A hybrid method for artifact removal of visual evoked eeg

Journal Pre-proof A HYBRID METHOD FOR ARTIFACT REMOVAL OF VISUAL EVOKED EEG Priyalakshmi Sheela (Conceptualization) (Methodology) (Software) (Formal analysis) (Writing - original draft), Subha D. Puthankattil (Supervision)Writing - reviewing and editing)

PII:

S0165-0270(20)30060-1

DOI:

https://doi.org/10.1016/j.jneumeth.2020.108638

Reference:

NSM 108638

To appear in:

Journal of Neuroscience Methods

Received Date:

18 October 2019

Revised Date:

27 January 2020

Accepted Date:

18 February 2020

Please cite this article as: Sheela P, Puthankattil SD, A HYBRID METHOD FOR ARTIFACT REMOVAL OF VISUAL EVOKED EEG, Journal of Neuroscience Methods (2020), doi: https://doi.org/10.1016/j.jneumeth.2020.108638

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A HYBRID METHOD FOR ARTIFACT REMOVAL OF VISUAL EVOKED EEG

Priyalakshmi Sheelaa, Subha D. Puthankattila,* a

Department of Electrical Engineering, National Institute of Technology, Calicut 673601, Kerala, India

Highlights

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Proposed noise removal scheme includes digital filters, ICA and TARA Independent Component Analysis eliminates ocular artifacts Transient Artifact Reduction Algorithm is employed to suppress other artifacts Performance metrics: Signal-to-noise ratio, sample entropy, correlation coefficient Performance comparison with wavelets, EMD variants and TVD methods

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Abstract Background

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The visual evoked Electroencephalogram (EEG) signals are useful indicators to explore the hidden neural circuitry in human brain. But these signals are highly contaminated with a plethora of artifacts arising from power interference, eye, muscle and cardiac movements. Since the interference components include neural activity also, the existing techniques result in the distortion of the underlying cerebral signals. New Method

Results

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To address the aforementioned problem, the current study proposes a hybrid method for denoising the visually evoked EEG responses. According to the proposed method, a cascade combination of digital filters, Independent Component Analysis (ICA) and Transient Artifact Reduction Algorithm (TARA) is utilized to suppress the artifacts. ICA technique automatically eliminates the ocular artifacts. The interference due to the remaining artifacts is removed through TARA.

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The artifact removal ability of the proposed heuristics is evaluated in terms of SNR, correlation coefficient and sample entropy. The ICA results exhibit an increase of 13.47% in SNR values on simulated signals and 26.66% on real data. The application of TARA on simulated and real signals results in further SNR gain of 6.98% and 71.51% respectively. Significant statistical difference is also observed in this method (𝑝 < 0.05). Comparison with Existing Methods This approach outperforms previous methods based on wavelets, enhanced variants of empirical mode decomposition and earlier versions of total variation denoising. Conclusion ICA-TARA effectively eliminates the major artifacts without compromising the interpretation of the underlying neural state in both simulated and real visual evoked EEG. Abbreviations: ADI-R, Autism Diagnostic Interview-Revised; ADOS-2, Autism Diagnostic Observation Schedule-2; ASD, Autism Spectrum Disorders; CEEMDAN, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise; EEG, Electroencephalogram; EEMD,

2 Ensemble Empirical Mode Decomposition; EMD, Empirical Mode Decomposition; ICA, Independent component analysis; LTI, Linear Timeinvariant; MTVD, Moreau-enhanced Total Variation Denoising ; PCA, Principal Component Analysis; TARA, Transient Artifact Reduction Algorithm; TVD, Total Variation Denoising; *Corresponding author at: Department of Electrical Engineering, National Institute of Technology, Calicut 673601, Kerala, India Tel.: +91-495-2286310 E-mail address: [email protected]

Keywords Electroencephalogram, Independent Component Analysis, Wavelets, Empirical mode decomposition, Total variation denoising, Transient Artifact Reduction Algorithm 1.

Introduction

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The visual evoked Electroencephalogram (EEG) represents the electrical activity of the brain in presence of a visual stimulus. In the context of increasing medical need over the last decades, visual evoked EEG responses has evolved as a significant diagnostic tool for monitoring and diagnosing various neurological disorders including schizophrenia, Alzheimer's disease, migraine headache and Autism Spectrum Disorders (ASD) (Sayorwan et al., 2018). These recordings are often contaminated by ocular artifacts (eye movements and eye blinks) and artifacts due to muscle movements, cardiac activities and powerline noise. Many of these artifacts have amplitude higher than that of the EEG recordings and their spectra overlap. As a result, they interfere and distort the results of signal analysis. Hence artifact removal is an integral part of any signal analysis technique. Moreover, the EEG responses lack a well-defined morphology (Bono et al., 2016). This in turn triggered copious research in developing techniques to decontaminate these signals.

