, = 0 , it indicates that different sub-images are independent and belong to different dimensionality. Besides, the representativeness of different sub-images ( Ak ) are characterized by its singular values. Therefore, we can effectively suppress the noise in EEG signal T-F image by truncating the rank of the noise contaminated image and obtain the low-rank approximation of the image. 2.2. EEG signal representation and reconstruction The T-FD, a joint representation of a signal in both time and frequency domains, has been proved to be powerful tool for the demonstration of nonstationary features embedded in a signal. To obtain the TFD of an EEG signal x (t ), several techniques are available, such as the continuous wavelet transform (CWT), and Wigner-Ville distribution (WVD) the short-time Fourier transform (STFT). The efficacy of CWT heavily depends on the appropriate selection of shape factor and scale, thus it is not convenient in application. The WVD, due to the presence of cross-terms between different components, its application is limited. However, the STFT algorithm is easy to implement, and the STFT spectrogram gives the energy distribution and reveals intrinsic non-stationary feature of the original signal x (t ). At the same time, STFT is reversible, thus makes the reconstruction of signal components from the noise suppressed T-F image possible. Therefore, this paper uses STFT to obtain the T-F image of the noise contaminated EEG signal. The STFT of a EEG signal x (t ), with window function ws (t ), can be formulated as

2.1. Theoretical backgrounds of EEG T-F image dimensionality reduction In matrix decomposition based image denoising approaches, the image dimensionality is used to describe the degree of freedom or possible independent pixel values in the image. In this sense, the image dimensionality can be regarded as a descriptor of the image rank which is defined as the number of independent image rows or columns. Obviously, high or low image rank corresponding to high or low image dimensionality. Motivated by the idea of dimensionality reduction based image noise suppression, an EEG signal T-F image noise suppression method is proposed for SSVEP response extraction. In the proposed EEG signal noise suppression method, the noise contaminated T-F image is decomposed into a set of sub-images. By blocking some noise-related sub-images, the reconstructed image by the remaining sub-images will has smaller rank, i.e. lower dimensionality, than the original one, and the noise suppressed T-F image is obtained. Since the singular value decomposition (SVD) method as a very powerful matrix decomposition and dimension reduction tool, is used to perform dimensionality reduction in the proposed method. A SVD of an M × N matrix A, representing the T-FD of the EEG signal x, is given by

+∞

TF (τ , f ) = x, ws, τ , f =

∫−∞

x (t ) ws (t − τ ) e−ift dt

(5)

Since the STFT technique is constrained by the Heisenberg uncertainty principle, that is, the localization in time domain and the resolution in frequency domain cannot be obtained simultaneously, either of them can only be enhanced at the cost of the other one [34]. Therefore, it is very difficult to obtain the accurate target frequencies directly from T-F image. It is necessary to transform the SSVEP response pattern in noise suppressed time-frequency domain back to time domain for further commands identification. The inverse STFT (ISTFT) can be mathematically presented as

x (t ) = (1)

1 2π

+∞

+∞

∫−∞ ∫−∞

TF (τ , f ) ws (t − τ ) eift df dτ

(6)

Therefore, in the proposed method, STFT is used to form a T-F image matrix for SVD based background noise suppression and artifacts cancellation in entire frequency-band. And then, the ISTFT is employed to transform the SSVEP response pattern to time domain for commands identification.

where U (M × M ) and V (N × N )are orthogonal matrices, and ∑ is an M × N diagonal matrix with singular values as below,

∑ = diag (δ11, δ 22, …, δkk , ⋯) and δ11 > δ 22 > ⋯ > 0

(4)

k =1

2. The proposed method

A = U ∑ VT

(3)

k =1

(2) 114

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2.4. Targets identification based on canonical correlation analysis

