Ocular Reduction in EEG Signals Based on Adaptive Filtering, Regression and Blind Source Separation
Authors
- First Online:
- Received:
- Accepted:
DOI: 10.1007/s10439-008-9589-6
- Cite this article as:
- Romero, S., Mañanas, M.A. & Barbanoj, M.J. Ann Biomed Eng (2009) 37: 176. doi:10.1007/s10439-008-9589-6
Abstract
Quantitative electroencephalographic (EEG) analysis is very useful for diagnosing dysfunctional neural states and for evaluating drug effects on the brain, among others. However, the bidirectional contamination between electrooculographic (EOG) and cerebral activities can mislead and induce wrong conclusions from EEG recordings. Different methods for ocular reduction have been developed but only few studies have shown an objective evaluation of their performance. For this purpose, the following approaches were evaluated with simulated data: regression analysis, adaptive filtering, and blind source separation (BSS). In the first two, filtered versions were also taken into account by filtering EOG references in order to reduce the cancellation of cerebral high frequency components in EEG data. Performance of these methods was quantitatively evaluated by level of similarity, agreement and errors in spectral variables both between sources and corrected EEG recordings. Topographic distributions showed that errors were located at anterior sites and especially in frontopolar and lateral–frontal regions. In addition, these errors were higher in theta and especially delta band. In general, filtered versions of time-domain regression and of adaptive filtering with RLS algorithm provided a very effective ocular reduction. However, BSS based on second order statistics showed the highest similarity indexes and the lowest errors in spectral variables.
Keywords
Electroencephalography (EEG)Electrooculography (EOG)Ocular artifactsRegression analysisAdaptive filteringBlind source separation (BSS)Independent component analysis (ICA)Introduction
Quantitative analysis of electroencephalographic (EEG) signals is a helpful support in the diagnosis of psychiatric and neurological disorders, and in the evaluation of drug effects in functional states of the brain. EEG changes are often quantified by the calculation of spectral variables in different frequency bands of clinical interest: delta, theta, alpha, and beta. It is known that non-cortical interferences, such as heart, ocular, and muscular activities, contribute to EEG recordings. Procedures to detect and remove these artifacts are very important and necessary because they could lead to wrong results and conclusions.
Ocular artifacts are the most relevant interference because they occur very frequently and their amplitude can be several times larger than brain scalp potentials. As the eyeball moves, the electric field composed by cornea and retina changes and it produces the electrooculographic (EOG) signals. Additionally, some neural activity is recorded by EOG electrodes because they are located near the head. Muscle activity associated with the eyes or near them can also interfere in the EOG signal. Ocular activity propagates across the scalp: vertical ocular projection following the anterior–posterior direction, and horizontal mainly affecting lateral–frontal scalp regions.7
Linear regression analysis is the most common approach for reducing eye movement artifacts. This method estimates and removes the EOG component existing in each EEG lead. However, regression procedures do not take into account the bidirectional contamination, i.e., EOG recording is also contaminated by cerebral activity, and consequently this cerebral information could be relevant and can also be cancelled in the EEG recordings after linear subtraction. Gasser et al.11 proposed previously to apply regression procedure a low pass filtering of EOG signals in order to reduce the cancellation of high frequency cerebral components from EEG data.
He et al.12 proposed the adaptive filtering by recursive least squares (RLS) algorithm which was applied to simulated data in He et al.13 in order to compare with time-regression procedure. However, the authors did not consider in their study the bidirectional contamination. They recognized that it would deteriorate the method and they pointed out modifications such as smoothing the reference EOG.
In addition, other approaches based on Blind Source Separation (BSS) have been proposed.18,22,31 BSS procedures decompose the multichannel EOG and EEG recordings into source components. Sources, which are related with artifacts, are deleted by removing their contributions onto the scalp sensors. The first proposed component-based procedure was Principal Component Analysis (PCA).20 However, it has several drawbacks related to the assumption of orthogonality between neural and ocular activities, and the difficulty to separate eye movement artifacts from cerebral activity when their amplitudes are similar. More recent approaches use blind source extraction based on Independent Component Analysis (ICA). Assumption for ICA-based techniques is that sources must be statistically independent, not just uncorrelated, and this is mostly true with regard to brain and ocular components.
