Sliding window higher-order cumulants for detection of eye blink artifact from short segments of single-channel EEG

Introduction

The prefrontal single-channel electroencephalography (EEG) system, offering portable and mobile monitoring capabilities, holds significant application value in neuroscience research and clinical diagnosis (Ali et al., 2022). As the core regulatory hub of the brain, the prefrontal cortex governs higher-order neural functions including executive control, decision-making, and motor coordination, while simultaneously participating in complex cognitive processes such as emotion regulation, attention modulation, and mental state integration. Through real-time monitoring of neural electrical signals in this region, researchers can accurately identify neural activity patterns associated with transitions from relaxed to focused states, facilitating an objective and quantifiable cognitive function assessment framework (Ahn, Ku & Kim, 2019). In clinical diagnostics, prefrontal EEG signal analysis is widely applied for biomarker detection in neurological disorders. It demonstrates significant value in early screening and disease monitoring of movement disorders, executive dysfunction syndrome, Foster-Kennedy syndrome, and other neurological conditions, providing reliable neuroelectrophysiological evidence for precision medicine (Dora & Biswal, 2020). However, similar to multichannel EEG, single-channel EEG remains susceptible to artifacts, particularly eye blinks, which can significantly affect prefrontal EEG and are difficult to manage or overcome experimentally (Shahbakhti et al., 2019).

For attenuating blink artifacts in single-channel EEG, various decomposition methods are commonly employed, including singular spectrum decomposition (Maddirala & Veluvolu, 2022a; Mary Judith, Baghavathi Priya & Mahendran, 2022; Yedukondalu & Sharma, 2023), wavelet decomposition (Maddirala & Veluvolu, 2022a; Sahoo & Mohapatra, 2022), empirical mode decomposition (Yan & Wu, 2022), and independent component analysis (Mary Judith, Baghavathi Priya & Mahendran, 2022; Sahoo & Mohapatra, 2022). However, such decomposition-based methods typically apply global filtering across the entire contaminated EEG signal instead of specifically targeting artifact-contaminated intervals. This approach may inadvertently remove both artifact-corrupted and intact neural components. Notably, emerging evidence suggests that precise temporal localization of blink events significantly improves artifact suppression efficacy while enhancing preservation of genuine neural activity (Maddirala & Veluvolu, 2022a, 2022b; Gao et al., 2023). This paradigm shift from global to targeted artifact removal thus represents a promising direction for improving EEG signal quality.

Currently, the primary methods to detect blink artifacts involve amplitude thresholding (Nolan, Whelan & Reilly, 2010), template matching (Valderrama, de la Torre & Van Dun, 2018), peak detection (Shahbakhti et al., 2021a), and derivative summation detection (Chang et al., 2016). However, most of these methods require empirically preset conditions, and few have explored whether the boundaries of blink artifact intervals are accurately recognized. Amplitude thresholding, which is based on a priori estimation of blink artifact amplitude, achieves the detection of blink peaks and thus blink position localization, but it does not accurately identify blink intervals. The peak detection method identifies the peaks using the variational mode extraction (VME) method (Shahbakhti et al., 2021a), and the boundaries of the artifact intervals are determined based on an empirical estimate of the blink interval width (400 ms) using the identified peaks. The template matching algorithm (Valderrama, de la Torre & Van Dun, 2018) was proposed to detect and eliminate eye blinks using an automatic threshold and template estimation. However, like the VME method, its blink template is fixed at 1,400 ms and does not precisely identify the boundaries of the exact blink interval. The method for multi-window detection of derivative summation (MSDW) can identify the start and end points of blink intervals (Chang et al., 2016). However, it requires the assumption that blink artifacts exhibit a triangular shape.

Therefore, it is necessary to establish an assumption-free detection approach capable of adaptively and more precisely identifying blink artifacts of varying durations by exploiting the inherent characteristic distinctions between EEG signals and blink artifacts. Hence, considering the differences in the non-Gaussian properties of EEG signals and blink artifacts, higher-order cumulants (HOCs) are introduced for distinguishing blink artifacts from EEG signals without a priori assumptions. Currently, the application of HOCs in ocular artifact processing still primarily involves combining them with various signal decomposition methods as previously mentioned, including blind source separation (Jamil, Jamil & Majid, 2021; Çınar, 2021; Gao et al., 2023), variational mode decomposition (Bisht et al., 2024), empirical mode decomposition (Teng et al., 2021), canonical correlation analysis (Yang et al., 2017), and wavelet transform (Shahbakhti et al., 2021b; Islam, Ghorbanzadeh & Rastegarnia, 2021). These methods identify and remove artifact components by calculating HOC values of the decomposed signals. However, HOCs still evaluate the decomposed signal components in their entirety. As previously mentioned, this global processing approach may compromise neural activity information within artifact-free segments. Nevertheless, these studies have laid a theoretical foundation for the effectiveness of HOCs in extracting non-Gaussian signal features, and it is precisely based on these validated findings that they provide the research impetus for our exploration into using HOCs directly for the accurate detection of blink artifacts.

