3.1 EEG windowing and sampling rate

The onEEGwaveLAD framework’s first step is selecting the window length for real-time EEG data collection (Fig 1, phase A). The term ‘real-time’ here clearly means ‘pseudo-real time’, the property of a system that receives data, processes it and returns results sufficiently quickly to perform meaningful actions at that time [30]. In other words, the underlying hardware must record a minimum amount of EEG data fast enough that subsequent processing becomes meaningful for a specific purpose [31]. We refer to this parameter as RTW_L. The larger the window, the later the post-processing, limiting the real-time effect. Secondly, the sampling rate S_r for data collection of an underlying recording system should be considered. For instance, the larger the sampling rate, the more data is collected in one second; therefore, the higher the quality of EEG data is, and the more granular the post-processing can be. Contrarily, a smaller sampling rate means less data quality and less post-processing effectiveness. The third factor to account for is the upper bound in the frequency domain that a designer/data collector can tolerate. For example, some might be interested in performing post-processing up to 512Hz, and others only up to gamma frequencies, roughly 80Hz. Given Nyquist’s theorem, a periodic signal must be sampled at over twice its highest frequency component. In other words, given an EEG window length RTW_L, and a sampling rate S_r, only frequencies up to ((RTW_L * S_r)/1000 * 0.5) can be meaningfully extracted from an EEG window. For example, given a 500ms window with a sampling rate of 1024Hz, only 500 * 1024/1000 * 0.5 = 256Hz can be meaningfully extracted. The fourth factor is the consideration of the length of certain artefacts. For example, while muscle movements are transient and fast in the time domain, with frequencies ranging within 20–300Hz [32], ocular artefacts are slower in time, with blinks, lasting longer (200ms to 700ms), with frequencies within 4–20Hz [33]. Therefore, if a denoising pipeline is focused on mitigating ocular artefacts in real-time, the window length should be approximately 700ms, with a minimum sampling rate of 40Hz. Certainly, a blink is not guaranteed to be fully contained in a single window. However, smaller windows might generate problems in identifying blinks. Another technical consideration is that these windows should contain a power of 2 points to allow an efficient decomposition of an underlying signal, as explained in the next section 3.2. The sampling rate, considerations of various artefacts in the time and frequency domains, and the decomposition strategy are interrelated. The onEEGwaveLAD pipeline is based on a sliding window technique, whereby consecutive windows of EEG data of length RTW_L are individually collected and submitted sequentially for post-processing, one by one.

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Fig 1. A schematic representation of the functioning of onEEGwaveLAD, an online EEG wavelet-based learning adaptive denoising framework.

https://doi.org/10.1371/journal.pone.0313076.g001

3.2 DWT multi-level decomposition

Once the window length and sampling rate are set, a single-channel Discrete Wavelet Transform (DWT) is executed. In detail, DWT decomposes a signal into an orthogonal basis obtained by dilation and time translation of a wavelet function Ψ(t), also known as mother wavelet (MW), and a scaling function Φ(t). This process returns a set of coefficients, now referred to as DWT coefficients. This decomposes a signal x(t) of length n into time-frequency components to a level m ∈ M, implemented via a hierarchical set of sub-band filters [34]. DWT was selected over the Continuous Wavelet Transform (CWT) because it can be efficiently implemented with the pyramidal scheme of Mallat [35], known as the sub-band coding scheme, with a computational complexity of O(|M| * n) [34]. Formally: (1) with: (2) (3) where C_m,n = < x, Φm, n > and d_m,n = < x, Ψm, n > are respectively the approximation and detail coefficients at level m. The scalar product is defined with . As mentioned before, to run DWT, one has to select a mother wavelet MT (Ψ(t)). Selecting this function is not a trivial problem in the literature [36]; the nature of an underlying signal and an application domain influences its selection [37, 38].