There are different algorithms and principles to estimate the components, generally based on second order and higher order statistics. However, most of the EEG studies with ICA application identify the artifactual source components by visual inspection following a time-consuming subjective criterion. Moreover, quantitative evaluation of the performance of each ocular correction method is difficult because it would be necessary to get available previous knowledge corresponding to the true ocular and cerebral activities, and this is not possible because they cannot be separately measured due to bidirectional contamination. There have been few empirical studies measuring the effectiveness of ocular reduction techniques on simulated data composed by mixtures of cerebral and ocular activities.19,32 However, these studies showed opposite conclusions: regression and PCA based algorithms were suggested in Wallstrom et al.,32 adaptive filtering was proposed in He et al.,12 and BSS techniques based on second-order statistics were recommended in Kierkels et al.19 and Romero et al.25 in spite of adaptive filtering was not evaluated in both. Moreover, in spite of the theoretical advantages of BSS based approaches, a very recent study based on real data and using expert scorers for identifying ocular artifacts concluded that regression procedure could significantly reduce ocular artifacts better than ICA when few EEG channels were available.27
Regarding simulated data, in Wallstrom et al.32 coefficients for the linear mixture were determined based partially on normalizing random variates. Due to this random mixture, simulated EEG signals did not correspond to specific EEG leads. In Kierkels et al.19 forced and fast ocular movements were simulated by Boundary element method (BEM). BEM calculated the potential at different positions in an arbitrary shape volume, and with representative tissues conductivity values taken from literature. Furthermore, the location of simulated brain dipoles was chosen randomly based on real data from one EEG channel. This study was based on situations with open eyes. In He et al.13 an arbitrary gain function for ocular propagation was used to obtain simulated EEG and EOG signals. This function was frequency dependent and constructed based on Gasser et al.10 In Romero et al.,25 simulated data was generated from spontaneous EOG and EEG signals with closed eyes and with normal (not fast forced) eye movements, which is the common procedure used in clinical routine. The simplest linear instantaneous mixtures were carried out by factors from regression coefficients and by using EEG recordings considered free of ocular artifacts with a not very restrictive condition. In the present study, simulated EEG and EOG data were obtained by more general linear mixtures whose coefficients were calculated by means of multi-input single-output (MISO) linear models applied to a database composed of real EEG and EOG recordings. A more restrictive condition than used in Romero et al.25 was applied in order to consider EEG recordings more free of artifacts. Bidirectional contamination, where EOG recordings are also interfered by some cerebral activity, was also taken into account by linear mixtures in both directions.
In this study, a fully automatic procedure for ocular correction from spontaneous EEG signals based on BSS described in Romero et al.25 was used. The objective of the present study was twofold. The first aim was to generate simulated EEG and EOG signals in order to reproduce a real clinical situation in practice. It was achieved by obtaining a proper propagation model of cerebral and ocular activities across the scalp based on the theory of system identification. The second aim was to evaluate the performance of different ocular reduction methods (linear regression, adaptive filtering and BSS) on this simulated data. This evaluation was quantitatively carried out by level of similarity, agreement, and spectral target variables used commonly in clinical EEG studies.
Methodology
Subjects and Instrumentation
Twenty-four young healthy volunteers of either gender (aged 22.50 ± 3.75 years) were selected for the study from a larger database. Spontaneous EEG and EOG signals, sampled at 100 Hz, were acquired during 10 non-consecutive 3-min periods following a vigilance-controlled condition with eyes closed. During the vigilance-controlled recordings, the experimenter tried to keep the volunteers alert by acoustic stimulation. Twelve subjects with normal-high eye movements (called ‘ocular group’) were selected following visual inspection of EOG signals. The remaining 12 volunteers (called ‘cerebral group’) were carefully chosen based on the criterion of no apparent eye movements (3 consecutive minutes with EOG amplitudes lower than 25 μV). Nineteen EEG recordings were obtained by means of scalp electrodes placed according to the international 10/20 system: Fp1, Fp2, F7, F3, Fz, F4, F8, T3, C3, Cz, C4, T4, T5, P3, Pz, P4, T6, O1, and O2, referenced to averaged mastoids. Additionally, vertical and horizontal EOG (VEOG and HEOG, respectively) signals were recorded. The VEOG signal was acquired from mid-forehead (2.5 cm above the pupil) to the average of one electrode below the left eye and one electrode below the right eye (2.5 cm below the pupil). The HEOG signal was obtained from the outer canthi. Multichannel EOG and EEG signals were recorded using a band pass filter between 0.3 and 45 Hz.
