EEG SIGNAL ENHANCEMENT USING MULTI-CHANNEL WIENER FILTER WITH A
SPATIAL CORRELATION PRIOR
Hayato Maki† , Tomoki Toda, Sakriani Sakti, Graham Neubig, Satoshi Nakamura
Graduate School of Information Science
Nara Institute of Science and Technology (NAIST), Japan†
maki.hayato.lt3@is.naist.jp
ABSTRACT
Event-related potentials (ERPs) of electroencephalogram (EEG) areoften used as features for brain machine interfaces or for analysis ofbrain activities. However, as EEG signals easily suffer from various
artifacts, ERPs are often collapsed and hard to observe. There areseveral attempts at using multi-channel EEG signals to enhance EEG
signals of interest and make ERPs more clearly observed. For example, a previous work has proposed a blind EEG signal separation
method using a multi-channel Wiener filter designed with a probabilistic generative model of observed EEG signals. This method
copes with the under-determination of EEG signal separation by assuming sparseness of each EEG component in the time-frequency
domain. Although this method blindly separates EEG signals into
individual EEG components using time-varying scaled spatial correlation matrices, target EEG components, such as P300 of ERP, areoften known in advance in some applications. In this paper, inspiredby this previous work, we propose a probabilistic EEG signal enhancement method using a multi-channel Wiener filter, newly incorporating prior information of the spatial correlation matrices related
to the target EEG component in the probabilistic generative model toimprove performance of EEG signal enhancement. An experimental
evaluation for P300 enhancement shows that the proposed method
significantly reduces artifacts.
Index Terms— EEG signal enhancement, ERP, Wiener filter,
spatial correlation prior
1. INTRODUCTION
Electroencephalography (EEG) is the recording of electrical activity
along the scalp. It has been used as a tool for medicine [1], cognitive science [2], and development of new brain machine interfaces(BMI) [3,4,5]. However, it is often hard to analyze and interpret
EEG signals because of their poor signal-to-noise ratio (SNR). EEG
recordings capture a mixture of endogenous brain activities and extraneous and physiological artifacts such as power grid noise, eyeblinks, or muscle activities, while signals of interest evoked by somebrain activities generally have lower energy than the artifacts [6].
For the above reasons, synchronous signal averaging is often employed, especially in the study of event-related potentials (ERPs).
The whole recording is cut into smaller intervals containing a single
stimulus. Each of these intervals is called a trial. Trial signals areaveraged synchronously, which attenuates signals from the artifacts
and background brain activities while preserving the amplitude ofsignals of interest. However, it is known that the ERP waveforms
have variability between both trials and subjects, so information islost by averaging [7].

978-1-4673-6997-8/15/$31.00 ©2015 IEEE

2639

Thus, techniques of artifact removal or feature extraction froma single-trial EEG data have become a highly active research topic
in neuroscience, engineering and signal processing [8,9]. One
framework for artifact removal using multi-channel EEG signals is
Independent Component Analysis (ICA) [10]. ICA defines a generative model for the observed multivariate data, which are assumed
to be linear mixtures of some unknown latent variables. The mixing
system is also unknown. There are two major assumptions in applying ICA to EEG signals. First, the ICA component projections
are summed linearly at scalp electrodes. Second, the time courseof EEG activity and artifacts are statically independent. ICA has
a limitation of the number of separable signal sources, up to N
sources from N electrodes. However, EEG signals are generated bynumerous synapses, so the number of electrodes is actually much
fewer than sources. This problem is called under-determined and
it is known to be essentially difficult to solve using linear filtering
including ICA.
Another approach uses a multi-channel Wiener filter that has
been proposed in the context of under-determined blind source separation [12,13] and applies it to EEG signals [14]. In [14], they
define an event as a phenomenon that contributes to an observation
signal, e.g. a cognitive process, an eye blink and so on, and assume
sparseness of each event in the time-frequency domain. They don’t
separate EEG signals into individual signals evoked by sources, but
separate by each event. This approach has the merit that noise reduction is done by a time-variant filter, while ICA is a time-invariant
filter. To design such a filter, they use a probabilistic generativemodel that models the contributions of each source to all mixturechannels in the time-frequency domain as zero-mean complex Gaussian random variables whose covariance matrix encodes the spatial
characteristics of the source.
In this paper, inspired by this previous work, we propose a probabilistic EEG signal enhancement method using a multi-channel
Wiener filter, newly incorporating prior information of the spatial
correlation matrices related to the target EEG component in theprobabilistic generative model. The previous work blindly separates
EEG signals into individual EEG components using time-varying
scaled spatial correlation matrices without any prior information.
However, target EEG components, such as P300 of ERP, are often
known in advance in some applications. This allows us to obtainprior information for the estimation of parameters and improve performance of EEG signal enhancement. In addition, we don’t have toselect the target event signal from the separated event signals as in
the conventional blind separation methods including ICA, because
the target signal corresponds to the mixture component with thetarget prior distribution.

