Adaptive Nonlinear Projective Filtering
Application to Filtering of Artifacts in EEG Signals
Bartosz Binias and Michał Niezabitowski
Silesian University of Technology, Faculty of Automatic Control, Electronics and Computer Science,
Akademicka 16 Street, 44-100, Gliwice, Poland
Keywords:
EEG, Electroencephalography, Adaptive Filtering, Artifact Filtering, Artifact Correction, Signal
Reconstruction, Nonlinear Projective Filtering, Nonlinear State Space Projection, Biomedical Signals.
Abstract:
In this work a novel approach to filtering of eyeblink related artifacts from EEG signals is presented. Pro-
posed solution, the Adaptive Nonlinear Projective Filtering (ANPF) algorithm, combines the classic approach
to adaptive filtering with algorithms from nonlinear state space projection family. Performance of described
method is compared with adaptive lter based on Normalized Least Mean Squares algorithm in terms of me-
dian Normalized Mean Squared Error. Data used in conducted research was simulated according to described
procedure. Such approach allowed for a reliable comparison and evaluation of algorithm’s signal correction
properties. Additionally, a real time modification of ANPF algorithm is proposed and tested. The analysis
of sensitivity to changes of parameter values was also performed. Achieved results were tested for statistical
significance. According to obtained scores ANPF significantly outperforms referential method during offline
processing.
1 INTRODUCTION
Artifacts related with eye movements are among the
most significant sources of noise and contamination
of electroencephalographic (EEG) data. Because the
frequency characteristics of ocular artifacts tend to
overlap with those of EEG, they make an analysis
of such signals not only less effective but, in many
cases, impossible (R. J. Croft, 2000; Correa et al.,
2007). Apart from frequency mixing this kind of con-
tamination is usually characterised by amplitudes that
are several times higher than typical range of useful
EEG signals. This results in a very low signal-to-
noise (SNR) ratio that makes this problem even more
demanding. Most commonly implemented approach
to dealing with contaminated segments of signal is
simply removing them from further analysis (Jung
et al., 2000; R. J. Croft, 2000). However, such ap-
proach leads to a significant loss of data which, is un-
acceptable in e.g. real-time analysis of EEG signal for
Brain-Computer Interface (BCI) applications (Binias
et al., 2016b). Another very popular branch of ap-
proaches is based on adaptive filtering algorithms ap-
plied either in time or frequency domain (Jung et al.,
2000; Binias et al., 2015; Binias et al., 2016b). These
methods require that at least one regressing channel
is provided. The most common source of such in-
formation is an electrooculogram (EOG) recording,
which can serve as reference for regression-based al-
gorithms (Jung et al., 2000). Although capable of pro-
ducing a very good results in attenuation of ocular ar-
tifacts, potential of these methods is weakened by big
sensitivity to changes of some parameters, that may
result even in destabilization of the whole filtering
process (Haykin and Widrow, 2003). Among other
techniques of filtering eyeblink related contamination
mentioned can be methods based on blind source sep-
aration. Those include Principal Component Analysis
(PCA) and Independent Component Analysis (ICA)
which rely on recorded EEG and EOG signals for
calibration (P. Berg, 1991; Jung et al., 2000). Espe-
cially, the ICA method when applied to large num-
ber of data recorded over many channels, can pro-
duce results of high quality. However, it must be
noted that this method works best in semi-automatic
approach, where supervision of experienced user (i.e.
expert) is required (Makeig et al., 2000). The con-
cept of nonlinear filtering of time series by locally
linear phase space projections has been derived us-
ing concepts from deterministic dynamical systems,
or chaos theory (Schreiber and Kantz, 1998). Such
methods will be referred to as Nonlinear Projective
Filtering (NFP) in this work. Although NFP was de-
signed for the purpose of filtering signals that are de-
terministically chaotic, this approach has been suc-
cessfully implemented for applications requiring de-
440
Binias, B. and Niezabitowski, M.
Adaptive Nonlinear Projective Filtering - Application to Filtering of Artifacts in EEG Signals.
DOI: 10.5220/0006414604400448
In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 440-448
ISBN: 978-989-758-263-9
Copyright © 2017 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
noising of biomedical signals such as electrocardio-
gram (ECG) and EEG (Kantz and Schreiber, 1998;
Richter et al., 1998; Kotas, 2009; Kotas, 2004; Gao
et al., 2011). NFP based approaches rely on phase
space reconstructions performed under Takens’ con-
ditions (Takens, 1981). Thistheorem has been also ef-
fectively utilized in analysis of nonlinear time series.
An example of such signals are, for instance, various
components of eye movement (Harezlak, 2017).
In this work a novel algorithm - the Adaptive
Nonlinear Projective Filtering (ANPF) is proposed
and validated for applications of artifact filtering
in EEG signals. Method is compared with adap-
tive filter based on Normalized Least Mean Squares
(NLMS) algorithm in terms of median Normalized
Mean Squared Error (NMSE). Additionally, a real
time modification of ANPF algorithm is proposed and
tested.