This article presents a sliding window HOC method for detecting blink artifacts, which offers two advantages: First, by incorporating HOCs, it can automatically distinguish between EEG signals and blink artifacts based on their non-Gaussian characteristics, effectively overcoming the limitations imposed by empirically preset conditions. Second, the sliding-window computation strategy generates time-varying HOC series that allow precise localization of the onset and offset boundaries of blink artifacts. Specifically, a sliding window is applied to the contaminated EEG signals, and HOCs are computed window by window. These HOC values are then used to preliminarily estimate the intervals of the blink artifacts based on the local maxima. Subsequently, the pre-detected intervals are further adjusted by incorporating the peaks of the blink artifacts within those intervals to improve the precision of the final detection. This study also evaluates the efficacy of the sliding window HOC method using semi-simulated and real data. The method is compared with the existing eye blink artifact detection methods, including VME and MSDW.

Materials and Methods

The sliding window HOC method

Based on the difference in Gaussian characteristics between EEG signals and eye blink artifacts, this article proposes a sliding window higher-order cumulant analysis method for detecting eye blink artifacts in EEG signals. In this approach, the target signal to be detected is the blink artifact, whereas the EEG background activity serves as the noise source. HOCs are employed to suppress the EEG noise, enabling the detection of the blink artifacts.

The main steps of our proposed sliding window HOC with further adjustments are summarized in Algorithm 1. Assuming that the contaminated EEG time series is $X\left(n\right),n=1,2,\dots ,N$. The sliding window HOC are defined as

(7) $$\begin{array}{rl}Czzz\left(k\right)& =cum\left(x\left(k\right),x\left(k+1\right),x\left(k+2\right),\dots ,x\left(k+winlen-1\right)\right),\\ k& =1,2,\dots ,N-winlen+1\end{array}$$where $cum$ denotes the HOC function and $winlen$ is the sliding window length. $Czzz\left(k\right)$ represents the HOC value of the $k$th sliding window of the contaminated EEG signals. Due to the difference in their Gaussian distributions, the HOC values increase when an eye blink signal is present within the sliding window. This enables the localization of the eye blink artifacts and facilitates the detection of these artifacts.

Algorithm 1:

Blink artifacts detection using the sliding window HOC method.

Input: Contaminated EEG $X\left(n\right)$ ( $n=1,2,\dots ,N$), $Fs$, $winlen$, $th{r}_1$, $th{r}_2$

Output: Final detected eye blink intervals [ $startpoint$ $endpoint$]

Initialization: $winlen=0.5\ast Fs$

{Step 1: Preliminary detection of blink intervals}

1:  for $n=1,2,\dots ,N-winlen+1$

2:     $Czzz\left(n\right)=cum\left(X\left(n\right)\right)$

3:  end

4:   $\theta ={\displaystyle \frac{median\left(\left|Czzz\right|\right)}{0.6745}\sqrt{2\log N}}$

5:   $Czzz\left(Czzz<\theta \right)=0;$

6:   $\left[pks,locs\right]=findpeaks\left(Czzz\right);$

7:   $segments$ {Points within $0.5\ast Fs$ of $locs$ are considered to be one artifact segment}

8:   $startpoint0=segments\left(:,1\right)$

9:   $endpoint0=segments\left(:,2\right)$

10: Step 2: Further adjustments to detected blink intervals (exemplified by D1D2 in Fig. 2)}

