Keywords

1 Introduction

An EEG signal is used to denote the electrical neural actions of brain. They have frequency content ranging from 0.01 to 100 Hz that varies from a few μV to 100 μV. Apart from the classic usage in medical fields, EEG has various other applications in neuromarketing, Brain–Computer Interfaces (BCIs), and biometrics. Among the aforesaid applications, the most versatile application is biometrics. By extracting the suitable features, EEG is used in human biometric recognition [1]. Since EEG signals have extremely small amplitudes and thus can easily be polluted by distinct artifacts such as ocular, muscular, cardiac, glossokinetic, and environmental, these artifacts have a perturbing effect on EEG classic bands. It is important to remove these artifacts so that features can be extracted fruitfully. To tackle these artifacts, innumerable methods and techniques have been discovered by different scholars for filtering of noise in the last few decades [2,3,4]. This comprises conventional filtering techniques which include bandpass filtering [1] as well as the algorithms used for blind source separation like ICA [5]. Also, simply eliminating noisy EEG instants is one of the frequently used ways. But this process involves checking the data manually, spotting noisy sections, and then finally removing those parts. This procedure is tough and results in undesirable information failure when there is a high strength of impurity [6]. A substitute to the aforementioned procedure is to eliminate the artifacts from the data which comprises different methods such as SWT [7], Independent Component Analysis (ICA) [5, 8], etc. ICA is a multichannel approach and it cannot be applied directly to single-channel EEG signal. It is used to extort statistically independent components from a set of measured components. James and Gibson [5] presented a technique which used ICA to expel ocular artifacts from EEG signals. The extracted components were not ordered. Devuyst et al. [9] proposed a modified ICA algorithm used to eliminate ECG noise [10, 11] in EEG or EOG but this method was computationally inefficient. Hyvarinen et al. [12] applied ICA to short-time Fourier transforms of spontaneous EEG but partitioning of impulsive brain actions into source signals was unsuccessful. Since ICA cannot be applied to a single channel, therefore the combinational approach of SWT and ICA is proposed. SWT is used to decompose the signal and ICA is applied. SWT–ICA components are reconstructed back from denoised signal.

The remaining part of this paper is organized as follows. Section 2 describes the proposed EEG signal denoising approach. The methodologies used at each stage are explained in detail in Sects. 2.1, 2.2, and 2.3, respectively. The experiments performed and the achieved results for the reconstructed EEG signals are reviewed in Sect. 3. Finally, Sect. 4 summarizes the concluded work.

2 Proposed EEG Signal Denoising Approach

Noise can be interpreted as a disturbance which affects the signal peaks and results in signal distortion. EEG signals are considered to exhibit chaotic behavior as they are generated by random processes. Addition of Gaussian noise (AWGN) to EEG signal declines the signal quality, and it becomes difficult to interpret its characteristics. Based on the proposed EEG denoising approach, first of all the noisy input EEG signal is decomposed using the SWT. After signal decomposition, the obtained approximate and detailed coefficients are processed using soft thresholding process. Among the various ICA algorithms, fast ICA is preferred for denoising [13] since it increases the computational efficiency. Finally, reconstruction is done to retrieve the processed denoised signal [2]. The complete methodology has been pictured as per the block diagram in Fig. 1.

Fig. 1
figure 1

Block diagram of EEG denoising

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Various sub-modules of the above block diagram are explained in the following subsection.

2.1 Stationary Wavelet Transform (SWT)

To preserve the translation invariance property, Stationary Wavelet Transform (SWT) is used. In this paper, SWT is chosen for decomposition using mother wavelet “symlet” up to six levels. The decomposition formulae of SWT are shown in Eq. (1).

$$ \begin{aligned} A_{j,k1,k2} & = \sum\limits_{n1} {\sum\limits_{n2} {h_{o}^{{ \uparrow 2^{j} }} \left( {n_{1} - 2k_{1} } \right)h_{o}^{{ \uparrow 2^{j} }} \left( {n_{2} - 2k_{2} } \right)A_{{j - 1,n_{{1,n_{2} }} }} } } \\ D_{j,k1,k2}^{1} & = \sum\limits_{n1} {\sum\limits_{n2} {h_{o}^{{ \uparrow 2^{j} }} \left( {n_{1} - 2k_{1} } \right)g_{o}^{{ \uparrow 2^{j} }} \left( {n_{2} - 2k_{2} } \right)A_{{j - 1,n_{{1,n_{2} }} }} } } \\ D_{j,k1,k2}^{2} & = \sum\limits_{n1} {\sum\limits_{n2} {g_{o}^{{ \uparrow 2^{j} }} \left( {n_{1} - 2k_{1} } \right)h_{o}^{{ \uparrow 2^{j} }} \left( {n_{2} - 2k_{2} } \right)A_{{j - 1,n_{{1,n_{2} }} }} } } \\ D_{j,k1,k2}^{3} & = \sum\limits_{n1} {\sum\limits_{n2} {g_{o}^{{ \uparrow 2^{j} }} \left( {n_{1} - 2k_{1} } \right)g_{o}^{{ \uparrow 2^{j} }} \left( {n_{2} - 2k_{2} } \right)A_{{j - 1,n_{{1,n_{2} }} }} } } \\ \end{aligned} $$
(1)

where \( A_{j,k1,k2} ,D^{1} {}_{j,k1,k2} \), \( D^{2}_{j,k1,k2} \), and \( D^{3}_{j,k1,k2} \) are the low-frequency components, the horizontal high-frequency component, vertical high-frequency component, and diagonal components of the SWT, respectively. \( h_{o}^{ \uparrow 2j} \) and \( g_{o}^{ \uparrow 2j} \) are used to denote that \( 2^{j} - 1 \) zeros are inserted between the two points \( h_{o} \) and \( g_{o} \) [14].