Simulated Data
Simulated EEG Signals
Neural sources (EEG_{s}) corresponding to 3-min consecutive epochs were obtained from the 19 EEG channels for each subject belonging to ‘cerebral group’ and selected from the entire large database. The selection criterion was that no samples from VEOG and HEOG signals exceeded 25 μV. This threshold was lower than 40 μV, which was used in a previous study,25 in order to better consider a reduced potential ocular activity in EEG data. Neural sources were obtained by high-pass filtering the EEG channels with a cut-off frequency of 0.5 Hz in order to reduce very low frequency components which could be possibly more related to ocular activity. Interference from ocular activity was added to the neural sources. This interference was calculated by estimation of linear models between EOG and EEG recordings following the procedure explained below.
Ten 5-s epochs with high EOG activity were chosen from each one of the 12 volunteers belonging to the ‘ocular group.’ A multi-input single-output (MISO) linear model was estimated for each 5-s epoch and for each lead. Models had two inputs corresponding to VEOG_{O} and HEOG_{O} signals (subindex_{O} referred to signals derived from the ‘ocular group’), and one output that was each one of the 19 EEG_{O} channels. Due to bidirectional contamination, it is well known that cerebral activity also affects to EOG signals. This activity was reduced for a better estimation of models in order to obtain the interferences from ocular activity. For this purpose, in each model, EEG_{O} and EOG_{O} channels, corresponding to outputs and inputs, respectively, were low-pass filtered with the cut-off frequency corresponding to highest value of the 99% (f_{99}) of the total energy of these VEOG_{O} and HEOG_{O} signals. Thus, the remainder 1% of signal energy was not considered as ocular activity (neural activity, electrode noise, power line interference, etc.) in the EOG_{O} recordings. The 99% cut-off frequencies obtained were 6.34 ± 4.04 and 8.20 ± 5.01 Hz for VEOG_{O} and HEOG_{O}, respectively, as mean and standard deviation for all epochs and volunteers. This consideration was supported by some studies which suggested that most of the high frequency range in the EOG signal is of neural origin.11 Besides, this low-pass filtering procedure on EOG_{O} and EEG_{O} did not cause apparently shift delays or variations in the ocular waveform.
Simulated EOG Signals
Ocular activity sources (EOG_{s}) corresponding to 3-min consecutive epochs were extracted from the two EOG channels for each volunteer belonging to ‘ocular group.’ Ocular sources were obtained by low pass filtering these EOG channels with the cut-off frequency corresponding to highest value of the 99% of their total energy. Interference from cerebral activity was added to the ocular sources. Analogously to simulated EEG signals, this interference was calculated by the estimation of linear models between EEG_{C} and EOG_{C} recordings (subindex_{C} referred to signals derived from the ‘cerebral group’) following an analogous procedure that is explained below.
EEG_{C} signals for the inputs were previously high-pass filtered with a cut-off frequency of 0.5 Hz in order to reduce very low frequency components which could be possibly more related to ocular activity. Besides, the target spectral variables used for the evaluation of ocular filtering performance were calculated in frequencies higher than 0.5 Hz. Thus, this high pass filtering did not affect results and conclusions but it permitted a better estimation of model in order to obtain the cerebral contamination. The selected order for N and M were 4 and 3, respectively, and were chosen by the same criterion as in section “Simulated EEG Signals.” Remainder steps of the procedure were analogous to the ones explained in section “Simulated EEG Signals.” Finally, four 256-order FIR filters were obtained for VEOG_{C}\( {\left[ {\ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{Fp}}1 \to {\text{VEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{Fp}}2 \to {\text{VEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{F}}7 \to {\text{VEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{F}}8 \to {\text{VEOG}}}} (k)} \right]} \) and HEOG \( {\left[ {\ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{Fp}}1 \to {\text{HEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{Fp}}2 \to {\text{HEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{F}}7 \to {\text{HEOG}}}} (k)\quad \ifmmode\expandafter\bar\else\expandafter\=\fi{b}_{{{\text{F}}8 \to {\text{HEOG}}}} (k)} \right]} \) channels from each volunteer belonging to ‘cerebral group.’
