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IEEE SIGNAL PROCESSING LETTERS, VOL. 12, NO. 12, DECEMBER 2005
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Adaptive Filters for Eye Blink Artifact Minimization From Electroencephalogram S. Puthusserypady, Senior Member, IEEE, and T. Ratnarajah, Senior Member, IEEE
Abstract—Two adaptive algorithms (time varying and exponentially weighted) based on the principles are proposed for the minimization of electrooculogram (EOG) artifacts from corrupted electroencephalographic signals. Performance of the proposed algorithms are compared with the least-mean-square (LMS) algorithm. Improvements in the output signal-to-noise ratio along with time plots are used for the comparison. It is found that the -based algorithms effectively minimize the EOG artifacts and always outperform the LMS algorithm. Index Terms—Blink artifacts, electroencephalogram (EEG), filtering.
I. INTRODUCTION
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LECTROENCEPHALOGRAM (EEG) is a measure of brain electrical activity recorded as changes in electrical potentials at different locations on the scalp. Electrooculogram (EOG) generated by eye movements and/or blinks is found to be the most significant and common artifact in EEG. Removal of EOG artifacts from corrupted EEG signals forms an important part of the EEG analysis. Many methods, such as rejection methods, eye fixation methods, EOG subtraction methods, independent component analysis (ICA)-based methods, principal component analysis (PCA)-based methods, neural network-based methods, etc., have been reported in the literature with varying success for minimization of EOG artifacts from EEG recordings [1]–[8]. EOG artifacts are generally high amplitude and low frequency in nature and affect the low-frequency region of EEG signals. Because of this spectral overlap between the EOGs and some EEGs, adaptive noise cancellation (ANC) techniques may be more appropriate [8]. Accordingly, in this letter, the problem of EOG artifacts minimization from EEG signals has been reformulated to an ANC framework. approach was introduced in robust control theory The on the hypothesis that the resulting minmax estimation techniques would be less sensitive to model uncertainties and parameter variations than conventional techniques [9]. These methods safeguard against the worst-case disturbances and therefore make no assumptions on the (statistical) nature of the -based adaptive techniques, namely, the signals. Two Manuscript received June 4, 2005; revised August 3, 2005. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yue (Joseph) Wang. S. Puthusserypady is with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore 117576, Singapore (e-mail:
[email protected]). T. Ratnarajah is with the ECIT, Queen’s University of Belfast, Belfast BT3 9DT, U.K. (e-mail:
[email protected]). Digital Object Identifier 10.1109/LSP.2005.859526
TV) and exponentially weighted ( time-varying ( EW) algorithms are derived for the effective minimization of EOG artifacts. Performances of these algorithms are compared with the popular least-mean-square (LMS) adaptive filtering algorithm. II.
SOLUTION TO ARTIFACT MINIMIZATION PROBLEM
An ANC scheme requires two inputs, namely, the primary and at least one reference input input . Here, is the signal of interest (EEG), is the artifact at the primary input sensor. is the and actual source (EOG) of this artifact, which is correlated to (i.e., ). is the measurement noise. We asand . The reference sume is filtered to produce an output that is as close input . The desired signal (estimate of EEG) is then given by as . obeys the following state–space model [9]: The signal
(1) is the filter coefficient where and vector of size is the artifact (actual) vector of size ( is the filter is the observed signal, and order). In the above equation, is the signal to be estimated. Here, includes the EEG and the model uncertainties . represents and is considered as an unknown the time variation in disturbance. Based on the above state–space model, two difadaptive filter formulations (time-variation problem ferent and exponentially weighted problem) are developed for the purpose of coping with time variations, nonstationarity, and model uncertainties. A.
-Based ANC Schemes The objective is to estimate
from . Let denote the estimate .
given the observations of We define the output estimation error as , where is adaptively updated such that is minimized. Furthermore, define the weighted and as follows: disturbances
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(2)
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where is an initial estimate of the state vector is a positive definite matrix reflecting the a priori knowlis to and is a positive edge of how close definite matrix that reflects a priori knowledge of how varies with time. For every rapidly the state vector , there exists a transfer operator choice of estimator from disturbances to the output estimation error , which is , where (forgetting factor that is denoted by chosen based on a priori knowledge of how fast the state matrix framework, robustness is ensured varies with time). In the by minimizing the maximum energy gain from the disturbances to the estimation errors. This leads to the following. optimal estimator Problem: Find an that satisfies the following: Fig. 1.
SNR
versus P for the proposed algorithms (input SNR =
020 dB).