In summary, the output of the complete DWT transformation of a x univariate EEG signal is a set of approximation and detailed coefficients for each of the various decomposition levels in M. These levels do not contain the same amount of coefficients. The pyramidal scheme splits the frequency band into two and applies a wavelet transformation to the highest band. The lower band is then split into two again, and the Wavelet Transform is applied recursively to the higher band of that split. When the output of the low-pass filter cannot be further decomposed, the decomposition scheme terminates. For example, with a window RTW_L = 1000ms (1 second), with a sampling rate of 1024Hz, the highest frequency component is 512Hz. Therefore, 512 coefficients at level 1 in the [256–512]Hz range of frequencies are produced, 256 at level 2 in the [128–256]Hz are generated and so forth. At the last level of decomposition, only one DWT coefficient is eventually produced, representing the frequencies in the range [0.5–1]Hz. The decomposition scheme produces fewer points at lower frequencies, leading to a decrease in time resolution. In other words, DWT offers poor resolution in the time domain of low frequencies and reasonable resolution in the time domain of high frequencies, providing an effective mechanism for data reduction. It is important to note that the number of decomposition levels depends on the length of the original signal. For a window of length RTW_L, then the number of decomposition levels is log₂RTW_L For the sub-band coding scheme to be efficient, and due to the successive sub-sampling by 2, the signal length must be a power of 2, or at least a multiple of power of 2. For this reason, the window length selection RTW_L should be of the power of 2.

Stretching or shrinking a mother wavelet MW located at a specific point in time leads it to see some or all of an underlying signal. In particular, wavelets applied near the edges of an observed EEG window of length RTW_L, inevitably extend their domain outside it. Consequently, the computation of DWT coefficients close to these edges is affected and should be interpreted and used carefully. The extent of the DWT coefficients affected by edge effects depends on the scale used, which is thus closely tied to the frequency under consideration. The higher the scale, the more significant the influence. This phenomenon is often called the cone of influence in the literature [39, 40]. Various techniques have been proposed to compensate for the effect on the DWT coefficients at the boundaries of an observed interval. For example, one focuses on symmetrically reflecting the signal at the border, and another periodically extends it. While interpreting DWT coefficients outside the cone of influence is essential, no formal, precise, agreed approach to determine the cone of influence at each scale exists [41, 42]. In this study, since the denoising pipeline under development has to work in real-time, the problem of the cone of influence is an important one, especially with a continuous stream of recorded EEG windows. While this pipeline can see backwards and consider past recorded data, it cannot see forward since data has not yet been recorded. In the former case, the problem of edge effects on the left border of a current EEG window w_c can be solved by concatenating it to its previous one w_c−1 and then passing such concatenation (conc = < w_c−1, w_c >) to the DWT decomposition. In this way, the left border of w_c is now in the middle of conc, so it is no longer affected by edge effects. In the latter case, this strategy cannot be applied to the right border of w_c since no window follows it. Therefore, a particular strategy is used, namely a smooth-padding mode, in which an underlying signal is extended according to the first derivatives calculated on the edges (straight line) [43]. This strategy introduces extra DWT coefficients that are eventually trimmed for the subsequent steps but guarantees a smoother DWT decomposition, minimising the edge effects.

3.3 Scaleogram formation

As described in the previous phase, the DWT decomposition of a signal occurs at various levels, each with a different amount of approximation and detailed coefficients focused on representing different frequency bands. Consequently, such DWT coefficients cannot be quickly inspected and visually reproduced over time. For this reason, scholars have introduced the notion of ‘scaleogram’, a visualisation similar to spectrograms but specifically suitable for DWT coefficients. On the one hand, more DWT coefficients exist at lower decomposition levels, representing higher frequencies. On the other hand, at higher decomposition levels, fewer DWT coefficients exist, representing lower frequencies. This asymmetry is resolved by replicating the DWT coefficients at lower levels, twice the amount of the DWT coefficients at the level just above it. In other words, the samples are repeated 2^m−1 times where m is the decomposition level. Consequently, it is possible to have the same amount of DWT coefficients for each decomposition level, forming a matrix. This scaleogram can facilitate visual energy inspection over time at different frequencies. In detail, the x-axis corresponds to time, and the y-axis corresponds to the decomposition scales, the levels (Fig 1, phase C, top scaleogram). The scale is the signal periodicity to which the transform is sensitive, and each value in the scaleogram represents the amplitude of the signal variation measured. In other words, these variations are located at specific times with specific periodicity. Unfortunately, the DWT coefficients at higher levels (lower frequencies) are generally more significant in magnitude than those at lower levels (high frequencies). Therefore, their impact is different if used in subsequent computations, with higher-level coefficients being more critical. A normalisation strategy is proposed to counteract this and assign the same importance to coefficients at the different decomposition levels (the scales). This divides each coefficient d at level m by 2^m with m starting at 1. with d_norm the normalised DWT coefficient at level m. The normalised scaleogram is a matrix n × m, with n the amount of normalised DWT coefficients per each of the m decomposition levels. n equates to the maximum frequencies that can be extracted from a signal of length RTW_L and sampling rate S_r. As mentioned in section 3.1, and according to Nyquist’s rule: with RTW_L in milliseconds, and S_r in hertz.