These FIR filters, that were specific for each one of the 12 volunteers, were applied to four leads of EEG_{C} sources (EEG_{Fp1 s}, EEG_{Fp2 s}, EEG_{F7 s}, and EEG_{F8 s}) in order to obtain EOG recordings (mixed EOG signals, VEOG_{m} and HEOG_{m}) from 12 simulated subjects:
Ocular Filtering Methods
Linear Regression
This method can easily be implemented but it causes distortion of the corrected EEG signals because it does not take into account the bidirectional contamination between ocular and cerebral activities. In order to improve the performance of the regression procedure, a variant of the method was proposed.11 Cancellation of cerebral information can be reduced by low-pass filtering with a cut-off frequency of 7.5 Hz the VEOG_{m} and HEOG_{m} signals before the application of regression subtraction.
Adaptive Filtering by Recursive Least Squares (RLS)
Although there are several adaptive filtering algorithms, RLS has shown best stability, efficiency and fast convergence. There are two parameters involved in the adaptive filtering method: the number of weights M and the forgetting factor λ. In theory, the value M is determined by characteristics of the EOG-EEG transfer function but the performance of the adaptive filter is not sensitive to this value, as it will be demonstrated in section “Ocular Artifact Removal.” The forgetting factor adjusts the weight of the previous samples to update the filter coefficients, and it depends on the stability of the relationship between the reference inputs (VEOG_{m} and HEOG_{m} signals) and the primary input (EEG_{i m} lead). Mathematically, λ is related to a window that indicates the number of previous samples that are used to calculate the current filter coefficients. The size of this window can be estimated by solving λ^{N }= 0.5, where N are the number of sample points. A study of the performance of adaptive filtering for several values of M and λ was performed and shown in section “Ocular Artifact Removal” in order to select their proper values.
Component Based Techniques
Component-based approaches decompose multichannel EOG and EEG data into a mixture of source ocular and cerebral signals. BSS problem assumes that a set of m recorded EOG and EEG channels are composed by a mixture of n source components, generally with n ≤ m. Corrected EEG signals can be recovered by a re-mixing process rejecting the ocular sources, i.e., using only the cerebral, or non-ocular, sources. There are several approaches to solve the so-called BSS problem which can be divided in second-order statistics (SOS) techniques and ICA algorithms based on higher-order statistics (HOS).
SOS techniques formulate the hypothesis that sources are only uncorrelated, which is a weak form of statistical independence. Two SOS-based methods were evaluated in this study: PCA and SOBI (Second-Order Blind Identification). PCA transforms multichannel data set by a rotation, in such a way that components in the new coordinates become uncorrelated and orthogonal. SOBI uses the time structure information provided by the sources to improve the estimation of the model. SOBI decomposition procedure consists on diagonalizing time-lagged covariance matrices.4
The difference between SOS- and HOS-based algorithms resides in how the sources are modeled: if sources are assumed mutually independent, HOS are essential to solve the BSS problem. There are several procedures to measure statistical independence, basically based on approaches of non-gaussianity, maximum likelihood estimation and mutual information.16 Two ICA algorithms were considered in this study: INFOMAX and FastICA. INFOMAX is an information theoretic based algorithm that obtains the independence maximizing the entropy of a neural processor output.3 FastICA is a computationally efficient algorithm that uses a fixed-point iteration scheme that allows faster convergences than gradient descent methods applied in other ICA algorithms. FastICA maximizes non-gaussianity as a measure of statistical independence based on the central limit theorem.15
Decomposition procedures were performed using the functions included in the ICALAB toolbox v3 for Matlab (http://www.bsp.brain.riken.jp/ICALAB/).6
- (1)
Relative power in delta band had to be greater than a specific high percentage.