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1.1. Related Works

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Most of the earlier studies utilized conventional linear time-invariant (LTI) filters (notch and bandpass filters) for eliminating powerline interference and other artifacts related to eye and muscle movements. In the assumption that most of the vital information in brain signals are concentrated in frequencies below 100Hz, many clinical investigations employed digital low pass and bandpass filters with cut-off frequencies below 100Hz (Catarino et al., 2013; Oberman et al., 2005; Sheikhani A, Behnam H, 2008; Sheikhani et al., 2008). To remove the effect of line noise, digital notch filters with notch frequencies 50Hz or 60Hz, were added in addition to other filters (Nowicka et al., 2016; Sheikhani A, Behnam H, 2008; Stroganova et al., 2007; Tsai et al., 2011). But filtering techniques resulted in the loss of neural information. Hence it was replaced by other methods based on regression and blind source separation (BSS). The regression method required a reference channel like Electrooculogram (EOG) to identify contaminated parts (Klados et al., 2011). Such reference channels are not available in the case of other artifacts like EMG. In many studies, ocular and muscle artifacts were eliminated through visual inspection of the measured signals. The data segments containing signal amplitude above a fixed threshold value were discarded as contaminated with eye blinks. The fixed threshold was estimated based on the measured vertical and horizontal EOG signals. BSS methods such as Principal Component Analysis (PCA), Canonical Correlation Analysis (CCA) and Independent Component Analysis (ICA) were used to decompose the mixed EEG signals into component signals and artifacts. ICA was more efficient and was adopted in many studies using extended Infomax ICA in EEGLAB toolbox (Milne et al., 2009; Nowicka et al., 2016) but it’s efficacy in removing EMG noise was not up to the mark. With the development of new ICA algorithms, ICA evolved as one of the best BSS technique for eliminating multiple artifacts (Nolan et al., 2010) The time-frequency localization property of wavelet transform was utilized in several studies and in combination with other BSS techniques for decontaminating the visual evoked EEG signals (Burger and Van Den Heever, 2015; Carmona, R.A. and Hudgins, 1994; Jadhav et al., 2014). Unlike wavelet decomposition technique, Empirical mode decomposition (EMD) does not need predefined basis functions and the basis function of EMD is derived from the signal itself. The EMD technique decomposes the signal into oscillatory components called intrinsic mode functions (IMFs). The noisy IMFs are excluded during signal reconstruction. One of the notable demerits of EMD technique is mode-mixing problem, which was circumvented through the development of Ensemble Empirical Mode Decomposition (EEMD). EEMD was further modified into Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to minimize the effect of residual noise in the modes. EMD and it’s modified versions in conjunction with BSS techniques have found immense utility in removing artifacts from the visual evoked brain responses (Chang et al., 2013; Kanoga et al., 2015; Molla et al., 2010; Patel et al., 2016a, 2016b). Successful efforts

3 were made to combine genetic algorithm and support vector machine to develop an automated denoising method for visual evoked brain signals (Abbaspour et al., 2019). Majority of these investigations were focused on blink rejection as ocular artifacts cause the most remarkable harm to the visual evoked EEG data. However, the EEG data from ASD subjects reveal the detrimental effect of other artifacts along with blinks thus necessitating its removal. With the growing body of research, new signal processing toolboxes were developed to deal away with multiple types of artifacts. Some ASD investigations employed toolboxes including FieldTrip (Fiebelkorn et al., 2013; Orekhova et al., 2014), Brain Vision Analyzer software package (Boersma et al., 2013) and BESA software (Takarae et al., 2016) for rejecting artifacts from visual evoked EEG. On account of the reviews from technical literature, it is found that the presence of artifacts still pose a great obstruction in the analysis of signals obtained from non-invasive modalities like visual evoked EEG responses. No optimal technique has been developed for every noisy scenario. It is highly dependent on characteristics of the signal and the type of artifacts present in it.