2.3. Optimal rank approximation based on minimum permutation entropy criterion

In our experiment, we implemented Canonical Correlation Analysis (CCA) for offline target identification. Mathematically, CCA is a nonparametric multivariable method proposed to reveal the underlying correlation relationship between two sets of multidimensional variables. The essence of CCA is finding a pair of linear transformations for the two variable sets such that the transformed two sets have maximum correlation coefficients. Since the basic idea of CCA based BCI systems is stimulus frequency recognition, therefore, the experiment procedure is simplified and subject-specific training is avoided. Considering the merits of CCA based target detection methods in EEG signal processing, recently it has been widely used in SSVEP-based BCIs [38,40]. Since EEG signals exhibit approximately the same frequency properties as the target stimulus in SSVEP-based BCIs. In this paper, CCA is used as a tool to measure the correlations between stimulus frequencies and the collected EEG signals. When the user gazing at one target, the CCA coefficient at its stimulus frequency will be the largest compared with the other stimulators. And the stimulator with largest CCA coefficient is considered as the desired target for communicative and environmental control. Suppose there are N targets with stimulus frequencies f1 , …, fK in the BCI system. In the CCA based target identification algorithm, the stimulus frequency fi (i = 1, …, K ) and SSVEP response signals are introduced into CCA for the calculation of correlation coefficients. The EEG signals, are depicted as X , and collected from C electrodes with time window of M sample points. The other set is the predefined stimulus signals Si , which combines the sinusoids and cosinusoids pairs at the same stimulus frequency and its harmonics. The stimulus signals are formed as

As aforementioned, the artifacts and background noise in EEG signal are suppressed by truncating the rank of the noise contaminated T-F image and obtain the low-rank approximation of the image. In order to conduct the noise suppression effectively, the intrinsic rank of the T-F image should be appropriately selected for low-rank approximation. If the rank, i.e. intrinsic dimension is set larger, much background noise will be introduced; if it is selected smaller, some SSVEP response pattern could be left out after conducting image dimensionality reduction. Therefore, an optimal rank approximation criterion should be employed to obtain the appropriate low-rank approximation of the T-F image. As a statistical metric method, the permutation entropy (PE) refers to the local order structure of the time series, which gives a quantitative complexity measures. The mathematical backgrounds of PE can be found in [36,37]. For the given time series {x(i),i = 1, 2, …, N}, a phase space reconstruction procedure is conducted to form a vector Xi = [xi , xi+τ, …, xi+(m−1)τ] with the embedding dimension m , and the lag τ . Here, Xi is arranged in an increasing order. For m different numbers, there are m! = 1 × 2×⋯×m possible order patterns (i.e. permutations). For a permutation with number π , let f (π ) denote its occurrence frequency, and then the relative occurrence frequency is p(π)=f(π)/(N − (M − 1)τ). The normalized permutation entropy of the time series is formulated as m!

Hp = − ∑

m =1

p (π )ln p (π )/ln(m!)

(7)

Theoretically, if the time series is very regular, the PE value is close to 0. However, if the time series is random, such as in the case of white noise, the PE value is approximately 1. In SSVEP-based BCIs, the SSVEP responses simulated by the visual flickers exhibit the same frequencies as the target stimuluses, and the waveforms are approximately sine or cosine curves. Therefore, a series of sinusoidal signals with different noise intense are simulated to investigate the relationship between the PE values and different signalto-noise ratios (SNRs). In this paper, the data length N = 128, the time delay τ = 3 and the embedded dimension m = 6 , they are selected according to Yan et. al [35]. The SNRs of the noise contaminated signals are varying between −20 dB and 30 dB. The relationship between the calculated PE and different SNR values is depicted in Fig. 1. Besides, in Fig. 2, the waveforms of the simulated signal with different SNRs are shown and the corresponding PE values are presented. It can be inspected from Figs. 1 and 2 that the PE values decrease when the SNR increases. On this basis, the minimum permutation entropy criterion is used in this paper to optimize the selection of rank when performing low rank approximation of the noise contaminated T-F image. The minimum permutation entropy criterion is conducted by measuring the PE values of the periodic impulse signals transformed through the inverse STFT of the corresponding noise suppressed T-F image.