ICASSP 2015

2. PREVIOUS WORK
Previous works [12,13] have proposed, in the context of underdetermined blind sound source separation, a blind signal separation
method using a multi-channel Wiener filter designed based on aprobabilistic generative model. This method has been successfully
applied to unsupervised EEG event signal separation using multichannel EEG signals [14], which we describe in this section.
2.1. Observation ModelIn this paper, we refer to the multi-channel EEG signal related to thek-th event simply as the “k-th event signal.” Given I channels, thek-th event signal ck (n, f ) = [ck,1 (n, f ), · · · , ck,I (n, f )]⊤ at timen and frequency f in the time-frequency domain is expressed as∑ck (n, f ) =hl sl (n, f ),
(1)
l∈Ek

hl

=

⊤

[h1l , · · · , hIl ] ,(2)where {·}⊤ is the transpose, sl (n, f ) is the source signal from various sources, such as synapse, muscle, and so on, given by a complex
value, Ek is a set of the sources activated in the k-th event, and hil
is the transfer function from the l-th source to the i-th channel assuming that 0 ≤ hil ≤ 1. The observed multi-channel EEG signal
is x(n, f ) = [x1 (n, f ), · · · , xI (n, f )]⊤ expressed asx(n, f ) =K∑

ck (n, f ),We assume that the probability density function of the source signal
sl (n, f ) is modeled by the following zero-mean complex Gaussian
distribution,p (sl (n, f )) = Nc (sl (n, f ); 0, vk (n, f )) ,l ∈ Ek ,(4)

where the variance vk (n, f ) varies in the time-frequency domain depending on the k-th event. Further assuming that the source signals
are non-correlated to each other, the probability density function of
the k-th event signal ck (n, f ) is modeled by a multivariate complex
Gaussian distribution as follows:

=
=

Rk

=

K
∏∑

αk Nc (x(n, f ); 0, vk (n, f )Rk ) , (10)n,f k=1

where αk is a prior probability of the k-th event signal to be active.
The model parameter set θ consists of αk , vk (n, f ), and Rk of each
mixture component.
2.3. Event Separation
2.3.1. Model Parameter Estimation
Given the observation signals x, the model parameter set is estimated by maximizing the likelihood function of the generativemodel given by Eq. (10) as follows:θ̂ = arg max p(x|θ).
θ

(11)

The EM algorithm can be effectively used in this maximization process. In the E-step, the following posterior probability is calculated
at each time-frequency slot,=∑K

αk Nc (x(n, f ); 0, vk (n, f )Rk )(. 12)
αk′ Nc (x(n, f ); 0, vk′ (n, f )Rk′ )k′ =1

In the M-step, the model parameter set is updated as follows:∑n,f mk (n, f )α̂k = ∑,′
n,f,k′ mk (n, f )2.2. Probabilistic Generative Model

Rck (n, f )=(3)where K is the number of events.

=n,fmk (n, f )k=1

p (ck (n, f ))time-frequency domain is modeled by a Gaussian mixture model asfollows:∏p(x|θ) =p(x(n, f )|θ)(13)

1
x(n, f )H R−1(14)k x(n, f ),I∑
mk (n, f )1x(n, f )x(n, f )H . (15)R̂k = ∑v̂k (n, f )mk (n, f )v̂k (n, f ) =

n,f

n,f

Note that v̂k (n, f ) and R̂k are iteratively updated as they depend oneach other.
2.3.2. Multi-channel Wiener Filter

Nc (ck (n, f ); 0, Rck (n, f )) ,[]E ck (n, f )ck (n, f )H(5)

vk (n, f )Rk ,
∑
hl h⊤
l ,

(7)

ĉk (n, f )=R̂ck (n, f )R̂x (n, f )x(n, f ),

(16)

(8)