3.4 Extended isolation forest and adaptive moving buffer

Each slice of the n × m matrix, as produced in the previous step, is a n-dimensional vector, a unique representation of the signal at a given point in time in the domain of DWT coefficients. The first assumption is that those vectors associated with artefacts in the underlying EEG signal they represent are rare and different from all the others. Thus, they can be considered anomalies. In general, many approaches have been devised to efficiently identify anomalies within a group of points in the one-dimensional space. Among these popular solutions are those based on statistics, classification-based, clustering-based, Nearest Neighbor-based, Information-theoretic and spectral techniques [44]. Unfortunately, while they can achieve remarkable accuracy in detecting anomalies, and with a linear time complexity in testing them, they are often computationally expensive in time and space during training, often with quadratic complexities [44]. The training phase is thus a bottleneck for developing real-time anomaly detection applications. Instead, a novel algorithm, the Isolation Forest (iForest), has a linear time complexity and a limited requirement for memory consumption [45]. This makes it an appealing candidate solution for developing a real-time EEG denoiser. The main advantages of this approach over the existing ones are multiple. Firstly, it is model-free, and no statistics or probabilities, including density estimation or statistics on the class distribution, are required. Secondly, it is fully unsupervised and does not require labelled ground truth. Thirdly, it has been proven effective on n-dimensional data, and, through a sub-sampling procedure, it effectively solves the problems of swamping, which means the vicinity of normal points to the anomalous one, and that of masking, when many anomalies exist [46]. The assumption behind this algorithm is that anomalies within data are specific points that are limited in cardinality and vastly different from most of the other points, thus making them easier to separate. In other words, anomalies are rare instances of a dataset, and their characteristics in an n-dimensional space should be drastically different from those of the other instances and, therefore, easily identifiable.

Given a dataset X = x₁, …, x_c, where each instance is of dimension c, iForest sum-samples a random portion of data X′ < X to construct a binary tree, namely an Isolation Tree (iTree). The branching process of such a tree is executed by picking a random dimension rd_i, with i in 1, 2, …, c, and a random split value sv, within the range of rd_i (sv ∈ [min(rd_i), max(rd_i)]). If the dimension rd_i of a particular instance of the dataset (data point) has a value smaller than sv, then such instance is assigned to the left branch of the iTree. In contrast, the instance is assigned to its right branch, splitting the data on the current node of the tree into two. This branching mechanism is then performed recursively for each instance of the dataset until a single point is isolated or a predetermined depth limit is reached. In other words, until the node has only one instance, or all the data at that node have the same values. Formally, an iTree is a data structure where each node T is either a leaf, an external node with no child, or an internal node with exactly two children nodes (T_l, T_r), and a condition defined by a dimension rd_i, and a split value sv, such that rd_i < sv determines the traversal of a data point to the left branch t_l, or the right branch T_r. When the iTree is fully grown, each point in the dataset X is isolated at one of the leaf nodes. Each data point x_i ∈ X has a specific path length h(x_i), which equates to the number of edges x_i traverses from the root to a leaf in the tree. Intuitively, an anomaly is a data point with a smaller path length since it can be isolated easily. The aforementioned recursive process called the training phase, is repeated IF_t times, creating an ensemble of iTrees, an isolation forest (iF). The identification of anomalies can be performed by a binary search with such a forest. In detail, similarly to the searching mechanism of the Binary Search Trees (BST) algorithm [47], the termination to a leaf node on an iTree means an unsuccessful search in the BST. Consequently, estimating the average path length h(x) of all the leaf nodes is equivalent to the unsuccessful search in the BST. Formally: (4) where |Y| is the size of the testing data Y, |X′| is the size of the random portion of data X′, H is the harmonic number that can be estimated by H(i) = ln(i) + γ (with γ = 0.5772156649 the Euler-Mascheroni constant). In other words, a(|X′|) is the average of h(x) given |X′|, and it can be used to normalise h(x) and obtain an estimation of the anomaly score for a specific data instance x ∈ X. Formally: (5) with E(h(x)) the average value of h(x) from the forest, the collection of iTrees. For any given instance x ∈ X, if s is smaller than 0.5, then x is likely to be a normal value (not an anomaly). In contrast, if s is close to 1, the instance x is likely to be an anomaly. Once an isolation forest is built, a test phase is executed whereby each instance of a test set Y = y₁, …, y_c is passed to each iTree of the forest, and an anomaly score is assigned to it. In this research, a particular version of the original Isolation Forest is used, namely the Extended Isolation Forest algorithm [48]. Such an extension solves the problem of bias in the original algorithm caused by tree branching. In detail, a feature and a value are chosen at each branching point, which is a form of bias since such a point is parallel to one of the axes. In contrast, the extended algorithm defines a random slope rs instead of selecting a feature and value for the branching cut and a random intercept ri. On the one hand, a Gaussian distribution can generate such a slope rs. On the other hand, the intercept ri can be generated from the uniform distribution with bounds coming from the sub-sample of data that has to be split. Formally, the branching criteria for the data splitting for a given point is (x − ri) * ≤ rs. One parameter of the Extended Isolation Forest is the extension level el, which is a number in the range [0, c − 1], with c the number of features (dimension) of an original instance x ∈ X. If el = 0, the extended version coincides with the original Isolation Forest Algorithm. Deviations from zero correspond to reductions of bias. Another parameter is the number of randomly sampled observations IF_S used to train each Extended Isolation Forest tree.