⎛ cos(2π⋅fi ⋅t ) ⎞ ⎜ ⎟ ⎜ sin(2π⋅fi ⋅t ) ⎟ 1 M ⎟ , t = , …, Si = ⎜ ⋮ fs fs ⎜ cos(2π⋅nf ⋅t )⎟ i ⎜⎜ ⎟⎟ sin(2 π ⋅ nf ⋅ t ) ⎝ ⎠ i

(8)

where fs is the sample frequency of EEG signals, and n is the number of the harmonics, which is determined by how many harmonics occurred in SSVEP response signals. Considering two multidimensional variables of X and Si , their linear transformations x = X T wx and si = S T wy , the essence of CCA is to find the weight vectors, wx and wy , which maximize the correlation between x and si through solving the following problem:

ρ (x, si ) = max

wx, wsi

E [xsiT ] E [xxiT ] E [si siT ]

= max wx, wsi

E [wxT XSiT wsi ] E [wxT XX T wx ] E [wsTi Si SiT wsi ] (9)

The maximum of ρ, which corresponding to the maximum canonical correlation between X and Si , is used to measure the significance for stimulus frequency fi (i = 1, …, K ) for target identification. 2.5. Summary of the proposed method for EEG signal Co-channel interference suppression Based on the aforementioned theoretical backgrounds, the scheme of the proposed method is demonstrated in Fig. 3 and the main procedures are listed as below. (1) For a noise and interference contaminated EEG signal x (t ), by using STFT as shown in Eq. (5), its T-F image matrix can be calculated as TF (τ , f ) of size M × N . (2) Using SVD to decompose the TF (τ , f )matrix via Eq. (1), obtain its left and right singular matrices U (M × M ) and V (N × N ), and the singular value matrix ∑ (M × M ), along with the image rank r , i.e. the dimensionality of the noise contaminated T-F image matrix.

Fig. 1. The relationship between the PE values and different SNRs.

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Fig. 2. The demonstration of the PE values of the sinusoidal signals with different SNRs.

canonical correlation analysis.

(3) Constructing the noise suppressed T-F image by image dimensionality reduction via n − rank approximation of the noise contaminated T-F image matrix, where n ∈ [1, r ]. (4) Transforming the vibration information in noise suppressed T-F image matrix back to time domain by ISTFT via Eq. (6), and obtain the extracted SSVEP response signal xn (t ) according to the n − rank truncation of the noise contaminated T-F image matrix. (5) Calculating the permutation entropy value PEn of xn (t ) via Eq. (7). Increasing the parameter n in n − rank approximation from 1 to r , repeat (3), (4), (5). (6) The noise suppressed signal which with minimum PE value is selected as the finally extracted SSVEP response for further

2.6. Illustration of the proposed method In SSVEP-based BCIs, users gaze at one of multiple visual flickers tagged by frequency or phase, resulting in SSVEPs that exhibit the same properties as the target stimulus [38]. Since the SSVEP response is very similar with cosine or sine stimulus waves used to control the motions of the visual flickers [39], therefore, a sine wave with interference is used to demonstrate the conduction steps of the proposed method. The simulated SSVEP response signal with transitory periodic cointerference is shown in Fig. 4(a), and the random noise contaminated

Fig. 3. The scheme of the proposed SVD based T-F image dimensionality reduction method.