(3) Here, is a positive constant defined as in (3). Once we have the estimate of [i.e., ], using any of the two algorithms, the desired EEG signal can be estimated as,
where
(7) (4) We shall assume, without loss of generality, that and have the special form and , where and are positive constants. Note that for a filter that varies slowly with time, will typically be very small. The above formulation can be used to handle two different scenarios: 1) the time-variation and 2) the exponentially weighted problem problem . 1) Time-Varying Algorithm: We have the following solution to the time-varying problem:
3) LMS Algorithm: An optimal estimation strategy for the time-invariant model is the well-known LMS algorithm, where robustness is ensured by minimizing the maximum (or worst-case) energy gain from the disturbances to the estimation error . The LMS algorithm is given by (8) where
is the learning rate parameter. III. RESULTS AND DISCUSSION
(5) Here, is the gain factor and is a positive constant defined as in (3). 2) Exponentially Weighted Algorithm: A forgetting factor is introduced, and the exponentially weighted algorithm is derived. This will allow the algorithm to track the time variations of the underlying models. In particular, the prediction error and and the disturbance energies are computed as , respectively
Two sets of data, each containing multiple channel EEG and four channel EOG segments of 134 s duration (sampled at 256 Hz), are used in this letter. EEG and EOG signals are filtered using two different 100-tap linear phase finite impulse response (FIR) band-pass (0.25–35 Hz and 0.25–11.5 Hz, respectively) filters. A. Simulated Data (acThe EEG signal recorded from the electrode position , and cording to the international 10–20 system) is used as the vertical “up” EOG signal (left eye) is used as . is at different SNRs to construct . Output SNR added to [defined in (9)] is used as the performance index for the quantitative comparison of the algorithms SNR
(6)
(9)
where is the total number of samples, and is the esti. The SNR values for the two algorithms mate of and the LMS algorithm are computed for varying values and dB) in Fig. 1. The simulation are plotted (for input SNR
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IEEE SIGNAL PROCESSING LETTERS, VOL. 12, NO. 12, DECEMBER 2005
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FOR
TABLE I DIFFERENT ADAPTIVE FILTERS PROPOSED
Fig. 3.
Fig. 2. Results of EOG artifact minimization using the proposed algorithms (simulated data). (a) Desired signal. (b) Corrupting EOG signal. (c) Corrupted EEG signal ( 20 dB). (d) Estimated EEG using LMS scheme. (e) Estimated EEG using TV scheme. (f) Estimated EEG using EW scheme.
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R versus P for the proposed algorithms for multiple EOG references.
in our study. Four different EOGs (two horizontal EOGs and two vertical EOGs) are used as reference inputs in this study. Horizontal EOGs are measured from the left and right eyes. Two vertical EOGs (vertical “up” and vertical “down”) are measured from the left eye position. Here, since the desired signal is unknown, an appropriate measure defined in (10) is used for a quantitative comparison of the algorithms
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parameters are , and . From Fig. 1, it can be seen that algorithms (SNR improvethe SNR performance of the dB better than the LMS algoments of the order of 25 dB) is rithm. Table I shows the SNR values of the noise minimization schemes at different input SNRs. It is clear from the table methods outperform the LMS algorithm consisthat the tently for all input SNR values. This may be attributed to the fact estimators guarantee the smallest possible estimathat the tion error energy over all possible disturbances (EOGs) of fixed energy and are therefore robust with respect to model uncertainties and lack of statistical information on the noise signals. , and signals along with the estiFig. 2 shows mated signals using the proposed algorithms at an input SNR of dB. From Fig. 2(c), the amplitude of the corrupting signal is so large that the EEG signal is not even visible by the naked using the three artifact minieye. The estimated signals TV, and EW) are shown in mization schemes (LMS, Figs. 2(d), (e), and (f), respectively. The corresponding SNR values are , 5.01, and 4.80 dB, respectively. From visual algorithms work comparison also, it can be seen that the from the contaminated EEG signal. better in estimating When using the LMS algorithm, the residual EOG is clearly seen in the time plots.
(10) is the ratio of the power of the ocular artifacts being removed from the primary signal to the power in the estimated EEG (the higher (bounded) the value of , the better the artifact minimization) [1]. The value of for multiple EOG references are computed for varying filter order and are plotted in Fig. 3. values corresponding to the use of one reference EOG (horizontal EOG) are low, indicating a poor artifact minimization. This may be attributed to the fact that the horizontal EOG may be less correlated to the EEG at the Fz electrode location and hence a low value of . When four reference EOGs are used, the values and above. The important obare high (2 and above) for servation is that using more EOG reference inputs improve the algorithms as compared to performance of the the LMS algorithm. The representative results of the proposed artifact minimization schemes are shown in Fig. 4. In Fig. 4(a), the EOG blink artifacts are clearly seen. In Fig. 4(b), the residual EOG artifacts are clearly visible showing the inferiority of the LMS algorithm, especially in the beginning. From Fig. 4(c) and (d), it can be seen algorithms minimize the EOG artifacts effectively that the from the recorded EEG signals. IV. CONCLUSION
B. Real EEG Data EEG recorded from F3, F5, Fz, F4, and F6 electrode locations according to the expanded 10–20 international system are used
In this letter, the power of adaptive algorithms ( TV and EW) for the minimization of EOG artifacts from corrupted EEG signals are demonstrated. These algorithms
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ACKNOWLEDGMENT The authors would like to thank Prof. J. W. M Bergmans of the TU/e for providing the required data. REFERENCES
Fig. 4. Demonstration of EOG artifact minimization using the proposed algorithms (real EEG data). (a) EOG-contaminated EEG signal recorded from Fz electrode location. (b) Estimated EEG using LMS scheme. (c) Estimated TV scheme. (d) Estimated EEG using EW scheme. EEG using
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are compared to the well-known LMS algorithm. From these studies on simulated as well as real signals, it is found that -based algorithms perform better and convincingly the outperform the LMS algorithm.
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