The above mechanism can identify the anomalous n−dimensional vectors among the m vectors of each normalised scaleogram, if any, as produced in the previous step for each EEG window. Ideally, more of these vectors are used as input to the Isolation Forest algorithm, and better anomaly detection can be performed. Theoretically, suppose such an algorithm is executed after collecting an EEG window of length RTW_L. Consider also that an isolation forest iF was trained with all vectors composing each normalised scaleogram of its preceding EEG windows. In such case, if an iF is trained after collecting each EEG window, increasing training data is produced over time; thus, a longer time is required to train it. However, while it is theoretically possible to include all the vectors of each normalised scaleogram collected up to a point in time, practically training an Isolation Forest with all such vectors requires a linear increment in time complexity, proportional to the number of recorder EEG windows. Consequently, testing an iF at a future point might cause technical issues because it might require more time than the established length of the EEG window (RTW_L), effectively hampering the effort to develop a real-time EEG denoiser. In other words, accounting for all the previous vectors of normalised scaleograms recorded up to a point in time is not ideal if a real-time denoising pipeline for artefacts in EEG signals is to be devised. For this reason, a moving, sliding buffer B_s of fixed capacity s is proposed to contain the n-dimensional vectors of the normalised scaleograms associated with the s recorded EEG windows occurring earlier than the one recorded in real-time. On the one hand, this fixed capacity resolves the technical challenges associated with the time complexity required to run the Isolation Forest algorithm and test the resulting model. On the other hand, the buffer’s ‘sliding’ property also makes the proposed artefact denoising pipeline adaptive. It is adaptive to the changing recording environment and inherently prone to the slow amplitude drifts of each EEG channel. These might be caused by the reduction of the scalp electrodes’ physical adherence or the drying of the conductive gel used, among other reasons. However, such consideration entails a second assumption behind this research study: genuine neural signals are recorded in most parts of this moving buffer, with a small portion of artefacts. While this is reasonable, identifying anomalous EEG segments will be hampered if the buffer contains mainly noise and artefacts. The investigation of this assumption is outside the scope of this study and will be the subject of future empirical investigations. Intuitively, solutions can be defined to check whether the sliding buffer mainly contains neural plausible signals.

3.5 Artefact identification

Once the extended Isolation Forest algorithm is run with the n-dimensional vectors of all the scaleograms saved in the moving buffer up to a time point for a given EEG channel, it produces a list of anomaly scores, one score for each vector. Subsequently, an anomaly threshold t_a is devised to discriminate abnormal n−dimensional vectors from the rest. As mentioned at the end of section 3.4, a rule of thumb suggests that a value of t_a = 0.5 can be confidently used to separate the n−dimensional vectors that behave normally from those that do not [45]. When the extended Isolation Forest algorithm is run with the n-dimensional vectors in the moving buffer, hereby referred to as the ‘training’ procedure, producing an Isolation Forest iF, it is then tested with the n-dimensional vectors associated with the normalised scaleogram of the current EEG window recorded in real-time (the B_s + 1th EEG window, with B_s the size of the moving buffer). This ‘testing’ procedure allows computing an anomaly score for each of the m n-dimensional vectors of the B_s + 1 normalised scaleogram (the current one) and extracting those with a value greater than the threshold t_a, if any. The timestamp of each of these abnormal vectors is saved in a list AT (anomalous timestamps). In other words, these timestamps, if any, represent the exact points in time within the current EEG window that contain abnormal behaviour (the anomalous vectors) and potential artefacts.