11:  $\left[P,O\right]=findpeaks\left(X\left(D_1:D_2\right)\right)$

12:  $D_{1m}=\left(D_{1}O\right)/2$

13:  $D_{2m}=\left(D_{2}O\right)/2$

14:  ${\mathrm{r}}_1={\displaystyle \frac{A_{1}O}{PO}}$

15:  ${\mathrm{r}}_2={\displaystyle \frac{A_{2}O}{PO}}$

16: while ${\mathrm{r}}_1<\mathrm{t}\mathrm{h}{\mathrm{r}}_1$

17:  $D_1=D_1+1$

18: end

19: while ${\mathrm{r}}_1>\mathrm{t}\mathrm{h}{\mathrm{r}}_1$

20:    $D_1=D_1-1$

21: end

22: while ${\mathrm{r}}_2<\mathrm{t}\mathrm{h}{\mathrm{r}}_2$

23:  $D_2=D_2-1$

24: end

25: while ${\mathrm{r}}_2>\mathrm{t}\mathrm{h}{\mathrm{r}}_2$

26:  $D_2=D_2+1$

27: end

28:  $startpoint=D_1$

29:  $endpoint=D_2$

30: return $startpoint,endpoint$

DOI: 10.7717/peerj-cs.3249/table-101

Figure 1 shows the block diagram of the sliding window HOC method, which is executed in two main steps: first, preliminary detection of eye blink intervals, and second, further adjustment of the detected intervals.

Preliminary detection of blink intervals

The preliminary detection of blink intervals refers to the preliminary localization of blink artifact intervals based on the sliding window HOC method, involving the determination of parameters that affect the accuracy of detection outcomes. The key parameter to be determined in this step is the size of the sliding window ( $winlen$). Given that the typical duration of blink artifacts ranges from 100 to 500 milliseconds (Chang et al., 2016), the preliminary detection phase must address two key requirements: first, ensuring the rough identification of time intervals containing blink artifacts; and second, guaranteeing that these initially detected intervals cover the peak positions of blink artifacts. This coverage is a critical parameter for subsequent further adjustment procedures. Based on these considerations, $winlen$ is empirically set to 500 milliseconds.

After the sliding window HOCs have been calculated based on the specified order and window size, the intervals containing blink artifacts are determined by identifying local maxima in the sliding-window HOCs that exceed a universal threshold $\theta$ (Chavez et al., 2018; Shahbakhti et al., 2021a). The universal threshold $\theta$ is calculated as follows:

(8) $$\theta ={\displaystyle \frac{median\left(\left|Czzz\right|\right)}{0.6745}\sqrt{2\log N}}$$where Czzz represents the sliding-window HOCs, and N denotes the length of Czzz series. After zeroing out Czzz values below threshold θ, we employ the $\left[pks,locs\right]=findpeaks\left(Czzz\right)$ function to identify local maxima, where $pks$ contains the peak amplitudes and $locs$ indicates their corresponding time indices. When the interval between two adjacent maxima is less than 0.5 * Fs sampling points (equivalent to 500 ms), these peaks are considered to belong to the same blink artifact segment. This approach enables preliminary determination of the blink artifact’s $startpoint$ and $endpoint$, as detailed in Algorithm 1.

Further adjustments to detected blink intervals

To address the detection deviation caused by the fixed sliding-window size (500 ms) in the preliminary detection stage-which fails to adapt to the dynamic variations in blink artifact durations-further adjustments are implemented. These adjustments dynamically refine detection intervals based on blink peak positions (see Fig. 2). The purpose of the two parameters, denoted as $th{r}_1$ and $th{r}_2$, is to optimize the detected blink intervals and estimate the precise temporal boundaries of eye blink artifacts. These parameters are intrinsically associated with the asymmetric characteristics of blink waveforms: $th{r}_1$ governs detection sensitivity for the leading edge, while $th{r}_2$ controls trailing edge adjustment. Their values dynamically adapt to slope variations determined by blink width and peak amplitude. Through an iterative optimization approach using a stepwise approximation algorithm for artifact boundary refinement, precise localization of blink artifact intervals is ultimately achieved.

As illustrated in Fig. 2, point P represents the peak of the actual blink artifact within the detected blink interval, and point O denotes its location. While TT’ refers to the actual blink artifact interval, D₁D₂ represents one example of preliminarily detected blink intervals. The primary purpose of further adjustment is to draw D₁D₂ closer to TT’. Exemplified by D₁D₂, the procedure is as follows: for D₁ of the D₁D₂, locate the centroid D_1m of the D₁O and calculate the magnitude of its corresponding actual blink signal. If the ratio ( ${\mathrm{r}}_1$) of this magnitude (A₁O) to the peak value (PO) is less than the predetermined threshold ( $\mathrm{t}\mathrm{h}{\mathrm{r}}_1$), point D₁ moves one sample point to the right until $\mathrm{r}$ exceeds $\mathrm{t}\mathrm{h}{\mathrm{r}}_1$, and then it stops moving. For D₂ of the D₁D₂, locate the centroid D_2m of the D₂O and determine the corresponding magnitude. If the ratio ( ${\mathrm{r}}_2$) of the magnitude (OA₂) to the peak value (OP) is less than the set threshold ( $\mathrm{t}\mathrm{h}{\mathrm{r}}_2$), point D₂ shifts one sample point to the left until $\mathrm{r}$ exceeds $\mathrm{t}\mathrm{h}{\mathrm{r}}_2$, after which it comes to a stop. This process yields the final refined start and end points of the blink artifacts after further adjustment, which represent the algorithm’s ultimate determination of blink artifact boundaries.