- (2)
Projection strength onto the EOG electrodes had to be higher than a threshold.
- (3)
Projection strengths onto the EEG electrodes had to follow a gradient decreasing from anterior to posterior brain regions.
- (4)
The maximum of the projection strengths on the EEG electrodes had to be higher than a threshold.
Once the components related with ocular artifacts were detected, corrected EEG signals were obtained by reconstruction of the components excluding the ocular related ones.
Evaluation of Ocular Artifact Reduction
Quantitative performance of each ocular correction technique was assessed by using similarity and the most important spectral target variables which are often utilized in clinical EEG studies. In previous studies,13,25,32 mean squared error was used to measure similarity between true and corrected EEG data, but it could not be the most appropriate index due to its dependence with the signals scaling. In this article, similarity of waveforms between original cerebral sources and the corrected EEG data was assessed by calculating the Pearson’s correlation coefficient between them. Additionally, Bland–Altman analysis is the most direct way to assess agreement between two quantitative measurements.5 In this analysis, the difference of the paired two signals (corrected or mixed EEG signals minus neural sources) is plotted against the mean of both signals, and agreement is achieved if the 95% of the data points lie within the ±1.96 standard deviation (range of agreement) of the mean difference. The more narrow the range of agreement, the more precise the method. Constant biases were checked by calculating the mean of the differences. Finally, regression was performed in order to evaluate proportional biases.
Results
Simulated Data
Additionally, extent of eye movement artifacts was evaluated by the topographical distribution pattern of the magnitude frequency responses in Fig. 2: DC gains decreased considerably from anterior to posterior locations for vertical eye movements, and they decreased following a lateral axis for horizontal eye movements. It agreed with the well known physiological information mentioned in section “Introduction.” This similarity as well as the hemispheric symmetry were logical and they provided consistency to the estimated propagation models and hence to the simulated signals.
Ocular Artifact Removal
For HOS-based BSS techniques, long data is generally recommended for applying the decomposition procedure.8 In this work, all BSS-based procedures were computed with different EEG segment durations from 5 to 180 s in order to evaluate their effect in filtering. Propagation factors in regression-based techniques were calculated considering the whole 3 min available because factors only depended on subject and electrode location at the scalp.1 Relative errors for all nine spectral target variables were calculated between initial cerebral sources and corrected EEG signals. Results showed that while PCA worked better in shortest segments, errors obtained for the other SOS-based technique (SOBI) were similar in all EEG segment durations longer than 5 s and minimum at 15 s. Finally, in spite of the decreased error in HOS-based procedures by increasing the segment duration, the lowest errors were obtained for SOBI algorithm in any case (around 5%). For further analysis, the epoch duration that provided the lowest error was used for each BSS-based technique: 5 s for PCA, 15 s for SOBI and 180 s for HOS-based algorithms.