3.6 Artefact reduction

Once the abnormal time locations, the list AT (anomalous vectors, in red in Fig 1) have been established, if any, for the n−dimensional vectors in the current EEG window, their deviations from normal behaviour, the potential artefacts, need to be mitigated. At this stage, the notion of a normalised scaleogram is forgotten, and the original, non-normalised scaleogram of the current EEG window is instead re-considered. This is because, eventually, the denoised pipeline proposed in this research will culminate in the output of a neural signal in the time domain by applying the inverse Discrete Wavelet Transform (DWT) on the denoised vectors for the current EEG window. This inversion requires a set of concatenated approximate and detailed DWT coefficients to generate a time series. If such coefficients are those normalised across levels (as described in section 3.3), then this inversion would not produce a denoised signal close to the original one but a different one, thus essentially and erroneously changing the underlying neural dynamics. For this reason, the non-normalised (original) DWT coefficients of the current EEG windows are considered and manipulated before being inverted into the time domain.

Artefact reduction usually includes removing or attenuating wavelet coefficients using a thresholding mechanism [49]. Technically, a threshold could be established by visually inspecting the wavelet coefficients. However, while this works in offline artefact reduction, it is unfeasible in online applications. Therefore, a common approach is to use the Universal Threshold considering all the wavelet coefficients and their standard deviation [50]. Subsequently, artefact reduction is usually implemented by applying a hard or a soft thresholding function on the wavelet coefficients [51]. Threshold values can be generated by considering all the wavelet coefficients for all the DWT levels or separately for each of them [52]. The latter case is relevant in EEG artefact removal applications where stationarity is not guaranteed [53]. For this reason, other approaches have been proposed to account for deviations from stationarity, where time-varying thresholds are defined by considering the statistical deviation computed over an ensemble of surrogate time series [54].

Inspired by this property of adaptivity, onEEGwaveLAD, via its sliding buffer, proposes an adaptive thresholding mechanism for DWT coefficients at the different DWT levels. This mechanism includes computing the medoid B_medoid of all the n−dimensional vectors in such moving buffer as the most representative point, whose sum of dissimilarities to all the other vectors is minimal. It is considered the most common behaviour of an underlying neural signal in the preceding EEG windows to the current one (with B_p, the number of windows in the buffer), including information about its frequencies over time. Additionally, motivated by wavelet theory [55] and the fact that the wavelet coefficients around a vector identified as anomalous are similar in magnitude, an expansion step E_s is introduced, defining how many neighboured vectors to those identified as anomalous should also be denoised. This is important because some neighbouring vectors might not have been identified as anomalies because they do not satisfy the anomaly threshold t_a. This expansion leads to a new list of timestamps AT_exp of anomalous vectors. Such a denoising mechanism aims to implement a smooth artefact reduction around each anomalous vector, not a sharp one. It also considers the neural mechanisms detected in the EEG data before the window is recorded. In detail, the denoising of the wavelet coefficients of the n−dimensional vectors in the expanded list AT_exp can be implemented via a mitigator vector Mtg, which is the complement of the distance of the specific DWT coefficients of a vector a in the list AT_exp, from the medoid B_medoid of the buffer B_s, divided by the max distance vector, always from the medoid, among the vectors in the buffer B_s. Formally: (6) with is the mitigating vector used to denoise every vector a in AT_exp. This mitigator is more aggressive for vectors far from the medoid (the potential artefacts) and softer for those close to it (the normal neural signal). The new vector of denoised DWT coefficients of each of the n−dimensional vectors in the expanded list AT_exp is its Hadamard Product, namely the element-wise multiplication, with the mitigator vector. Formally: (7) It is important to observe that even if an n−dimensional vector is identified as anomalous, and because its denoised version is computed element-wise, some of its DWT coefficients can be reduced more aggressively, for example, at some specific scale (frequency) than others. Future extensions of this might include a mechanism that mitigate only certain frequencies known to be important for a particular artefact, for example such as blinks.