Performance metrics

In order to assess the accuracy of blink artifact detection, both direct accuracy metrics and indirect artifact reduction effectiveness metrics are employed.

Accuracy metrics

Accuracy metrics offer a straightforward means of evaluating detection algorithms. To assess the accuracy of the blink detection methods in more detail, both rough and fine assessment metrics have been used.

Rough assessment metrics are employed to evaluate the algorithm’s ability to locate blink artifacts. A detection is classified as a rough true positive ( $\mathrm{T}{\mathrm{P}}_{\mathrm{r}}$) if it overlaps with any actual blink artifact, and as a rough false positive ( $\mathrm{F}{\mathrm{P}}_{\mathrm{r}}$) when no overlap occurs with genuine blink regions. These metrics include the rough true positive rate ( $\mathrm{T}\mathrm{P}{\mathrm{R}}_{\mathrm{r}}$) and rough false positives per sample ( $\mathrm{F}\mathrm{P}\mathrm{P}{\mathrm{S}}_{\mathrm{r}}$), calculated as follows:

(10) $$TP{R}_r={\displaystyle \frac{T{P}_r}{numberofEOGs}}$$

(11) $$FPP{S}_r={\displaystyle \frac{F{P}_r}{durationofpureEEG}}$$where $T{P}_r$ stands for the number of correctly detected eye blinks, while $numberofEOGs$ denotes the total number of actual eye blinks. $F{P}_r$ indicates the number of false positive detections, and $durationofpureEEG$ represents the total duration (in samples) of artifact-free EEG. Since true negatives (TN) are undefined for continuous signals (Valderrama, de la Torre & Van Dun, 2018), $\mathrm{F}\mathrm{P}\mathrm{P}{\mathrm{S}}_{\mathrm{r}}$ is evaluated over temporal intervals, making it equivalent to the false positive rate (FPR). However, these rough metrics are inadequate for assessing endpoint recognition precision of blink artifacts.

The fine assessment metrics are designed to assess whether the method can accurately estimate the boundaries of the eye blink artifacts. Therefore, we define the fine assessment metrics by introducing the concept of “error tolerance” (Chang et al., 2016), based on the fact that blink artifacts blend with genuine EEG signals, creating boundary ambiguity that necessitates a permissible error range to avoid overly stringent determinations. Figure 3 illustrates the basic concept of error tolerance. “Ground truth” refers to the exact range of an eye blink artifact. If an error tolerance is specified for the two boundaries of the artifact, actual errors (false positives or false negatives) found within these “error tolerance” ranges are considered part of correctly detected artifact ranges. The error tolerance includes false negative tolerance (FN tolerance) and false positive tolerance (FP tolerance). FN tolerance is defined as the ratio of the tolerated FN region to the length of the ground truth segment for each artifact, since the width of each artifact varies. In contrast, the FP tolerance is defined as a fixed time interval (in seconds) extending from the boundaries of the ground truth segment for each artifact. In our implementation, FP tolerance ranges from 0 to 0.1 s and FN tolerance ranges from 0 to 40 percent of the ground truth segment (Chang et al., 2016). Specifically, the FN tolerance range of 0–40% is chosen based on the physiological characteristics of blink artifacts and signal ambiguity. Since blink artifact waveforms exhibit gradual rising and falling slopes, strictly defining their boundaries could lead to missed detections. A 40% FN tolerance means allowing a 40% margin of error relative to the artifact’s duration near its boundaries (e.g., allowing an 80 ms tolerance for a 200 ms artifact). This range covers the transition zone between artifacts and EEG signals in most practical cases, ensuring detection sensitivity while preventing excessive leniency that could introduce significant noise interference. The FP tolerance range of 0.0–0.1 s is chosen to effectively distinguish blink artifacts from other transient interference. A 0.1-s FP Tolerance accommodates the duration of brief disturbances while avoiding misclassification of longer noise (such as motion artifacts) as blinks. In addition, the figure also shows four different possible detected eye blinks.