Pearson’s correlation coefficient for EOG correction procedures (mean of all the simulated subjects)
Area | EOG correction algorithms | ||||||||
---|---|---|---|---|---|---|---|---|---|
Non-corrected | Regression | Filtered regression | RLS | Filtered RLS | PCA | SOBI | INFOMAX | FastICA | |
Anterior | 0.385 | 0.740 | 0.881 | 0.730 | 0.871 | 0.640 | 0.909 | 0.782 | 0.675 |
Central | 0.667 | 0.968 | 0.980 | 0.968 | 0.982 | 0.930 | 0.986 | 0.954 | 0.899 |
Posterior | 0.851 | 0.989 | 0.992 | 0.988 | 0.993 | 0.976 | 0.993 | 0.986 | 0.965 |
All EEG channels | 0.631 | 0.891 | 0.950 | 0.888 | 0.945 | 0.840 | 0.961 | 0.902 | 0.841 |
Statistical increases between Pearson’s correlation coefficient for EOG correction procedures (paired t-tests were used between Method A vs. Method B)
Method A | Method B | |||||||
---|---|---|---|---|---|---|---|---|
Non-corrected | FastICA | PCA | RLS | Regression | INFOMAX | Filtered RLS | Filtered Regression | |
SOBI | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.009 | p < 0.013 | p < 0.016 |
Filtered regression | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.024 | ns | |
Filtered RLS | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.001 | p < 0.040 | ||
INFOMAX | p < 0.001 | p < 0.009 | p < 0.012 | ns | ns | |||
Regression | p < 0.001 | p < 0.005 | p < 0.006 | ns | ||||
RLS | p < 0.001 | p < 0.005 | p < 0.006 | |||||
PCA | p < 0.001 | ns | ||||||
FastICA | p < 0.001 |
Parameters extracted from Bland–Altman analysis (mean of anterior EEG channels and mean of all the simulated subjects)
Parameter | EOG correction algorithms | ||||||||
---|---|---|---|---|---|---|---|---|---|
Non-corrected | Regression | Filtered regression | RLS | Filtered RLS | PCA | SOBI | INFOMAX | FastICA | |
95% Confidence interval (±) | 46.054 | 9.641 | 6.646 | 10.061 | 7.260 | 12.836 | 6.152 | 11.977 | 17.723 |
Correlation coefficient | 0.759 | 0.492 | 0.300 | 0.407 | 0.222 | 0.246 | 0.132 | 0.269 | 0.392 |
Slope of regression line | 1.198 | −0.381 | −0.136 | −0.307 | −0.096 | −0.084 | −0.069 | 0.221 | 0.431 |
Results for the other brain areas (central and posterior) were similar when comparing between methods: 95% confidence range, that were lower in general for central and specially posterior areas, decreased in all methods with respect to non-corrected EEG signals and their minimum was found for SOBI algorithm (±2.419 and ±1.643 in central and posterior leads, respectively).
Percentage errors (%) in spectral variables for EOG correction procedures (mean of all EEG channels and mean of all the simulated subjects)
Spectral variables | EOG correction algorithms | ||||||||
---|---|---|---|---|---|---|---|---|---|
Non-corrected | Regression | Filtered regression | RLS | Filtered RLS | PCA | SOBI | INFOMAX | FastICA | |
Total power | 47.89 | 22.54* | 11.17** | 22.03^{*} | 10.56** | 20.53* | 4.32** | 19.52* | 43.04 |
ABS delta | 151.78 | 19.86** | 19.78** | 18.57** | 18.35** | 18.83** | 8.46** | 29.89** | 43.10** |
ABS theta | 3.78 | 20.39** | 18.92** | 20.32** | 18.54** | 22.41** | 3.88 | 21.77** | 53.97** |
ABS alpha | 0.98 | 24.91** | 5.44** | 24.77** | 5.27** | 22.54** | 1.89* | 13.46** | 34.93** |
ABS beta | 0.87 | 22.06** | 0.82** | 22.19** | 0.87 | 23.56** | 4.39** | 20.59** | 67.97** |
Mean ABS variables | 41.06 | 21.95 | 11.23* | 21.58 | 10.72* | 21.57 | 4.59** | 21.05 | 48.60 |
REL delta | 45.24 | 9.93** | 12.21** | 10.29** | 11.00** | 11.47** | 5.10** | 9.07** | 9.03** |
REL theta | 17.33 | 8.14* | 10.69* | 7.37** | 10.84* | 4.68** | 3.17** | 5.58** | 8.71** |
REL alpha | 18.45 | 8.21** | 9.47* | 8.12** | 8.98** | 6.17** | 3.47** | 5.87** | 7.75** |
REL beta | 18.50 | 14.41 | 18.64 | 12.59 | 17.52 | 6.73^{**} | 3.59^{**} | 6.47^{**} | 12.76 |
Mean REL variables | 24.88 | 10.17** | 12.75** | 9.59** | 12.09** | 7.26** | 3.83** | 6.75** | 9.56** |
Mean all variables | 33.87 | 16.72* | 11.90** | 16.25* | 11.33** | 15.21* | 4.25** | 14.69* | 31.25 |
Real Data
Discussion and conclusion
Ocular artifacts in EEG data are a significant trouble in the diagnosis of dysfunctional neural states and in the evaluation of drug effects on the brain. Most used techniques to reduce them from spontaneous EEG signals are based on regression analysis. Adaptive filtering is another approach also proposed for this purpose. Additionally, BSS procedures have been recently applied in order to consider the mutual contamination between cerebral and ocular activities. In this study for BSS-based methods, an automated procedure using logical rules, which were based on spectral and topographical information, was used in order to identify those components related to eye activity. Quantitative comparison of performance of these different ocular reduction methods required simulated signals where ocular and cerebral activities must be known a priori.