Material and Methods

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This work, in particular, has identified a cascade type of artifact removal techniques for effectively eliminating artifacts from the EEG responses measured during visual stimuli. The proposed technique is a combination of different digital filters, ICA and a modified variant of total variation denoising (TVD) termed as Transient Artifact Reduction Algorithm (TARA), all connected in cascade. The rest of this paper is organized as follows: Section 2 explains about the acquisition of simulated and real visual evoked EEG signals. It also elucidates the proposed artifact removal technique. Section 3 illustrates the results obtained under each method and gives a comparative analysis of the different techniques based on signal-to-noise ratio, correlation coefficient and sample entropy. In addition, the results are validated through statistical analysis. Conclusions are drawn in Section 4.

2.1 Simulated Data

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As the impact of the visual stimulus is more evident in the occipital region, visual evoked EEG signals from O1, O2, Oz and POz electrode locations are investigated here. These simulated signals are obtained based on the study by Aznan et al. (Aznan et al., 2019). The major artifacts considered are the interferences due to power line, ocular and muscle activities. These are artificially simulated and mixed with the simulated data (Abdullah et al., 2014; Delorme et al., 2010). Power line interference is removed with the aid of a digital notch filter before testing the signals with the proposed technique. 2.2 Real Data Acquisition

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The EEG signals were recorded from 10 individuals with ASD who satisfied DSM 5 criteria using Autism Diagnostic Interview-Revised (ADI-R) and Autism Diagnostic Observation Schedule-2 (ADOS-2), in response to visual stimuli. The stimuli consisted of vertical circular gratings oscillating at 3.76 Hz at varying contrasts (5,10,20,.....90%, 10 levels) presented for different trials. Each trial set contained EEG signals measured for 6.5s during application of stimulus and 0.5s prior and post to it. The detailed description of the data used in this study is available in the research study conducted by Takarae et al. in 2016 (Takarae et al., 2016). The recorded EEG signals were sampled at 1kHz.The artifacts caused by power line interference have been removed by using a digital notch filter with cut-off frequency at 60 Hz. For removing periodic noise, a digital Butterworth low pass filter with passband frequency of 70 Hz and stopband frequency of 100 Hz has been employed. 2.3 Methods 2.3.1

Independent component analysis

Independent component analysis (ICA) is a kind of blind source separation technique that transforms multidimensional mixed signals into statistically independent components. This technique also results in the reduction of dimension of data. Over the years, ICA has been effectively used for the elimination of ocular artifacts. The ICA is more advantageous in that it ensures statistical independence among output patterns while PCA only guarantees that they are uncorrelated. FastICA is a popular algorithm for separating a set of linearly mixed statistically independent sources. The mathematical model of ICA is as follows (Hyvarinen and Oja, 1997): 𝑝 = 𝐵𝑞 + 𝑛

(1)

4 where 𝑝 and 𝑞 are N-dimensional vectors of observed signals and independent source components given by 𝑝 = (𝑝1 , 𝑝2 , … … , 𝑝𝑛 )𝑇 and 𝑞 = (𝑞1 , 𝑞2 , … . . , 𝑞𝑛 )𝑇 while 𝑛 represents the noise component and 𝐵 is the unknown mixing matrix. The main aim is to retrieve 𝑞 from 𝑝 using the transformation 𝑢 = 𝑊𝑝 = 𝑊𝐵𝑞

(2)

where 𝑢 is the estimated independent components and 𝑊 is the demixing matrix.

Transient Artifact Reduction Algorithm

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Numerous algorithms have been developed to determine the demixing matrix 𝑊 among which Joint Approximate Diagonalization of Eigen-matrices (JADE), SOBI, FastICA and Infomax are the most commonly used ones. In this study, we have used an improved version of FastICA algorithm known as efficient FastICA (EFICA). Owing to it’s asymptotic efficiency, EFICA is preferred in noisy scenario (Zbynek Koldovský, Petr Tichavský, 2006). In this paper, the EFICA algorithm is implemented using EEGLAB toolbox. The independent components containing ocular artifacts are identified with the aid of fractal dimension criterion and therefore excluded in the reconstruction stage (Gómez-Herrero et al., 2006). This method yields EEG signals freed of ocular artifacts. Most of the noise components are rejected by ICA technique but for higher levels of contamination, ICA algorithm may not be sufficient. This highlights the need of a secondary denoising technique.