Based on the concept of “error tolerance”, we define the fine assessment metrics which include the fine true positive rate ( $\mathrm{T}\mathrm{P}{\mathrm{R}}_{\mathrm{f}}$) and the fine false positives per sample ( $\mathrm{F}\mathrm{P}\mathrm{P}{\mathrm{S}}_{\mathrm{f}}$).

(12) $$TP{R}_f={\displaystyle \frac{T{P}_f}{T{P}_f+F{N}_f}}$$

(13) $$FPP{S}_f={\displaystyle \frac{F{P}_f}{durationofpureEEG}}$$where $T{P}_f$, $F{N}_f$ and $F{P}_f$ stand for the correct, missed and false duration in samples of detected eye blinks, respectively. The $durationofpureEEG$ is still the total duration in samples of the pure EEG.

Artifact reduction effectiveness metrics

Artifact reduction effectiveness metrics can serve as an indirectly assessment of blink detection accuracy. Better removal of blink artifacts alongside better retention of valid EEG indicates more accurate recognition of blink artifacts. The study conducts indirect verification of artifact detection accuracy by applying the same wavelet denoising method after the three blink artifact detection algorithms. Specifically, the discrete wavelet transform (DWT) is used to filter the contaminated intervals using the db4 mother wavelet at a decomposition level of 3. To quantify the artifact reduction performance, we use the correlation coefficient ( $\mathrm{C}\mathrm{C}$) and the relative root mean square error ( $\mathrm{R}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$) in the time domain. Additionally, the mean absolute error ( $\mathrm{M}\mathrm{A}\mathrm{E}$) is employed in the frequency domain.

$\mathrm{C}\mathrm{C}$ can reflect the ability to perserve the original EEG signal during the denoising process. $\mathrm{C}\mathrm{C}$ is calculated as

(14) $$\mathrm{C}\mathrm{C}={\displaystyle \frac{cov\left(x\left(n\right),\widetilde{x\left(n\right)}\right)}{{\sigma }_{x\left(n\right)}{\sigma }_{\widetilde{x\left(n\right)}}}}$$where $x\left(n\right)$ and $\widetilde{x\left(n\right)}$ are the pure EEG and filtered EEG signals, $cov$ and $\sigma$ are the covariance and standard deviation, respectively. The closer $\mathrm{C}\mathrm{C}$ is to 1, the better the noise reduction.

$\mathrm{R}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ is defined as

(15) $$\mathrm{R}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{RMS\left(x\left(n\right),\widetilde{x\left(n\right)}\right)}{RMS\left(x\left(n\right)\right)}}$$where $RMS\left(x\left(n\right)\right)$ and $RMS\left(\widetilde{x\left(n\right)}\right)$ represent the root mean square of the true and denoised EEG signals, respectively, and for an effective artifact reduction approach, the RRMSE value will be low.

MAE is employed to evaluate the performance in the frequency domain. $p\left(f\right)$ and $p_m\left(f\right)$ are the power spectrum of the contaminated and rectified EEG respectively. The MAE is defined as follows:

(16) $$MAE={\displaystyle \frac{{\sum }_{f=a}^b\left|p\left(f\right)-p_m\left(f\right)\right|}{b-a}}$$where $b-a$ refer to the frequency range of a particular band.

For semi-simulated data, where the ground truth is known, MAE is used to evaluated EEG retention across the full frequency range (1–40 Hz) after artifact reduction. Results indicate effective artifact reduction, reflected in small MAE values. For real data, however, the lack of ground truth makes it impossible to calculate CC and RRMSE. MAE across the full frequency range (1–40 Hz) is also incalculable. Instead, MAE was always computed within the $\alpha$ band due to blink artifact frequencies extending beyond the $\alpha$ band (Noorbasha & Sudha, 2021; Yedukondalu & Sharma, 2023). It should be noted that insufficient artifact removal can still result in low MAE values in the α band. For instance, an MAE value of 0 in the $\alpha$ band without artifact reduction signals adequate EEG preservation, not complete artifact elimination. Thus, we employed the MAE ratio ( $MA{E}_{ratio}$) of the low frequency band (1–10 Hz) to the high frequency band (10–40 Hz). This metric evaluates the algorithm’s efficacy in eliminating artifacts while preserving EEG signals.