In this study, simulated EEG and EOG data were obtained by means of real data recorded according to the common procedure used in clinical routine. For this purpose, linear MISO models corresponding to ocular and cerebral activity contaminations were identified by using an autoregressive structure with exogenous inputs. Although the same model orders were used to cerebral and ocular contaminations through the same medium which is the head, higher and different orders in both contamination could have been selected. However, the identification would not improve sensitively because the FPE was not much smaller (see Fig. 1) and it is known that an unnecessary complex model could produce artifacts. It does not imply that ocular and cerebral propagations are frequency dependent, a topic that has been questioned. Bioelectromagnetism considers that volume conduction is instantaneous for frequencies lower than 1000 Hz; in other words, frequency dependence of ocular propagation is negligible.23 It is yet to be definitively demonstrated whether ocular propagation is frequency dependent or independent. In fact, any volume conductor has both resistive and capacitive properties. Nevertheless, the detailed capacitive properties of neocortex at the very low frequency components of most interest in EEG and EOG (0.5–20 Hz) have not been widely studied, but the available evidence suggests that capacitive effects have minimal influence on EEG volume conduction.24 On the other hand, other studies have taken the assumption that ocular propagation exhibits frequency-dependent behavior and apply techniques for artifact cancellation based on filtered EOG signals.10,13,29,33
In this work, for ocular contamination, magnitude frequency responses seemed to correspond to a low pass filtering procedure (see Fig. 2). However, to analyze them in more detail permitted to observe that it was not exactly thus. In this way, 3-dB bandwidths (frequency at which the gain drops 3 dB) of these FIR filters were calculated: 1.71 ± 0.76 Hz for vertical and 3.11 ± 1.94 Hz for horizontal EOG in all channels. These bandwidths corresponded to the 96.67 ± 0.01 and 97.76 ± 0.01% of the total energy of the vertical and horizontal EOG sources, respectively, for all subjects and channels. Thus, almost whole ocular propagation could be considered practically frequency-independent which was consistent to what would be expected from biophysics knowledge. Regarding cerebral activity contamination, the magnitude frequency responses from pre-frontal and lateral frontal sites to EOG locations (see Fig. 3) corresponded to quasi all-pass filters in the EEG frequency range and they could be approximated by constant propagation coefficients. Their filter gains showed a higher contamination in the vertical ocular channel than in the horizontal one.
Other studies that have been previously published compared ocular reduction methods in simulated EEG signals. However, the following approaches had not been compared so far: linear regression, adaptive filtering and BSS. Besides, filtered versions of the linear regression, which was already applied in Wallstrom et al.,32 as well as of the adaptive filtering, which was suggested but not applied in He et al.,13 were included in this study. Additionally, performance of these methods was quantitatively evaluated by similarity between sources and corrected signals and by errors in the spectral target variables used commonly in clinical EEG studies.