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background noise. However, a higher rank approximation introduces more background noise than the SSVEP features, thus the PE value increases rapidly and monotonically in this interval. When n is larger than 5, the PE value closes to its maximum amplitude and changes a little. It demonstrates that the sub-image which lies in a higher dimensionality containing a little information about the original raw T-F image, and the extracted SSVEP response signal is seriously contaminated by background noise. Therefore, n = 1 is selected in low rank approximation for T-F image noise suppression based on dimensionality reduction. Applying the T-F image dimensionality reduction method with optimal selected rank approximation by minimum permutation entropy criterion, the noise-suppressed T-F image can be obtained as depicted in Fig. 5(c) (i.e. T-F image of the finally extracted signal). It can be visually inspected from Fig. 5(c) that the background noise and interference are almost totally filtered out and the periodic SSVEP response features are clearly uncovered. Finally, the ISTFT is used to transform the noise suppressed T-F image in time-frequency domain to time domain. The reconstructed signal is shown in Fig. 5(d), in which the noise components are successfully wiped off and the periodic features of the SSVEP response are enhanced. The T-F image of the background noise and interference components filtered out by the proposed method is depicted in Fig. 6. It can be observed from Fig. 6 that the noise components spread in the whole T-F image. It indicates that the proposed method is able to suppress the background noise in whole T-F image and is robust to interferences. The above illustration and the performance of the proposed method for simulated EEG signal processing indicate that the proposed SVD based T-F image dimensionality reduction method is effective for EEG signal noise and interference cancellation in entire T-F space and the SSVEP response features can be successfully uncovered for further analysis.

Fig. 4. (a) The simulated SSVEP response signal with interference, (b) the random noise contaminated signal.

signal is depicted in Fig. 4(b). It can be visually inspected from Fig. 4(b) that the waveform of SSVEP response is seriously corrupted by the random noise. In order to obtain a more accurate target identification result, the SSVEP features should be effectively extracted. The proposed method is applied to suppress the background noise and interference in Fig. 4(b). The T-F image of the original signal is firstly obtained as presented in Fig. 5(a) by performing STFT on the original signal. In the T-F image, the SSVEP features are very vague and the entire T-F image is heavily contaminated by the background noise and interference. And then, SVD is used to decompose the T-F image matrix, its left and right singular matrices along with singular value vector are obtained. The noise suppressed T-F image matrix is formed by truncating the rank of the noise contaminated image matrix, and the ISTFT is applied to reconstruct the de-noised SSVEP response signal. The permutation entropy values of the extracted signal extracted by different rank approximations are calculated for optimal rank determination. The relationship between the rank n in low-rank approximation and PE values of corresponding reconstructed signal are presented in Fig. 5(b). As depicted in Fig. 5(b), the PE value exhibits its minimal value at n = 1, that is, the extracted SSVEP response signal with least noise and interference. Whenn varies from 1 to 5, the PE value increases rapidly. It indicates that the first 5 sub-images contain most information of the original T-F image, and each sub-image is considered representative and conveys important SSVEP features or

3. Experimental validation 3.1. Experimental setup and data collection The visual stimuli targets were presented on a 21" EIZO FlexScanT966 CRT monitor with a high refresh rate (setting 100 frames/s, measured ~98 frames/s) and a resolution of 1280×800 pixels. The stimuli were arranged in a 6×4 matrix, and tagged with

Fig. 5. (a) The T-F image of the original noise contaminated signal; (b) the relationship between the rank n in low-rank approximation and PE values; (c) the noise and interference suppressed T-F image; (d) the reconstructed SSVEP response signal.

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WPT filtered signals are shown in Fig. 8, in which most of the target frequency components are uncovered with highest amplitude. It indicates that for the signal with a relative high SNR, the traditional band-pass filtering is effective for signal enhancement. However, since the essence of WPT is bandpass filtering, due to its shortcomings, the target frequencies in the CCA spectrums indicated by red boxes are still very difficult to be identified. For comparison, the proposed method is applied to further suppress the background noise and interference which was processed by the WPT based filtering. The T-F image is firstly obtained by performing STFT on the original EEG signal. And then, SVD is used to decompose the T-F image matrix, its left and right singular matrices along with singular value vector are obtained. Applying the T-F image dimensionality reduction method with optimal selected rank approximation by minimum permutation entropy criterion, the noise suppressed T-F image matrix is formed by truncating the rank of the noise contaminated image matrix. The ISTFT is employed to reconstruct the de-noised SSVEP response signal. The CCA coefficient spectrums related to the de-noised EEG signals are shown in Fig. 9. It can be visually inspected from Fig. 9 that most of the CCA coefficients related to the target frequencies which depicted by red dashed lines are uncovered and with maximum values. Especially for the CCA spectrums indicated by green boxes, the target frequencies which is very vague in Fig. 8 can be effectively identified. From a point of quantitative view, most of the CCA coefficients corresponding to the target frequencies are magnified and close to or much higher than 0.5, while that of the background noise components are suppressed and with very small values. In order to quantify the performance of the proposed method, the comparison of the CCA coefficients at the target frequencies between the original EEG signals and the noise suppressed EEG signals are demonstrated in Fig. 10. The CCA coefficients of the denoised signals by the proposed method are much higher than that of the original signals and the WPT filtered signals. Therefore, by application of the proposed method, the background noise and interference components are further suppressed and the SSVEP response is effectively enhanced.