Results

Results of parameters determination

The parameters of the sliding window HOC method include $th{r}_1$and $th{r}_2$. For the chosen semi-simulated data (containing varying blink artifact intervals and different SNRs), we calculated the mean values of $TP{R}_f$ and false positives per second $FPP{S}_f$ across different combinations of $th{r}_1$ and $th{r}_2$, then plotted corresponding ROC curves. As shown in Fig. 4, the ten colored lines indicate $th{r}_1$ values ranging from 0.0 to 0.9, while the ten circles along each line (arranged top to down) correspond to $th{r}_2$ values from 0.0 to 0.9. These collectively form the ROC curves for all parameter combinations. The maximum Youden index value of the ROC curve is 0.9422, corresponding to $TP{R}_f$ = 0.9679 and $FPP{S}_f$ = 0.0257. This optimal point (indicated by the third circle from the top on the bold purple line) represents the combination $th{r}_1$ = 0.4 and $th{r}_2$ = 0.2. Thus, $th{r}_1=0.4$ and $th{r}_2=0.2$ were identified as the optimal parameters for subsequent analysis.

Results of semi-simulated data

Results from the semi-simulated data involved comparing the precision of three distinct blink detection methods and the denoising effectiveness generated based on these detection methods.

Table 2 illustrates the rough accuracy metrics for the proposed sliding window HOC, VME, and MSDW methods across various SNRs. The results show that the proposed method achieved consistently higher Youden index values across all SNRs, indicating superior rough detection accuracy. Figure 5 presents the ROC curves of the fine assessment metrics of each method under varying FP and FN tolerances. These results indicate that the proposed method exhibited the highest $\mathrm{T}\mathrm{P}{\mathrm{R}}_{\mathrm{f}}$ at any given $\mathrm{F}\mathrm{P}\mathrm{P}{\mathrm{S}}_{\mathrm{f}}$.

Table 2:

The results of rough assessment metrics.

	SNR	SNR ≤ −4	−4 < SNR < 0	0 dB
TPRr	Sliding window HOCs	1.000	0.993	0.945
	VME	0.990	0.976	0.853
	MSDW	0.266	0.215	0.192
FPPSr	Sliding window HOCs	2.08E−04	2.39E−04	2.81E−04
	VME	3.49E−03	4.51E−03	5.30E−03
	MSDW	1.29E−04	1.28E−04	1.26E−04
Youden index	Sliding window HOCs	1.000	0.993	0.945
	VME	0.987	0.971	0.847
	MSDW	0.266	0.215	0.192

DOI: 10.7717/peerj-cs.3249/table-2

Note:

Rough true positive rate (TPRr), rough false positives per sample (FPPSr) and the Youden index obtained at different SNRs with the sliding window HOC method, the VME method, and the MSDW method.

Figure 6 and Table 3 display indirect artifact reduction effectiveness metrics for the semi-simulated data, including CC, RRMSE and MAE in subplots (A), (B) and (C), respectively. The data indicates that the sliding window HOC-based blink artifact detection method attained the highest CC value, the lowest RRMSE value, and the lowest MAE value, demonstrating its exceptional artifact reduction capability.

Table 3:

Results of artifact reduction effectiveness metrics.

Detection methods	Sliding window HOCs	VME	MSDW
CC	0.935 (0.046)a	0.914 (0.078)b	0.909 (0.094)c
RRMSE	0.128 (0.077)a	0.186 (0.234)b	0.225 (0.414)c
MAE	1.634 (0.424)a	1.770 (0.670)b	1.748 (0.574)b

DOI: 10.7717/peerj-cs.3249/table-3

Note:

Values are presented as mean (std). Groups sharing the same superscript letter are not significantly different (p > 0.05, Bonferroni-corrected), while different letters indicate statistically significant differences.

Results of real data

Fig. 7 compares blink artifact detection results in real data using the sliding window HOC, VME, and MSDW methods, alongside power spectra of wavelet-denoised signals following blink detection. Specifically, Fig. 7A demonstrates that the sliding window HOC method more accurately localized artifact occurrence intervals than the other two methods. Figure 7B reveals that the sliding window HOC-based filter achieved improved detection of blink artifacts in the low-frequency range while providing superior signal preservation in the high-frequency range- particularly within the EEG β-band, as shown in the magnified region (Maddirala & Veluvolu, 2021).

Figure 8 and Table 4 present box plots of the calculated $MA{E}_{ratio}$ values across three real datasets. These results confirm that the sliding window HOC-based filter outperformed both the VME and the MSDW methods in attenuating blink artifacts while preserving EEG signals.

Table 4:

MAE_ratio result for real data.