R̂ck (n, f )=mk (n, f )v̂k (n, f )R̂k ,

(17)

(6)

l∈Ek

R̂x (n, f )where {·}H is the complex conjugate transpose. The spatial covariance matrix Rck (n, f ) is factorized into the time-frequency invariant spatial covariance matrix Rk and the time-frequency variant
variance component vk (n, f ).
We also assume that only one event signal is active in each timefrequency slot as follows:x(n, f ) = cz(n,f ) (n, f ),Using the estimated spatial covariance matrices related to individual
event signals, a multi-channel Wiener filter is designed as follows:(9)

where z(n, f ) is the index of the active event signal. Consequently,
the probability density function of the observation signals x in the

2640

=

−1

K
∑

R̂ck (n, f ),

(18)

k=1

where ĉk (n, f ) is the k-th event signal separated from x(n, f ).
2.4. Problem
This method does not use any prior information for estimation of
spatial correlation matrices and blindly separates EEG signals into
individual EEG components using time-varying scaled spatial correlation matrices. However, target EEG components, such as P300 of
ERP, are often known in advance in some applications, which allows

In BMI or analysis of brain activities, we often know which event
we would like to enhance, such as P300 of ERP, motor imagery, or
steady state visual evoked potentials (SSVEP). In such a case, weneed to enhance the target EEG event signal from the observed EEG
signal, rather than blindly separating it into multiple EEG event signals. Moreover, we can also record EEG signals related to the target
event beforehand and use them as prior knowledge for enhancement.
In this section, we propose an EEG signal enhancement method thatincorporates prior distributions of the spatial covariance matrices tothe conventional blind separation framework.

5

5

5

10

10

15

15

20

25

Index of channels

Index of channels

5

5

15

25

Index of channels

3. PROPOSED EEG SIGNAL ENHANCEMENT METHOD

Index of channels

us to obtain prior information for the estimation of spatial correlation
matrices. In addition, separated signals have permutation ambiguity,
so we have to select the target event signal from the separated event
signals as in the conventional blind separation methods including
ICA.

15

20

25

25

5
5

5

10

10

15

25

15
15

20

15

20

25
25

25

5

10

5

15

10

20

15

25

20

5

25

10

5

Target

15

10

20

15

25

20

25

Non-Target

Fig. 1. Visualization of the spatial correlation matrices, the left
is calculated using target trials and the right is calculated using
non-target trials. Both axes represent channels. Darker slots havestronger correlations.
{R1 , · · · , RK }, as follows:

3.1. Spatial Correlation Priorθ̂

The Wishart distribution is known as the conjugate prior distribution of the precision matrix of a multivariate Gaussian distribution
with known mean vectors. The prior distributions of time-frequency
invariant spatial covariance matrices are designed as follows:
(
)
(
)
1 [
1 −1 q−I−1
−1
−1 ]
2
p R−1
|Ψ
,
q
=
|R
|
exp
−
Tr
Ψ
R
, (19)
k
k
k
k
Z k
2
where Z is the normalizing constant, Ψk is a I-by-I symmetric positive definite matrix, and q is the degrees of freedom.
Using previously recorded multi-channel EEG signals related toa specific event, we can determine the hyper parameters, Ψk and q
as follows:∑ ′Ψk =xk (n, f )x′k (n, f )H ,
(20)
=

N F,

arg max p(R|x, θ \R , Ψk , q)=

arg max

θ

θ

∏

(21)

where x′k (n, f ) is the pre-recorded EEG signal at time n and frequency f , N is the total number of time frames, and F is the total
number of frequency slots.
It is ideal to use the event signal ck but it is essentially difficult torecord such a signal because the recorded EEG signal easily suffersfrom multiple events. In this paper, we use carefully recorded EEG
signals to establish a contrast between signals in which the target
event exists or doesn’t exist. For instance, if we apply our proposed
method to P300 ERP enhancement, we record several EEG signals
in which P300 ERP is supposed to be observed and also record EEG
signals in which P300 ERP is supposed to not be observed. Then, we
calculate hyper parameters using each of these to develop the priorprobability distribution for P300 ERP and that for the backgroundEEG signals, respectively. We may also be able to create prior probability distributions for other specific events, such as an eye blink.
3.2. EEG Signal Enhancement with Spatial Correlation Prior
Given the observation signals x, the model parameter set θ is estimated by maximizing the posterior probability density functionof the time-frequency invariant spatial covariance matrices, R =2641

p (x(n, f )|θ)

n,f

(22)