Fig. 6. TFD of the background noise and the artefact components.

different frequencies. The horizontal and vertical intervals between two neighbouring stimuli were 4 cm and 3 cm, respectively. The program was developed under MATLAB (Mathworks, Inc). EEG signals were referenced to a unilateral earlobe, grounded at frontal position (Fpz), and sampled at 1200 Hz using a g. USBamp (g.tec Inc., Austria) system. Event triggers that indicate the onsets of visual stimuli were sent from the parallel port of the computer to the EEG system and recorded on an event channel synchronized to the EEG data. The subjects were seated in a comfortable chair 70 cm in front of the monitor in a dim room. This study performed a simulated BCI experiment to record data for offline analysis. In the experiment, subjects were asked to gaze at one of the visual stimuli indicated by the stimulus program in an incremental order for about 5 s, and complete all trials. Subjects were asked to change their concentration to the next target within the same 2 s duration. After that, all stimuli started to flicker simultaneously for 5 s on the monitor. 3.2. The application of the proposed method for EEG signal preprocessing In order to assess the performance of the proposed technique, two EEG data sets with different stimulus frequencies have been used. The stimulus frequency of the first data set ranges between 5.2 Hz and 14.4 Hz, while the second data set with stimulus frequency varies between 24.4 Hz and 33.6 Hz.

3.2.2. Case 2:EEG signals with heavy background noise In order to investigate the performance of the proposed method in the case of heavy background noise or interference, the data set with stimulus frequency varies between 24.4 Hz and 33.6 Hz is used in this study. The underlying correlation relationship between the collected EEG signals and the reference signals are obtained as demonstrated in Fig. 11 by conducting CCA. It can be observed from Fig. 11 that the amplitudes of the correlation coefficients at the stimulus frequencies, indicated by red dashed line, are very vague and the stimulus frequencies of the desired targets are hardly identified. Since the frequency band 5.2–14.4 Hz is used as stimulus frequency in our BCI system, besides the CCA spectrum are seriously contaminated by the background noise in the low frequency range, therefore, a band-pass filtering is often applied for EEG signal enhancement. The CCA spectrum of the WPT filtered EEG signal is depicted in Fig. 12, in which the noise components between 0 and 5 Hz are effectively suppressed. However, due to the drawbacks of the band-pass filtering which left the noise component in the pass-band un-processed, consequently, the weak SSVEP features are buried in the heavy background noise. It can be visually inspected from Fig. 12 that the target frequencies in the obtained CCA spectrums are still vague, therefore, the traditional WPT based band-pass filtering is invalid in the case of heavy background noise or interference. In order to uncover the target frequency information in the CCA spectrums demonstrated in Fig. 12, the proposed method is conducted on the band-pass filtered EEG signals to further suppress the background noise and interference. It should be noted that the minimum permutation entropy criterion is not applicable in this case in which the SSVEP features are seriously contaminated by the background noise. In