𝑢(𝑛) = 𝑠(𝑛) + 𝑔(𝑛) where

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The sparsity-based denoising techniques have replaced the conventional linear time-invariant (LTI) filters in the past few years. Total Variation Denoising (TVD), which is a non-linear filtering technique has turned into an attractive alternative to existing denoising methodologies. The most notable features of TVD are it’s ability to retain the sharp discontinuities and avoid pseudo-Gibbs phenomena. Unlike a conventional low-pass filter, TV denoising is expressed in the form of an optimization problem and is applicable only for piece-wise constant signals. The cost function defining the optimization problem is minimized so as to obtain the output of the TVD filter. TV denoising is implemented by solving the optimization problem with the aid of suitable algorithms. Total variation denoising assumes that the noisy data 𝑢(𝑛) is of the form (3)

𝑢(𝑛) − blink-free noisy signal

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𝑠(𝑛) − piece-wise constant signal 𝑔(𝑛) −White Gaussian noise

The signal 𝑠(𝑛) is determined by solving the unconstrained optimization problem 1

2 𝑁−1 𝑎𝑟𝑔𝑠 min { ∑𝑁−1 𝑛=0 |𝑢(𝑛) − 𝑠(𝑛)| + 𝜆 ∑𝑛=1 |𝑠(𝑛) − 𝑠(𝑛 − 1)|} 2

λ – regularization parameter to control the degree of smoothing

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where

(4)

The first term in equation (4) represents the variations of the original 𝑠(𝑛) from 𝑢(𝑛) and the second term is a measure of the fluctuations within the signal 𝑠(𝑛). The aim of the optimization problem is to vary λ in such a way so as to minimize the difference between 𝑠(𝑛) and 𝑢(𝑛). Transient Artifact Reduction Algorithm (TARA) is a modified version of TVD. In this technique, the noisy signal 𝑢(𝑛) is modeled as the sum of the low-pass component 𝑙(𝑛), additive white Gaussian noise 𝑔(𝑛), type1 artifact 𝑠1 (𝑛) and type 2 artifact 𝑠2 (𝑛). 𝑢(𝑛) = 𝑙(𝑛) + 𝑠1 (𝑛) + 𝑠2 (𝑛) + 𝑔(𝑛)

(5)

5 Type1 artifacts refer to the sparse component and it’s derivatives within the signal while type 2 artifacts include step discontinuities or it’s approximations. Compared to an earlier TVD version known as Simultaneous Low Pass Filtering/Compound Sparse Denoising (LPF/CSD) which removed only type1 artifacts, TARA eliminates type2 artifacts also which in turn improves the quality of the denoised signal. In addition, TARA employs non-convex penalty functions which gives a more accurate estimation of the underlying transients. The optimization problem is formulated as in (Selesnick et al., 2014b). 1

2 {𝑠̂1 , 𝑠̂2 } = 𝑎𝑟𝑔 𝑚𝑖𝑛 𝑠1, 𝑠2 { ‖𝐻(𝑢 − 𝑠1 − 𝑠2 )‖2 + 𝜆0 ∑𝑛 ∅0 ([𝑠1 ]𝑛 ) + 𝜆1 ∑𝑛 ∅1 ([𝐷𝑠1 ]𝑛 ) + 𝜆2 ∑𝑛 ∅2 ([𝐷𝑠2 ]𝑛 )} 2

where

(6)

𝐻 is the high-pass filter 𝜆0 , 𝜆1 and 𝜆2 are the regularization terms

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∅0 , ∅1 and ∅2 are the non-convex penalty functions

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The first term of equation (6) refer to the data fidelity term while the other three terms form the penalty functions corresponding to type 1 and type2 artifacts. The regularization terms are varied in such a way so as to minimize the noise. The equation (6) can be rewritten in terms of banded matrices for fast computation. 1

−1 −1 2 {𝑠̂1 , 𝑠̂2 } = 𝑎𝑟𝑔 𝑚𝑖𝑛 𝑠1, 𝑠2 { ‖𝐻𝑢 − 𝐵𝐴 𝑠1 − 𝐵1 𝐴 𝐷𝑠2 ‖2 + 𝜆0 ∑𝑛 ∅0 ([𝑠1 ]𝑛 ) + 𝜆1 ∑𝑛 ∅1 ([𝐷𝑠1 ]𝑛 ) + 𝜆2 ∑𝑛 ∅2 ([𝐷𝑠2 ]𝑛 )}

where 𝐴, 𝐵 and 𝐵1 are banded matrices

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𝐷 and 𝐴−1 are matrices representing LTI systems

(7)

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Here, the optimization problem is solved using majorization-minimization approach. TARA offers an additional advantage that it can be parametrized in terms of shape parameters (𝛳, 𝛽) and pseudo-noise standard deviation 𝜎 instead of (𝜆0 , 𝜆1 , 𝜆2 ). The regularization parameters are evaluated as follows (𝜆0 , 𝜆1 ) = (𝛳𝜆0 ∗ , (1 − 𝛳)𝜆1 ∗ ),