Datasets	Sliding window HOCs	VME	MSDW
Data1	9.785 (10.478)a	5.523 (5.796)b	0.000 (3.712)c
Data2	13.450 (10.223)a	10.925 (5.431)b	10.861 (9.427)b
Data3	15.961 (11.055)a	10.275 (6.373)b	8.489 (9.743)c

DOI: 10.7717/peerj-cs.3249/table-4

Note:

Values are presented as median (interquartile range). Groups sharing the same superscript letter are not significantly different (p > 0.05, Bonferroni-corrected), while different letters indicate statistically significant differences.

Discussion

This study proposes a sliding window HOC method for detecting artifacts in single-channel EEG. The method’s performance was evaluated using semi-simulated data and real data through direct accuracy metrics and indirect artifact reduction effectiveness metrics. Results demonstrate that: (1) the method can accurately detect blink artifact boundaries in single-channel EEG signals; (2) the method is fully automated as no human involvement is required; and (3) detection leverages the distinct Gaussian characteristics differentiating EEG signals from blink artifacts. In comparison to the VME method, which is limited to positive blink peaks and preset blink intervals, and the MSDW method, which has specific requirements for blink morphology, this method is considered to be more robust.

The sliding window HOC method focuses on accurately identifying blink artifacts. This process not only locates artifacts initially through HOCs, but also precisely determines their start and end positions via further adjustment. While most single-channel EEG blink artifact studies focused on localization (Valderrama, de la Torre & Van Dun, 2018; Shahbakhti et al., 2021a; Maddirala & Veluvolu, 2022a, 2022b), few addressed boundary-specific recognition (Chang et al., 2016). Although the proposed algorithm does not remove blink artifacts, it accurately detects contaminated intervals in single-channel EEG. This capability is essential for future effective artifact removal while preserving the EEG signal.

To improve blink artifact detection accuracy, this study introduces a crucial refinement step- further adjustments to detected blink intervals-following preliminary detection. This step dynamically identifies the precise boundaries of blink artifacts using a dual-threshold system ( $th{r}_1$ and $th{r}_2$), overcoming the limitation of fixed-window methods in adapting to variable-duration blinks. To determine the optimal thresholds, a systematic experimental design was employed: 5,940 (108 × 11 × 5) contaminated EEG segments were constructed by varying blink durations (100–500 ms) and SNR levels (–8 to 2 dB). Results demonstrate peak performance at $th{r}_1$ = 0.4 and $th{r}_2$ = 0.2 (Youden index = 0.9422; Fig. 4), significantly improving recognition accuracy across blink characteristics. The further adjustments step enhances the sliding window HOC method, enabling more precise dynamic detection.

The performance of the sliding window HOC method is compared with the VME and MSDW methods. For both semi-simulated data and real data, the results indicate that the sliding window HOC method outperforms both VME and MSDW. This was demonstrated using semi-simulated data generated by mixing blink artifact of varying durations with 377 segments of EEG signals at different SNRs. The sliding window HOC method demonstrates superior performance in direct detection accuracy when compared to other methods. Regarding rough assessment metrics, the sliding window HOC method exhibits the highest Youden index value. While the FPPS of the MSDW algorithm is marginally lower than that of the proposed sliding window HOC method, its $\mathrm{T}\mathrm{P}{\mathrm{R}}_{\mathrm{r}}$ is considerably lower than that of the HOC method. Overall, the proposed method is superior to other methods in terms of its capability to localize blink artifacts (see Table 2). In terms of fine assessment metrics, the ROC curves plotted for different combinations of FP and FN tolerances demonstrate that the HOC method has the highest recognition accuracy. This suggests that the HOC method is capable of identifying the boundaries of blink artifacts with the greatest precision (see Fig. 5). Regarding the artifact reduction effect achieved based on the detection methods, the sliding window HOC-based filter shows a higher CC value, lower RRMSE value, and higher MAE (see Fig. 6 and Table 3), indicating better performance in artifact reduction. Despite demonstrating superior performance compared to the other two methods, the detection efficacy of the proposed sliding window HOC method shows a gradual decline as the SNR increases. This phenomenon is characterized by a decline in the CC and an increase in the RRMSE, signifying that variations in SNR have a discernible impact on detection accuracy. This phenomenon is primarily attributable to two factors: Firstly, following the preliminary detection of blink artifact boundaries, the method must accurately localize blink peaks within these boundaries. However, higher SNR levels amplify the influence of blink artifact amplitudes on EEG signals, potentially leading to localization errors during the preliminary detection phase. Secondly, in the subsequent adjustment phase, the method employs these identified blink peaks in conjunction with predefined thresholds, which may reduce the effectiveness of the adjustment. The combined effect of these two factors results in a decline in overall performance in high-SNR environments.