3.2.1. Case 1:EEG signals with relative low noise intense The CCA coefficient spectrums of the first data set with stimulus frequency ranges between 5.2 Hz and 14.4 Hz are depicted in Fig. 7. Though most of the CCA coefficients in Fig. 7 exhibit some local maximum values in the spectrum, the amplitudes corresponding to target frequencies indicated by red solid lines are less than 0.5 and not the highest. Therefore, due to the heavy background noise and strong interferences, the directly application of the CCA based target identification method will obtain a wrong target identification result by maximum CCA coefficient tracking. Since the background noise and interference in the frequency band approximate 0–5 Hz is very heavy, therefore, a bandpass filtering based on wavelet packet transform (WPT) is applied. In order to wipe off the background noise in the low frequency band, the decomposition level was set 7 and the decomposed nodes except the first one are used for filtered signal reconstruction. Since the basic idea of SSVEP-based BCIs is to detect the desired commands through identifying the SSVEP target stimulus frequency in EEG signals. Besides, the SSVEP responses in EEG signals exhibit approximately the same waveform properties as the target stimulus in SSVEP-based BCIs. Therefore, CCA is used as a tool to measure the correlations between stimulus waveforms and the de-noised SSVEP response signals. And the stimulator with largest CCA coefficient is considered as the desired target for communicative and environmental control. The CCA spectrums of the 118

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Fig. 7. The CCA coefficient spectrums of the original EEG signals with stimulus frequencies range between 5.2 Hz and 14.4 Hz.

Fig. 8. The CCA coefficient spectrums of the band-pass filtered EEG signals with stimulus frequencies range between 5.2 Hz and 14.4 Hz.

the EEG signal obtained by band-pass filtering. As a consequence, the weak SSVEP information is successfully enhanced and thereby most of the SSVEP target frequencies in the EEG signals can be effectively identified.

our experiment, we find the sub-image reconstructed according to the second largest singular value conveys most of the SSVEP information and is selected as the optimal dimension in this case. By performing the T-F image dimensionality reduction algorithm, the CCA coefficient spectrums corresponding to the de-noised signals are depicted in Fig. 13. Compared with Fig. 12, most of the CCA coefficients at stimulus frequencies indicated by red dashed lines are prominent and these corresponding to the noise components are suppressed. Therefore, by conducting the proposed T-F image dimensionality reduction method, the intrinsic SSVEP responses are effectively extracted and the stimulus frequencies are dominant in the CCA coefficient spectrums. As a consequence, most of the desired target can be accurately identified. The amplitude of CCA coefficients at the target frequencies in the CCA spectrums corresponding to the original signal, the band-pass filtered signal by WPT and the EEG signal extracted by the proposed method are depicted in Fig. 14. It can be observed from Fig. 14 that the amplitudes of the CCA coefficients obtained by the proposed method are highly magnified, when compared with the original EEG signal and

4. Discussions and conclusions Aiming at the shortcomings occurred in the current EEG signal denoising approaches, an interference suppression method based on T-F image dimensionality reduction is proposed in this paper. The image noise suppression method based on singular value decomposition provides a novel idea to extract the SSVEP response features from noisy EEG signals in time-frequency domain. The proposed method decomposes the periodic SSVEP response feature or background noise of the original raw signal into a set of independent TFD sub-images, and subtracts the noise component in the whole time-frequency space by low rank approximation. Therefore the noise component can be effectively wiped off and the SSVEP response features in timefrequency space can be enhanced significantly. The experimental 119

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Fig. 9. The CCA coefficient spectrums of the de-noised EEG signals by the proposed method.

Fig. 10. The comparison of the CCA coefficients at the target frequencies between the original signals and the de-noised signals.

Fig. 11. The CCA coefficient spectrums of the original EEG signals with stimulus frequencies range between 24.4 Hz and 33.6 Hz.

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Fig. 12. The CCA coefficient spectrums of the band-pass filtered EEG signals with stimulus frequencies range between 24.4 Hz and 33.6 Hz.

Fig. 13. The CCA coefficient spectrums of the de-noised EEG signals obtained by the proposed method.

Fig. 14. The comparison of the CCA coefficients at the target frequencies between the original signals and the de-noised signals.

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results indicates that the proposed method can effectively detect the weak SSVEP response features and provide a promising approach for single electrode EEG signal co-channel noise suppression.

[19]

[20]

Acknowledgment

[21]

This research is supported by the National Natural Science Foundation of China (No. 51475360), which is highly appreciated by the authors.

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