0≤ 𝛳≤1

(8)

𝜆2 = 𝜆1 ∗ ,

𝛽 ϵ [1, 2]

(9)

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𝜆0 ∗ =3‖𝑝0 ‖2 𝜎 𝜆1 ∗ =3‖𝑝1 ‖2 𝜎

(10) (11)

where 𝑝0 and 𝑝1 refer to the impulse responses of the LTI filters 𝐻𝑇 𝐻 and 𝐻1𝑇 𝐻 respectively The utilization of non-convex penalty functions ∅𝑖 requires the setting of non-convexity parameters 𝑎𝑖 as given below. 𝑎0 =0.5‖ℎ‖22 /𝜆0 , 𝑎1 =0.5‖ℎ1 ‖22 /𝜆1 , 𝑎2 =0.5‖ℎ1 ‖22 /𝜆2

(12)

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where ℎ and ℎ1 are the impulse responses of the systems 𝐻 and 𝐻1 described by 𝐻 = 𝐴−1 , 𝐻1 = 𝐵1 𝐴−1

(13)

The values of 𝛳, 𝛽 and 𝜎 are fixed keeping in view to preserve the non-convexity of the cost function. In this study, 𝛳 =0.05, 𝛽=1.4 and 𝜎=1 are considered for real data. In case of simulated data, the parameter values are taken as 𝛳 =1, 𝛽=1 and 𝜎=0.1. 2.3.3

Performance Metrics

Sample entropy (SampEn) is a non-linear measure that indicates the complexity of a time series. Due to the presence of more regular patterns, SampEn of eye blinks are lesser than that of other artifacts (Liao and Fang, 2013; Mahajan

6 et al., 2013). SampEn is computed for the noisy and ICA-denoised signals. An increase in SampEn value indicates reduction of blinks. SampEn of the EEG responses having 𝑁 length is calculated using the algorithm given in (Liang et al., 2015). 𝑆𝑎𝑚𝑝𝐸𝑛(𝑟, 𝑚, 𝑁) = − ln

𝐹𝑚 (𝑟)

(14)

𝐺 𝑚(𝑟)

where 𝐹 𝑚 (𝑟) and 𝐺 𝑚 (𝑟) are the total number of template matches estimated at embedding dimension 𝑚 and 𝑚 + 1 within a distance of 𝑟.

2.3.4

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The correlation coefficient is another measure evaluated to measure the similarity between two signals. The value lies in the range [0,1] with 1 indicating higher correlation and 0 indicating lower correlation. In this study, cross-correlation is computed in two ways. While dealing with simulated data, it is computed between denoised and original signal. But in case of real data, due to the unavailability of the original signal, cross-correlation is calculated between noisy and denoised signals. A high correlation is expected in the case of simulated data while a low value is favourable for real data. Signal-to-noise ratio (SNR) is the ratio of the power of signal to that of noise in decibels. In this work, SNR is evaluated for the signals prior and post to the application of various denoising methods.

Proposed Technique

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The proposed denoising technique for the EEG responses evoked through visual stimuli includes a series of digital filters, ICA and TARA methods. The framework of the proposed technique is as shown in Fig. 1.

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Fig. 1. Framework of the proposed denoising technique

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The interference due to powerline and high frequency spurious signals are eliminated through digital notch and low pass filters with notch frequency at 60Hz and passband frequency of 70Hz respectively. The ocular artifacts being one of the major contributors are removed through ICA method. This is accomplished with the help of EFICA in EEGLAB toolbox. The effectiveness of this method is evaluated using SNR and SampEn. An increase in SNR and SampEn is an indication of effective removal of blinks from the signals. The remaining transient artifacts are eliminated employing TARA, a modified variant of TVD technique. TARA removes both type 1 and type 2 artifacts from the blink removed signals. To highlight the ability of TARA method in denoising, the EEG responses freed of blinks are subjected to denoising techniques based on wavelets and variants of empirical mode decomposition and TVD. A comparison regarding the denoising capability is made using SNR, sample entropy and correlation coefficient. Increased SNR always points to enhanced signal power in the denoised signal which is highly desirable. A considerable decrease in cross correlation between the signals prior and post to artifact removal is favourable for real data while high correlation is expected with simulated original signal. The elimination of blinks imparts a larger value to sample entropy. The procedure involved in the proposed algorithm is outlined below: 1. 2. 3. 4.