Time and frequency results indicated that all methods reduced significantly the ocular contamination from EEG data. However, corrected EEG signals from frontal regions showed that a partial neural component was also subtracted by regression, adaptive RLS- and PCA-based methods, possibly due to the mutual contamination between EEG and EOG signals (see Fig. 5). This cerebral information removal was partly reduced in the alpha and beta bands for regression and RLS techniques by applying a low-pass filter to EOG recordings before subtraction. Other BSS procedures based on SOS or HOS found more appropriate, and not necessarily orthogonal like PCA, source components. Assumptions about source modeling are different in SOS- and HOS-based algorithms: while SOS methods extract uncorrelated sources, HOS-based techniques use statistic information (like higher-order cumulants, entropy or maximum likelihood estimation) in order to obtain sources by minimizing an approximation of mutual information. Ocular sources extracted by HOS-based algorithms contained generally some cerebral activity, especially in anteriorly placed electrodes while it did not happen with SOBI algorithm. Errors between spectral variables for initial cerebral sources and corrected EEG signals calculated with HOS-based algorithms decreased when increasing data length, but they were far from the low errors obtained with some SOS-based methods (see Table 4: 31.25% for FastICA (n.s., when compared to non-corrected errors) and 14.69% for INFOMAX (p < 0.015) compared to 4.25% for SOBI (p < 0.001), in average). Similar errors and correlation values were obtained for INFOMAX, regression and adaptive filtering methods. Topographic distributions showed that errors were located at anterior sites and especially in frontopolar and lateral–frontal regions. Additionally, filtered version of linear regression and adaptive filtering provided good results in average: 0.950 and 0.945 for Pearson’s correlation coefficients, and 11.90 and 11.33% for errors in spectral variables, respectively. However, correlation coefficients were much higher and errors much lower for SOBI algorithm (see Tables 1 and 4: 0.961 and 4.25% in average, respectively). Moreover, agreement level by 95% confidence ranges using Bland–Altman analysis was narrower for SOBI algorithm (see Table 3). This algorithm did not show either constant or proportional bias. Consequently, this method showed much higher similarity between EEG sources and corrected EEG signals.
BSS-based approaches are based in some a-priori hypothesis: sources must be uncorrelated for SOS-based algorithms, and statistically independent for HOS-based ones. In the present paper, BSS techniques were used to separate ocular from cerebral activities in order to eliminate the former. The fact that ocular and cerebral activities in a simulated subject came from different real subjects ensured the statistically independence between these activities. Additionally, in all cases, normalized correlations between each ocular (two) and each cerebral (19) sources were calculated. Results showed that correlation values were always lower than 0.023 indicating the fulfillment of the a-priori hypothesis of uncorrelatedness for SOS-based methods. In the case of SOBI, a-posteriori correlations between ocular activities and corrected-EEG signals were calculated for each subject. Results showed values lower than 0.062 indicating a poor level of correlation. Analogously, statistical independence was assessed by calculating the normalized cross mutual information14 between ocular and cerebral sources. Cross mutual information quantifies the amount of information gained about one signal from the measurement of a second one. Normalized mutual information is zero when signals are independent, while it has a maximum value of one if both signals are identical. Results showed values between ocular and cerebral sources lower than 0.004 indicating that they were statistically independent. Moreover, mutual information was also calculated between ocular activities and INFOMAX-based corrected EEG signals obtaining values always lower than 0.030.
Besides, these results can be considered another test of validation of the ocular reduction effectiveness: very low values of correlation and mutual information between ocular sources and corrected EEG signals ensured that there were no relation between them and hence ocular contamination was efficiently removed from EEG data.
Thus, time and frequency results indicated that SOBI algorithm reduced better the ocular artifacts preserving by far more cerebral activity (see Figs. 5 and 8). This algorithm, that is simple, fast to compute and robust, presented the lowest errors in all leads using only short data segments of 15 s. Because HOS-based methods needed longer durations, sources were less stationary which is one of the assumptions of BSS. Besides, SOBI algorithm used the temporal structure provided by EOG and EEG data to achieve the separation. In this case, the use of additional well-defined second-order statistics (as covariances at different time lags) improved the estimation of the BSS model and the separation of ocular and cerebral sources.
Finally, based on artificially generated both spontaneous and corrupted EOG and EEG recordings, we concluded that SOBI was the most effective and efficient techniques for eye movement reduction with respect to similarity between sources and corrected EEG signals and to spectral target variables that are frequently used in a clinical real situation, even when available data length was short.
Acknowledgment
This study was partially supported by CICYT (TEC2008-02754/TEC del Ministerio de Ciencia e Innovación) from Spain.