3.7 Multi-level composition

Eventually, the last step in the overall denoising pipeline is the concatenation of the non-normalised n−dimensional vectors with those that went through the artefact reduction phase, as described in the previous section 3.6, preserving their time appearance. This concatenation represents the denoised scaleogram for an underlying length signal n. At this stage, the DWT coefficients in this scaleogram have been repeated 2^m−1 times for each decomposition level m, as already described in section 3.3. To properly re-convert them into the time domain, they must be reshaped, and the repetitions removed (reshaper-removal in Fig 1). Specifically, for the first decomposition level, with a window of length RTW_L, with a sampling rate S_r in hertz, k = ((RTW_L * S_r)/1000 * 0.5) DWT coefficient exists. Consequently, for each decomposition level m, only k/2^m−1 coefficients are unique and not repeated; the other must be removed. This can be done by taking the first DWT coefficient for every 2^m−1 coefficient at a level m. This reshaping procedure results in more DWT coefficients at lower decomposition levels, representing higher frequencies, and fewer at higher levels, representing lower frequencies. In particular, this has the same shape as the output of Eq 1, with denoised approximate coefficients for a signal of length n and denoised detailed coefficients for each decomposition level m ∈ M. These are subsequently passed through the inverse Discrete Wavelet Transformation (DWT) (inversion of Eq 1) for their conversion back into the time domain. Formally: (8) where and are respectively the sets of denoised approximation and detail coefficients. This eventually returns a corrected signal x^den(t), which is the denoised version of the original signal over time.

3.8 Summary of parameters of onEEGwaveLAD

In synthesis, the onEEGwaveLAD pipeline has a set of parameters dependent on the type of artefact that needs to be removed, the nature of the recorded EEG signal, and the strategies used to detect and reduce noise in it:

• Real-time EEG Window Length (RTW_L): the length in milliseconds of a recorded EEG segment for dealing with real-time denoising;
• Sampling rate (S_r): the number of points, in Hertz, of the recorded EEG segment, for dealing with the granularity of denoising;
• Mother wavelet(MW): a function used for decomposing the recorded EEG segment, employing the DWT decomposition scheme; this function should be as similar as possible to the prototypical shape of the artefact being removed;
• Buffer capacity (B_s): the amount of EEG windows composing the sliding buffer for storing the past EEG signal’s behaviour to the current recorded window; this is for implementing the adaptiveness of the denoising framework to the non-stationarity of the recorded EEG signal;
• IF Sub-sampling size (IF_S): the number of randomly sampled observations used to train each Extended Isolation Forest tree;
• Number of IF trees (IF_t): the number of trees to learn by the Extended Isolation Forest Algorithm;
• Anomaly threshold (t_a): a threshold for deeming a vector of n-dimensions (the decomposition scales) as an outlier given its anomaly score computed by the extended Isolation Forest model;
• Expansion step (E_s): the number of points to consider around each anomalous vector that has to be denoised.

4.1 Data understanding

The N170 dataset of the ERP-CORE (Compendium of Open Resources and Experiments) was selected (https://doi.org/10.18115/D5JW4R). It includes EEG data from 40 participants (25 female, 15 male; mean years of age = 21.5, SD = 2.87, Range 18–30; 38 right-handed) from the University of California, Davis community who were exposed to a visual discrimination paradigm for isolating the face-specific N170 response. Each participant reported their native English competence, normal colour perception, normal or corrected-to-normal vision, and no neurological injury or disease history. As suggested in [56], participants who exhibited a significant portion of artefacts from a visual inspection were removed. This led to a final dataset containing EEG data from 37 participants, and only raw data was considered for this experiment. The recording length averages 581 seconds with a standard deviation of 55 seconds across participants. EEG data was recorded using a Biosemi ActiveTwo recording system with active electrodes (Biosemi B.V., Amsterdam, the Netherlands) from 30 scalp electrodes, placed according to the 10/20 International System (FP1, F3, F7, FC3, C3, C5, P3, P7, P9, PO7, PO3, O1, Oz, Pz, CPz, FP2, Fz, F4, F8, FC4, FCz, Cz, C4, C6, P4, P8, P10, PO8, PO4, O2). P01 was assigned to the common mode sense (CMS) electrode, with the driven right leg (DRL) electrode at PO2. Signals were low-pass filtered using a fifth-order sinc filter with a half-power cutoff at 204.8 Hz and then digitized at 1024 Hz with 24 bits of resolution. Electrodes were placed lateral to the external canthus of each eye to record the horizontal electrooculogram (HEOG). In addition, a vertical electrooculogram (VEOG) was recorded using an electrode placed below the right eye. Further details on how data was collected and the original context of application to Event-Related Potential research can be found in [57]. The primary rationale for selecting such a dataset is the public availability of the ERP-CORE. This was prepared by a well-known research group in neuroscience, which suggested that researchers could use it to test new hypotheses by reanalyzing the existing data in novel ways and to test newly developed data processing procedures, as is eventually done in this research study.