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Fetch the input: Raw visual evoked EEG signal Power line interference removal: A digital notch filter with notch frequency 60Hz is employed. Elimination of periodic noise: A digital low pass filter with passband frequency of 70Hz and stopband frequency of 100Hz effectively removes high frequency spurious signals. Removal of ocular artifacts: EFICA algorithm is utilized. i. Decompose the filtered signals into spatial independent components ICs. ii. Identify artifactual ICs using fractal dimension criterion. iii. Reconstruct the blink free signals from non-artifactual ICs. Rejection of the remaining transient artifacts with the aid of TARA technique. i. Identification of type 1 and type 2 artifacts from the blink removed signal.

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ii. Subtracting the identified artifacts from the blink free signal. Retrieve the output: Artifact free visual evoked EEG 2.4 Comparison with Existing Techniques

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To evaluate the performance of the proposed approach in comparison to the state-of-the-art, previous techniques based on wavelets, EMD variants and TVD methods are taken into account. The most popular wavelet denoising approach is based on shrinkage where the EEG signals are decomposed into wavelets and noise is eliminated using thresholding and shrinkage (Donoho, 1994). In EMD, the denoised signal is reconstructed by excluding the noisy IMFs from the whole signal. The notable demerits of EMD technique are mode-mixing and end-effect that adds significant error through repeated sifting process (Tyagi and Yadav, 2017). To circumvent mode-mixing problem, Ensemble Empirical Mode Decomposition (EEMD) was developed. EEMD involves addition of independent series of Gaussian white noise to the signal which is further decomposed using EMD followed by averaging of the resultant IMFs (Agarwal, M. and Priyadarshani, 2014). However, EEMD reconstructed signals contains residual noise thereby resulting in different varied number of modes. To overcome this problem, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) was introduced which provided a faithful reconstruction of the original signal (Torres et al., 2011). In CEEMDAN, a mode is computed by adding noise in each decomposition thus obtaining a unique residue in each stage. Since the first IMF contains most of the high frequency noise, it is excluded in the reconstruction stage to form denoised signal.

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The basic TVD algorithm cannot efficiently remove noise from signals which can neither be confined to a particular frequency band nor given a sparse representation. As a result, Selesnick et al. derived a variant of TVD called Simultaneous Low-Pass Filtering TVD (LPF/TVD) which incorporates the benefits of both LTI filters and TVD (Selesnick et al., 2014a). In this technique, the noisy signal is composed of sparse-derivative component along with a low-frequency component and a noise term. An optimization-based approach is utilized to estimate these components from the noisy signal. LPF/CSD is a more generalised version of LPF/TVD in which the signal itself is considered to be sparse itself and contains a sparse derivative (Selesnick et al., 2014a). Hence two regularization parameters are included in the optimization problem. The denoised signal obtained through LPF/TVD has transient artifacts at it’s end-points. These unwanted artifacts are avoided in sparsity assisted signal smoothing (SASS) technique which is an extension of LPF-TVD (Selesnick et al., 2017a). It is suitable for signals that have jump discontinuities in it’s derivative but is otherwise smooth. While LPF/TVD and LPF/CSD are limited to signals with first order sparse derivatives, SASS approach can be implemented on 𝐾-order sparse derivatives. Compared with wavelet-based denoising, this method does not induce any artifacts. Moreau-enhanced Total Variation Denoising (MTVD) technique employs a penalty function which is both non-separable and non-convex (Selesnick et al., 2017b). Compared to the previous TVD techniques, this kind of penalty function preserves the convexity of the cost function while guaranteeing a unique solution. The jump discontinuities within the signal can be estimated with the aid of this new penalty. The parameter values of different methods considered for comparison is shown in Table 1.

Results and Discussion

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In this section, the proposed method is tested on both simulated and real visual evoked EEG signals. After removing power line interference and periodic noise with the aid of digital filters, the visual evoked EEG signals are subjected to ocular artifact removal. The ocular artifacts including eye blinks almost always co-occur with the visual evoked EEG as the real data is measured from a group of individuals with ASD (Shultz et al., 2011). These artifacts have a very high detrimental effect on the quality of the underlying neural signal. Hence elimination of these artifacts is of utmost importance. Fig. 2 shows the effectiveness of ICA technique in the removal of ocular artifacts on real data. In this stage, EFICA is chosen as the ICA algorithm due to it’s robustness in noisy environment.

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Fig. 2. Ocular artifact removal using ICA. (a) Real visual evoked EEG signal before using ICA. (b) Real visual evoked EEG signal after using ICA.