For real data, results from three different databases show that the sliding window HOC-based filter achieves a higher $MA{E}_{ratio}$ (see Fig. 8 and Table 4), suggesting it is better at attenuating blink artifacts while retaining valid EEG signals. The causes of these results may include: (1) the sliding window HOC method is more accurate in locating the interval boundaries of blink artifacts, resulting in better recognition and filtering effects. (2) the VME and MSDW methods may require further parameter adjustments to improve blink artifact detection. This is particularly true for the VME methods, which fails to recognize blink intervals in many real data fragments; consequently, its $MA{E}_{ratio}$ is set to 0. This suggests that these algorithms have slightly poorer robustness compared to the sliding window HOC method. Another advantage of the sliding window HOC method is its low CPU time requirement, making it suitable for online and semi-real time applications.

While the proposed sliding window HOC method has been verified to be effective for detecting blink artifacts, several shortcomings require further investigation: (1) The current validation was conducted using specific electrode configurations and recording devices. The method’s performance may vary across different EEG hardware (e.g., dry vs. wet electrodes), montages, or sampling rates. Future studies should evaluate the approach’s robustness across diverse acquisition systems and experimental paradigms. (2) While our validation has demonstrated the method’s efficacy for isolated blink artifact detection, its performance in real-world EEG recordings - which often contain complex mixtures of muscle artifacts, line noise, and various ocular movements - requires further investigation and methodological enhancements. To address these more challenging scenarios, several key developments would be necessary: establishing comprehensive artifact-specific HOC profiles that capture the distinct higher-order statistical signatures of each major contamination type; implementing a hierarchical decision-making framework that intelligently combines multiple discriminative features beyond HOC; and developing robust integration strategies with established artifact handling techniques, such as employing independent component analysis (ICA) for muscle artifact removal and adaptive notch filtering for power line interference suppression. This multi-pronged approach would significantly improve the method’s practical utility in noisy, real-world EEG applications. (3) The two thresholds are determined from semi-simulated data generated by mixing one blink segment (and its duration variations) with 108 pure EEG segments at different SNRs. To enhance universal adaptability, future work should select blink waveforms from a wider range of subjects and recording devices to produce richer semi-simulated data for threshold calibration. (4) The current method can only identify single intervals within short segments; overlapping intervals may be misidentified as a single blink. Parameters for evaluating different blink intervals should be added to enable detection of multiple, separate blink artifacts. (5) This study only detects blink artifacts and does not include the detection of horizontal electrooculograms. Considering the fact that horizontal electrooculograms also have different Gaussian characteristics with EEGs, the sliding window HOC methods can be used to detect horizontal electrooculograms in further work.

Furthermore, our future research will pursue three key directions: First, we will optimize the computational complexity of HOCs to significantly improve processing efficiency while preserving algorithmic advantages, thereby better meeting real-time application requirements. Second, we will develop novel blink artifact removal algorithms. Building upon the high-precision artifact identification method proposed in this study, these algorithms aim to provide a more comprehensive solution to single-channel blink artifact filtering, achieving accurate artifact elimination, preservation of original EEG rhythm power characteristics, and with minimal impact on filtered EEG rhythm power. Third, while this study primarily focuses on single-channel EEG applications, future work will be extended to multi-channel EEG scenarios. By incorporating multi-channel EEG features, we intend to develop targeted solutions for the recognition and filtering of blink artifacts in multi-channel EEG systems. Finally, it should be noted that although this study has demonstrated the superior performance of the sliding-window higher-order cumulant method within the traditional signal processing framework, the rapid advancement and widespread application of deep learning technologies suggest that future research should focus on exploring integration strategies combining higher-order statistical features with deep learning models.

Conclusions

This article proposes the sliding window HOC method for accurately detecting blink artifacts in single-channel EEG. The detection accuracy and general applicability of the method are validated using both semi-simulated and real data. By utilizing the difference in Gaussian characteristics between EEG signals and blink artifact signals, the results from both semi-simulated and real data demonstrate that the proposed sliding window HOC method outperforms VME and MSDW in terms of accuracy metrics and artifact reduction effectiveness metrics. Therefore, this method proves suitable for detecting blink artifacts in single-channel EEG applications.

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