4.2 Instantiation of onEEGwaveLAD

The onEEGwaveLAD pipeline described in section 3 is instantiated for ocular artefact identification and reduction, specifically for blinks (and not saccades) with the parameters listed in Table 1.

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Table 1. Parameters of an instantiation of the onEEGwaveLAD pipeline for blink identification and reduction for the Fp1 and Fp2 EEG channels.

https://doi.org/10.1371/journal.pone.0313076.t001

The Real-time EEG Window Length of 1 second is selected because of the typical blink length: between 100 and 400ms [58]. In the best case, the rationale is to have a length long enough to include the entire blink duration. The sampling rate was kept at the original, 1024Hz. Since this is a multiple of a power of 2, this aligns with the suggestions related to the efficiency of the sub-band coding scheme of DWT multi-level decomposition, as described in section 3.2. The Mother Wavelet selected is ‘Sym4’, a near symmetric (least asymmetric), orthogonal and biorthogonal function of the Daubechies family of wavelets, already used in experiments dealing with ocular artefacts [59, 60]. This is chosen because its shape highly resembles an ocular eye blink [61] (Fig 2, middle) with a positive peak. The buffer capacity is chosen to be 10, 15, and 20 windows, which, given their length of one second, correspond to 10, 15, and 20 seconds, respectively. Three options are tested to evaluate their impact on the overall denoising capacity of the proposed pipeline, keeping the sub-sampling size invariant. The Isolation Forest algorithm’s sub-sampling size is set to 512, which equates to the number of DWT coefficients in a single EEG window given a sampling rate of 1024. Considering the buffer capacity options mentioned before, the Isolation Forest sub-samples have 512 DWT coefficients, respectively, out of 5120, 7680, and 10240, which are the number of DWT coefficients in the three buffer capacities (10%, 6%, 5%). Such sizes are believed to help tackle the problems of swamping and masking when detecting anomalies using the Isolation Forest algorithm. The number of trees chosen as a parameter for such an algorithm is 100, a reasonable number to learn a robust forest for discriminating anomalies. The anomaly threshold to consider a n−dimensional vector of DWT coefficients as an anomaly is 0.55. This is slightly more stringent than the rule of thumb described in section 3.5. In other words, if the anomaly score, computed by using the Isolation Forest model, of each vector composing the normalised scaleogram of the current EEG window (the last recorded), trained with all the vectors associated with the normalised scaleograms of the previous EEG windows saved in the moving buffer, is above 0.55, then it is considered an anomaly, a specific outlier. Eventually, the expansion step is tested against eight options: 0, 5, 10, 15, 20, 25, 30, 35. Once anomalous DWT coefficients in the current EEG window are found, if any, an expansion step of 35 means that 35 points to their left and 35 points to their right are marked as DWT coefficients that also require reduction. If such expansion exceeds the boundaries of the current EEG windows, they are clipped (0 to the left side and 512 to the right side). In other words, the expansion does not exceed the boundary of the current EEG window (containing 512 coefficients). These options are tested to investigate the impact of such expansion on the denoising capacity of the proposed pipeline. As mentioned in section 3.6, the reasoning is that artefacts are not only on the DWT coefficients deemed anomalous but, given their transient nature, also in their neighbourhood.