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Sample entropy and SNR are evaluated on the evoked signals before and after the application of ICA. Table 2 shows the improvement in SNR and SampEn after the application of ICA on the dataset (simulated and real signals). It is observed that the SampEn has increased considerably in the ICA denoised signals thereby indicating reduction in blink artifacts. An improvement in SNR is also noted which in turn highlights the quality of the denoised signals.

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Since different varieties of real EEG artifact examples are not available, the artificially simulated artifacts may not always resemble the real contamination of the signals. As a result, it is observed that the increase in performance measures when tested on simulated signals is less compared to that of real data. Similar studies employing other ICA algorithms such as fastICA (Albera et al., 2012; Hsu et al., 2012), Infomax-ICA (Xue et al., 2006), Extended-InfomaxICA and Influential ICA (Goh et al., 2017) were already reported in synthetic, normal and epileptic EEG. These studies focused on the removal of ocular and muscle artifacts and showed enhanced performance in terms of artifactto-signal ratio and root mean square error. Some variants of EMD were also found useful in suppressing blinks in visual evoked EEG responses (Patel et al., 2017). As evoked EEG signals have low SNR and numerous artifacts, the suppression of artifacts giving minimal distortion to the EEG information is highly essential. Hence this study has chosen EFICA for blink removal. The other EEG studies have utilized ICA in conjunction with other denoising methods based on wavelets (Mahajan and Morshed, 2015; Mowla et al., 2015) and EMD variants (Salsabili et al., 2015; Soomro, 2013) in order to enhance it’s denoising capability. But only few studies focused on dealing with multiple artifacts. In this work, after removing the artifacts related to eye movements and eye blinks, the EEG signals are further subjected to other denoising techniques including wavelet-based denoising, EMD, EEMD, CEEMDAN and several TVD versions so as to eliminate the remaining transient artifacts. The efficacy of the denoising techniques under consideration is determined by computing SNR and correlation coefficient. Tables 3 and 4 give the values of the average correlation coefficient and average change in SNR computed in all the methods taken for study.

The impact of different artifact rejection methods on the simulated and real visual evoked EEG responses freed of eye blinks are illustrated in Fig. 3 and Fig. 4.

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Fig. 3. (a). Blink removed simulated signal after ICA. (b). Wavelet denoised signal. (c). EMD denoised signal. (d). EEMD denoised signal. (e). CEEMDAN denoised signal. (f). LPF/TVD denoised signal. (g). LPF/CSD signal. (h). SASS denoised signal. (i). MTVD denoised signal. (j). TARA denoised signal

Fig. 4. (a). Blink removed real visual evoked EEG after ICA. (b). Wavelet denoised signal. (c). EMD denoised signal. (d). EEMD denoised signal. (e). CEEMDAN denoised signal. (f). LPF/TVD denoised signal. (g). LPF/CSD signal. (h). SASS denoised signal. (i). MTVD denoised signal. (j). TARA denoised signal

10 It is observed that majority of the underlying brain activities are suppressed along with the artifactual components in wavelet-based, EMD, EEMD, CEEMDAN, LPF/TVD, LPF/CSD, SASS and MTVD methods. This is evident from the decrease in SNR computed in each case. Based on SNR comparison in real and simulated data, TARA emerges as the most efficient method for rejecting the residual noise after blink removal. An increase in SNR is an indication that this methodology offers least distortion to the more useful EEG information in the recorded signals. The correlation coefficient is computed between original signal and denoised signal in the case of simulated data. A high correlation coefficient is favourable. But in real visual evoked EEG signal, the signal freed of artifacts is expected to have very less resemblance with that of noisy signal which in turn points to a low correlation coefficient. The comparison based on average correlation coefficient on simulated data also reveals TARA as a promising denoising tool. But the comparison of correlation coefficient on real data shows LPF/TVD as the better one closely followed by TARA. Since LPF/TVD offers very poor SNR change, TARA is chosen as the apt one. Earlier, TVD techniques were successfully implemented in EEG studies based on depression and Alzheimer diseases (John et al., 2018; Puthankattil and Joseph, 2012). But no study has used a combination of TVD in conjunction with other approaches.

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In addition, statistical analysis is conducted among the nine different methods on the dataset in order to validate the results. The denoising performance is tested with a multivariate general linear model (GLM) using SNR and correlation coefficient as the dependent variables and method as the fixed factor. Bonferroni’s correction is employed to conduct subsequent post-hoc tests and results are considered significant for 𝑝 < 0.05. TARA exhibits statistically significant results compared to other approaches in terms of SNR. On the other hand, while working with real data, both TARA and LPF/TVD gives significant statistical differences on the basis of correlation coefficient. But owing to the appreciable increase in SNR, TARA is chosen over LPF/TVD. The results support the argument that ICATARA eliminates majority of the artifacts causing minimal distortion to the underlying neural activity.