K
∏
(
)
p R−1
k |Ψk , q , (23)k=1where θ \R is the model parameter set except for R. This maximization process can also be effectively solved with EM algorithm. The
following auxiliary function is maximized with respect to θ,(∑Q =mk (n, f ) log(αk ) − I log(vk (n, f ))
n,f,k

)
1
x(n, f )H R−1
x(n,
f
)
k
vk (n, f )(K[])∑ q−I −11+
log |R−1
Tr Ψk R−1
k |−
k
2
2
+ log(|R−1k |) −

k=1+ Const.

n,f

q

=

(24)

In the E-step, the posterior probability mk (n, f ) is calculated at eachtime-frequency slot as shown in Eq. (12). In the M-step, α̂k andv̂k (n, f ) are updated as shown in Eqs. (13) and (14), and Rk is
updated as follows:
(
1
1
Ψk
R̂k =
∑
q−I −1
2+
mk (n, f )2n,f∑ mk (n, f )H
x(n, f )x(n, f ),(25)+v̂k (n, f )n,fwhere v̂k (n, f ) and R̂k are iteratively updated as they depend oneach other. Finally, the target event signal is extracted from the observed EEG signals using a multi-channel Wiener filter as describedin Section 2.3.2.
In the proposed enhancement method, we don’t have to selectthe target event signal from the separated event signals as in the conventional blind separation method, because the target signal corresponds to the mixture component with the target prior distribution.
We may also deal with event signals not modeled with the prior distributions by just using additional mixture components without theprior distributions.

0.95
0.9
0.95

10
0
−10
−100

0

100

200

300

400

500

600

700

800

No Prior
Amp. (µV)

30
20
10
0
−10
−100

0

100

200

300

400

500

600

700

800

0.850.9
0.85
0.8
0.8

0.75

0.75

raw

0.7

raw
no priorno prior
proposed
proposed

0.7

0.65
0.65

0.6

0.6

Proposed30

Amp. (µV)

Correlation coefficients

20

Correlation coefficients

Amp. (µV)

Raw
30

11 1

20

8
222
444
88
The
numberof signals
averaged
The number of signals averaged

1616

16

10
0
−10
−100

0

100

200

300

400

Time (msec)

500

600

700

800

Fig. 2. Comparison of single-trial EEG waveforms. These are, in theorder of appearance, the raw signal, the signal denoised by the previous method using no prior, and the signal denoised by the proposed
method.

4. EXPERIMENTAL EVALUATION
4.1. Data Acquisition
The EEG data were recorded from a single subject with 27 channels
at positions of the extended 10/20-System. The measured signal was
digitized at 1000 Hz and downsampled to 200 Hz. We conducted
the oddball paradigm experiment, which is a classical experimental
design evoking an ERP P300. The subject was presented a sequenceof two types of audio stimuli in random order, one is a 2000 Hz
sine wave and the other is a 1000 Hz one. 1000 Hz sounds were
frequently (200 times) presented and 2000 Hz sounds were rare (50times). The subject was told that the rare 2000 Hz sound was the target and to count the number of presentations of target stimuli during
the experiment. It has been found that P300 usually appears around300ms after the target stimuli [15]. After the oddball paradigm, thesubject was told to be relaxed and we recorded an EEG signal during
the resting state for 2 minutes.
Twenty-five EEG signals during target stimuli are chosen at random to use learn hyper parameters and the remaining twenty-fivesignals are used as test data. The test data are separated using the previous method without prior and the proposed method. Both methods
assume the number of events K = 2. The learned hyper parameters
are visualized in Fig. 1.
4.2. Evaluation