4.3 Evaluation

A ground truth is required to test the capacity of onEEGwaveLAD for detecting and removing blinks with the specific instantiation described in the previous section. Identifying blinks via an offline analysis of the entirety of a recorded EEG signal has been proven not to be a complicated problem [62, 63]. This can be done with a peak detection algorithm on specific uni-variate signals, such as that recorded by a vertical EOG electrode (VEOG), if present [64]. Alternatively, in its absence, Fp1 and/or Fp2 can be used [65]. Unfortunately, peak detection algorithms suffer from the problem of manually setting a threshold that can be used to discriminate blinks in a uni-variate signal [66]. Lower thresholds might lead to identifying few blinks, decreasing true positives, while higher thresholds can increase false positives. In this experiment, the VEOG channel is selected, given its availability in the chosen dataset (ERP-CORE/N170), and a peak detection algorithm (algorithm 1) is adopted to extract a list of potential peaks.

Algorithm 1 Peak detection algorithm

procedure PeakDetection[VEOGsig], k

 [VEOGsig_fir] ← firwin([VEOGsig], 1, 10)

 [VEOGsig_abs] ← abs([VEOGsig])

 [VEOGsig_sqrt] ← sqrt([VEOGsig_abs])

 VEOGsig_max ← max([VEOGsig_sqrt])

 VEOGsig_std ← std([VEOGsig_sqrt])

 VEOGsig_th ← (VEOGsig_max − VEOGsig_std)/k

 peaks ← findPeaks(VEOGsig_fil, VEOGsig_th)

 return [peaks]     ▷ Peaks locations

end procedure

A filtered VEOG signal, achieved by applying a Firwin filter in the range [1, 10]Hz, is converted to absolute values and root squared. The resulting signal’s max and standard deviation are computed, and the threshold is established with a tunable k value passed as input. Tuning this value can result in more blinks detected, which can be detrimental to false positives, or fewer blinks, which can be detrimental to true positives. Eventually, a function for finding peaks given the filtered VEOG and the established threshold is run, and a list of peak locations is computed. Many of these functions exist in the literature, and one can select the most appropriate. Such a peak detection algorithm is subsequently invoked with different increasing k values to find true positives and a particular multi-channel selection strategy to filter false positives, as in the pseudo-code in S1 Appendix 7.1. In particular, it is known that a blink has a positive charge in the cornea, close to the pre-frontal channels, especially Fp1 and Fp2, and a negative charge in the retina, in the occipital channels, especially in O1, O2, Oz [67, 68]. Frontal channels (F) are affected by the positive charge, less than the pre-frontal ones (Fp). The parietal occipital channels (PO) are affected by the negative charge, but higher than the occipital ones (O). A loop goes through various options for parameter k and either stops at the last option, or when the number of identified true positive blinks does not improve for some consecutive times (patience). The topographic maps associated with these peaks, computed using the multi-channel information at that given time, are manually visually inspected for a final confirmation, and their timestamps are saved in a list of true blinks.

For each EEG window, the signal-to-noise ratio (SNR) is computed for the original (raw) signal and its denoised version for the channels Fp1 and Fp2. A denoised EEG window is considered a true positive if onEEGwaveLAD had identified at least one anomalous n−dimensional vector in its DWT space. The hypothesis is that the onEEGwaveLAD real-time denoising pipeline is expected to have better SNR ratios for the true positive blinks but similar ratios for the true negatives. In the non-blink EEG windows, the SNR will be the same for false positives since no artefact will be identified, and thus, no reduction of their EEG signals will be performed. Similarly, the false negative EEG windows will be modified since the onEEGwaveLAD will erroneously identify some parts as anomalous. However, in this case, the SNR in the false negative EEG windows is expected to be lower than in the true positive regions. For this, the Jensen-Shannon (JS) divergence between the probability distributions of the original signal in the true positive EEG windows and the denoised signal in the same windows is expected to be higher than that in the false negative EEG windows. The JS metric, grounded on information theory, returns a value between zero and one, with zero indicating that the two underlying probability distributions are identical, and one determines that they are entirely different. It was adopted because it offers a way of calculating the drift between original and denoised EEG signals. It is a symmetric metric, meaning that the order of the two underlying distributions does not impact the resulting divergence computation. Similarly to the Kullback-Leibler (KL) divergence, it can be thought of as a measure of the distance between two data distributions aimed at showing how they differ from each other. However, in contrast to the KL divergence, a mixture probability distribution derived from the two underlying distributions is used as a baseline when comparing them instead of a static distribution that needs to be assumed before computation.

In synthesis, the goal is to demonstrate that onEEGwaveLAD can effectively denoise artefactual intervals but not alter non-artefactual intervals, thus changing genuine neural activity.