4

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To the best of our knowledge, this approach is the first attempt to combine ICA with a variant of Total variation denoising and has proved to be highly effective in removing the artifacts. It has also succeeded in preserving the necessary neural information in the signal. Conclusion

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In this study, we have proposed a new hybrid methodology for the elimination of artifacts from the contaminated EEG segments measured during visual stimuli in ASD group. This technique presents a cascade combination of ICA and TARA and is general enough to encompass all the major artifacts that creep into the visual evoked EEG signals. The SNR and correlation coefficient results reveal that the proposed technique offers minimal distortion to the EEG signals while eliminating the major artifacts including eye blinks. The proposed approach is also compared with the previous methodologies including wavelet-based, EMD and its variants and other versions of TVD thereby highlighting it’s efficiency as an artifact rejection technique.

CREDIT AUTHOR STATEMENT

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Priyalakshmi Sheela: Conceptualization, Methodology, Software, Formal analysis, Writing- Original draft preparation

Subha Dharmapalan Puthankattil: Supervision, Writing- Reviewing and Editing,

11 Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of Interest The authors report no conflict of interest. Acknowledgements

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We would like to thank Dr. Yukari Takarae, Former Assistant Professor, Department of Psychiatry, University of Texas Southwestern Medical Center, Dallas, Texas, USA for sharing the visual evoked EEG data of ASD group.

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15

CEEMDAN

LPF/TVD

LPF/CSD

SASS

Nstd=0.2 I=500

Nstd=0.2 I=500

Nstd=0.2 I=500

Nstd=0.2 I=500

λ =1

λ =1

𝜆0 =0.005 𝜆1 =1 λ =1 λ =1

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MTVD

Nstd- noise standard deviation, I-ensemble size Nstd- noise standard deviation, I-ensemble size λ - regularization parameter to control the degree of smoothing 𝜆0 ,𝜆1 -regularization parameters associated with the sparse and sparse derivatives λ - regularization parameter to control the degree of smoothing λ - regularization parameter to control the degree of smoothing 𝛳, 𝛽- shape parameters 𝜎- pseudo-noise standard deviation

Parameter values for real data N=7 mother wavelet- sym7

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TARA

𝛳 =1, 𝛽=1, 𝜎=0.1

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Table 1: Parameter values considered in the methods taken for comparison

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EEMD

N-decomposition levels, mother wavelet

Parameter values for simulated data N=7 mother wavelet- db10

𝜆0 =0.005 𝜆1 =1

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Wavelet-based denoising

Parameters

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λ =1 λ =1 𝛳 =0.05, 𝛽=1.4, 𝜎=1

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ICA

Measures Avg SNR Change (%) Avg Sample Entropy Change (%)

Simulated Signals 13.4649

Real Data 26.6663

6.8951

48.6947

Table 2: Percentage change in average SNR and average sample entropy in ICA denoising on simulated and real data

Methods

Measures Average SNR Change Average Correlation (%) Coefficient

1.

Wavelet-based denoising

2.

EMD

3.

EEMD

4.

CEEMDAN

-0.0858

5.

LPF/TVD

-0.2641

6.

LPF/CSD

-0.0111

7.

SASS

8.

MTVD

9.

TARA

-0.0782

0.5074

-0.0856

0.5179

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0.5176 0.4003 0.6116

-0.2620

0.4004

-0.2989

0.2958

6.9824

0.6958

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0.6245

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-0.2382

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Sl. No.

17 Table 3: Performance comparison of different denoising methods based on average correlation coefficient and average change in SNR on simulated data Sl. No

Methods

Measures Average SNR Change Average Correlation (%) Coefficient -66.7552 0.8166

Wavelet-based denoising

2.

EMD

-3.5203

0.9150

3.

EEMD

-0.0039

0.9999

4.

CEEMDAN

-0.0035

0.9999

5.

LPF/TVD

-0.4269

0.2367

6.

LPF/CSD

-7.7161

7.

SASS

-0.4267

8.

MTVD

-0.0020

9.

TARA

71.5104

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1.

0.9711

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0.9996 0.9999 0.2786

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Table 4: Performance comparison of different denoising methods based on average correlation coefficient and average change in SNR on real data