2.2 Soft Thresholding

Soft thresholding is used for denoising EEG signal [15] by applying it to transform-domain representation of the signal. It shrinks the noisy coefficients above the threshold and makes the algorithms more manageable. After SWT decomposition, soft thresholding is applied to the obtained detailed coefficients. For soft thresholding, the following nonlinear transform is used shown in Eq. (2) [16]:

$$ \hat{z}(x) = {\text{sign}}(x) \cdot \left( {\left| x \right| - \left. {T_{h} } \right)_{ + } } \right. $$
(2)

Here, x denotes the noisy coefficient, z denotes the noise-free coefficient, and n represents noise. The aim is to estimate w from the noisy observation y. The estimate will be denoted as \( \hat{z} \). Because the estimate is dependent on the observed (noisy) value x, estimate can be denoted as \( \hat{z}(x) \) as shown in Eq. (3).

$$ \hat{z}(x) = \left\{ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {x + T_{h} ,} & {x < T_{h} } \\ \end{array} } \\ {\begin{array}{*{20}c} {0,} & { - T_{h} \ll x \ll T_{h} } \\ \end{array} } \\ {\begin{array}{*{20}c} {x - T_{h} } & {T_{h} < x} \\ \end{array} } \\ \end{array} } \right. $$
(3)
$$ T_{h} = \frac{{\sqrt 2 \sigma_{n}^{2} }}{\sigma } $$
(4)

where Th is the threshold.

2.3 Fast ICA

ICA is an approach which extracts statistically independent components from the set of measured signals. ICA algorithm is suitable when the number of sources is greater than the number of channels, i.e., it can be applied to multiple channels only. In the case of single channel, the combination of SWT and ICA has been applied presently. Among various ICA algorithms, fast ICA is used because fast ICA is an efficient and popularly used algorithm for blind source separation [17]. It is computationally efficient and requires less memory over other algorithms as it estimates the independent components one by one. It also has the advantage of multicomponent extraction, and the system performance is not degraded. The modeling of ICA is done by Eq. (5) stated as

$$ Z = A_{m} \cdot s_{D} $$
(5)

where Z denotes the observed matrix, sD indicates the determined sources, and Am denotes the separating matrix. ICA is majorly used to identify the separating matrix X so as to attain the independent components under the prerequisites of independent criteria.

$$ s_{D}^{ * } = X \cdot Z $$
(6)
$$ X = A_{m}^{ - 1} $$
(7)

If coefficients sD* are regarded as independent sources, then a procreative linear statistical model is acquired. Additionally, if Am is assumed to be squared and invertible, the standard ICA model [1] is required. In this work, fast ICA approach [17, 18] is applied to the disintegrated signals to calculate mixing and separating matrices (Am and X, respectively) as well as to the matrix of independent components. Subsequently, the significant sources are selected according to obtained SNR values. Hence, the independent component with the maximum SNR value is the reconstructed signal.

3 Results and Discussions

The EEG recordings during visual relaxation used in this work were downloaded from PhysioBank ATM [19, 20]. The database comprises EEG recordings from 14 subjects with duration of 10 s each. The signals were exported in the .csv format. Using the database, different magnitudes of AWGN noises with SNR values ranging from 5 to 20 dB were added by simulation. Decomposition using SWT was performed with mother wavelet symlet and decomposition level 6. Soft thresholding was then applied to the decomposed EEG signals. Fast ICA using the kurtosis technique was adopted and implemented to attain maximized non-Gaussianity. The convergence criteria (C = 0.00 and max. iterations = 100) were assumed to minimize Gaussianity. After this, the reconstructed EEG signals are obtained as presented in Fig. 2.

Fig. 2
figure 2

a, b Original EEG signals 1 and 2, respectively of SNR  = 10 dB. c, d Noisy EEG signals 1 and 2, respectively, of SNR  = 10 dB. e, f Reconstructed EEG signals 1 and 2, respectively, of SNR  = 10 dB

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The performance evaluation and comparison of various obtained results are done using the parameter SNR. Figure 2 shows experimentation of SNR(noise) = 10 dB on two different signals. The SNR of reconstructed signal was 25.20 and 26.05 dB, respectively. This experiment was repeated for various values of SNR, i.e., 5, 10, 15, and 20 dB, respectively. Table 1 shows the comparison of results on the basis of several SNR values. The observed trend shows that on increasing the SNR(noise), the SNR of reconstructed signal goes on decreasing. These obtained results clearly present the efficiency of the proposed approach. Higher SNR values of the reconstructed signals prove that the applied algorithms have worked efficiently.

Table 1 Various results obtained with varying SNR (dB) values using SWT–ICA on signal#1
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4 Conclusion

In this work, a methodology has been proposed for the denoising of single-channel EEG signal on the principle of combined usage of SWT–ICA approach. Here, the artifacts modeled as Gaussian noises on varying SNR values are added to the original EEG signal and then processed through the proposed algorithm. This approach presents high SNR values of the reconstructed EEG signals over the single-channel small-scale database. The maximum value of SNR of reconstructed signal is obtained at the lowest value of SNR(noise), i.e., 5 dB. The conclusion can be made that the proposed approach eliminates the noise at higher rate on lower SNR values. For future prospects, the processed EEG signal can be used for numerous applications like human biometric authentication, clinical and research applications, etc. Proper preprocessing enhances recognition accuracy for biometric applications. The proposed approach facilitates the usage of single-channel EEG for various applications.