Fig. 3. Mean of correlation coefficients between the reference signal
and averaged trial signals. The x-axis that is log-scaled with base 2
represents the number of signals averaged. The y-axis is correlation
coefficient
target signal, and use the distance from this signal as an automatic
evaluation measure. To do so, we averaged 25 target trials of EEG
data as a reference signal, and evaluate the performance of the proposed method and previous method with no prior by calculating correlation coefficients between the reference signal and noise reduced
signals with only a single or a few trials.
Fig. 3 illustrates the performance of noise reduction combinedwith synchronous averaging. To calculate the correlation coefficientsfor each number of signals averaged, we first select 25 random setswith the appropriate number of signals, average the signals in eachset, measure the correlation coefficient for each averaged signal, thentake the mean of the correlation coefficients for the 25 sets. The
performance of noise reduction of proposed method was superior to
the previous method and generally needs only half as many trials toachieve a signal of the same quality as previous methods.
5. CONCLUSION
In this study we proposed a method to improve the performanceof parameter estimation of a multi-channel Wiener filter for EEG
signal noise reduction. While previous works doesn’t use a priorinformation for the estimation of spatial correlation matrices, weused a Wishart distribution as a prior. The experimental evaluation
showed the effectiveness of using the prior to estimate the parameters and performance of noise reduction was improved compared tothe method without a prior. Future work will consider setting a priordistribution for other parameters and adaptation of hyper parameters
learned from other people.
6. ACKNOWLEDGEMENT

A comparison of waveforms of a single-trial EEG signal in the time
domain is shown in Fig. 2. It can be seen that the raw signal iscontaminated by artificial spikes. The Wiener filter with no priordoes little to remove these spikes, but the proposed method largely
succeeds in removing them. Consequently, the appearance of ERP
of P300 evoked by target stimuli is more clearly shown.
To perform further quantitative analysis, we assume that the synchronous averaging provides a reasonable approximation for the true

2642

Part of this work was supported by JSPS KAKENHI Grant Number
24240032.

7. REFERENCES[1] Keith H Chiappa. Evoked potentials in clinical medicine. Lippincott Williams & Wilkins, 1997.
[2] Wolfgang Klimesch. EEG alpha and theta oscillations reflectcognitive and memory performance: a review and analysis.
Brain research reviews, 1999.
[3] Guido Dornhege. Toward brain-computer interfacing. MITpress, 2007.
[4] Fabien Lotte, Marco Congedo, Anatole Lécuyer, and Fabrice
Lamarche. A review of classification algorithms for EEGbased brain-computer interfaces. Journal of neural engineering, 2007.
[5] Brent J Lance, Scott E Kerick, Anthony J Ries, Kelvin S Oie,
and Kaleb McDowell. Brain-computer interface technologies
in the coming decades. Proceedings of the IEEE, 2012.
[6] Otavio G Lins, Terence W Picton, Patrick Berg, and Michael
Scherg. Ocular artifacts in EEG and event-related potentials I:
Scalp topography. Brain topography, 1993.
[7] André Mouraux and Gian Domenico Iannetti. Across-trial averaging of event-related EEG responses and beyond. Magnetic
resonance imaging, 2008.
[8] Benjamin Blankertz, Ryota Tomioka, Steven Lemm, Motoaki
Kawanabe, and Klaus-Robert Müller. Optimizing spatial filters
for robust EEG single-trial analysis. IEEE Signal Processing
Magazine, 2008.
[9] Benjamin Blankertz, Steven Lemm, Matthias Treder, Stefan
Haufe, and Klaus-Robert Müller. Single-trial analysis and classification of ERP components - A tutorial. NeuroImage, 2011.
[10] Aapo Hyvärinen, Juha Karhunen, and Erkki Oja. Independent
component analysis. John Wiley & Sons, 2004.
[11] Arnaud Delorme, Terrence Sejnowski, and Scott Makeig. Enhanced detection of artifacts in EEG data using higher-order
statistics and independent component analysis. NeuroImage,
2007.
[12] Ngoc QK Duong, Emmanuel Vincent, and Rémi Gribonval.
Under-determined reverberant audio source separation using afull-rank spatial covariance model. IEEE Transactions on Audio, Speech, and Language Processing, 2010.
[13] Ryutaro Sakanashi, Shigeki Miyabe, Takeshi Yamada, andShoji Makino. Comparison of superimposition and sparsemodels in blind source separation by multichannel Wiener filter. Proceedings of the Annual Summit and Conference of
the Asia-Pacific Signal and Information Processing Association (APSIPA ASC), 2012.
[14] Yusuke Kurihana, Shigeki Miyabe, Tomasz M Rutkowski,
Yoshihiro Matsumoto, Takeshi Yamada, and Shoji Makino. (inJapanese) Signal separation of EEG using multivariate probabilistic model. IEICE Technical Report MBE, 2013.
[15] Steven J Luck and Emily S Kappenman. The Oxford handbookof event-related potential components. Oxford university press,
2011.

2643