2 MATERIALS
Evaluation of eye blink correction and filtering arti-
facts in EEG signals is inextricably linked with the
problem of selection of a proper referential, uncon-
taminated signal. Since EEG signals are recorded
with the disturbance already additively mixed, there
is no precise way to extract the original, desired com-
ponent. Two approaches to that problem can be men-
tioned here. First one is based on the use of real EEG
recordings (Binias et al., 2016b). This approach re-
lies on time indexes marked by researchers. How-
ever, since these are mostly subjective, only approx-
imate information of method’s accuracy is provided.
Additionally, since it is impossible to recover the ex-
act morphology of uncontaminated signal, there is no
unambiguous way of evaluating how accurate was re-
construction of the filtered signal. A second approach
to described problem requires use of simulated EEG
data (Binias et al., 2015). Since both artifact-free
EEG and additive artifact components are available,
it is possible to reliably evaluate artifact filtering and
signal correction methods. This can be achieved e.q.
by comparing the original, uncontaminated EEG data
with filtered signal. This approach was utilized in this
research.
EEG signals are characterized by low amplitudes
(normally in range from 0.5 to 100 µV)and bandwidth
mostly located below 100 Hz (Binias et al., 2015).
Some characteristic frequency ranges can be distin-
guished from EEG recordings. These are often re-
ferred to as brainwaves (Teplan, 2002; Nunez and
Srinivasan, 2006; da Silva, 1991). Delta (below 3
Hz) waves are commonly associated with deep sleep
(Teplan, 2002). Although, theta activity (3 7 Hz)
has been observed during cognitive visual process-
ing (Grunwald et al., 1999) it is generally attributed
to states of drowsiness. States of wakeful relaxation,
or tiredness are dominated by alpha waves (8 12
Hz). This activity can also be increased by closing
eyes (Teplan, 2002; da Silva, 1991). Normal waking
consciousness, alertness and an active concentration
are related to beta range (1329 Hz) (Teplan, 2002;
Craig et al., 2012). The role of gamma waves (over 30
Hz) remains an active topic of a research. EEG signal
s(n) can be modelled as an additive mixture of K si-
nusoidal components oscillating with frequencies f
k
,
which are evenly distributed across given frequency
range starting at 0 Hz and ending at F
lim
= 100 Hz.
In this work K = 200. Let us assume that φ
k
is the
pseudorandomly generated initial phase of k-th fre-
quency component of s(n), n is a discrete time index
and w
a
(k) is the amplitude of said component. Then,
the equation used for generation of simulated EEG
time series can be formulated as in (1)
y(n) =
K
k=1
w
a
(k)sin(2π f
k
n+ φ
k
). (1)
To ensure that the power spectrum density function
of simulated output will be similar to that of realistic
EEG, signal amplitudes of each frequency component
were chosen accordingly to a typical power spectrum
characteristics of EEG signals. In general, it can be
assumed that during states of focused relaxation, al-
pha activity will be dominant with some small beta
influence (Teplan, 2002; Binias et al., 2015). There-
fore, amplitudes w
a
of the individual frequency com-
ponents can be approximated by normal distribution
with mean value randomly selected from alpha wave
range µ
f
= 8 12 Hz and standard deviation σ
f
ad-
justed so that the maximal value equals to F
lim
= 100
Hz (Binias et al., 2015). For the simulation purposes
all frequency values lower than zero were rejected.
Then, for remaining frequencies formula (1) was ap-
plied. An exemplary relation between amplitudes and
frequencies of simulated EEG signals is presented in
Fig. 1. A comparison of simulated EEG time course
with a real one is shown in Fig. 2. Presented exem-
plary signal was recorded accordingly to procedure
utilized for the purpose of different research (Binias
et al., 2016a).
Three main types of eye movement related arti-
facts in EEG can be distinguished. These are eye
blinks, eye movements (saccades) and scalp or fa-
cial muscle contractions (short time, high amplitude
spikes) (Binias et al., 2015). This research is entirely
focused on eye blink artifacts. Morphology of such
contamination is shown in Fig. 3. Presented exem-
Adaptive Nonlinear Projective Filtering - Application to Filtering of Artifacts in EEG Signals
441
0 10 20 30 40 50 60 70 80 90 100
[Hz]
0
10
20
30
40
50
60
70
80
90
[ V]
Figure 1: Exemplary relation between amplitudes and fre-
quencies of simulated EEG signals (own source).
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
[s]
-50
0
50
[ V]
Simulated EEG time series
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
[s]
-50
0
50
[ V]
Real EEG time series
Figure 2: Examples of simulated and real EEG time courses
(own source).
plary signal was recorded accordingly to procedure
utilized for the purpose of different research (Binias
et al., 2016a).
In this work, morphology of such artifacts has
been approximated by function presented in (2). An
exemplary time course of that function is shown in
Fig. 4:
b(n) = w
b
U
n
σ
b
2π
e
1
2
(
nµ
b
σ
b
)
2
. (2)
In formula (2) n < N
0
/2;N
0
/2 > is a discrete time
variable. If total duration of simulation is denoted by
T
0
and sampling frequency is represented by f
s
, then
N
0
= f
s
T
0
(T
0
= 1 s and f
s
= 200 Hz in this work).
Mean of Gaussian distribution function µ
b
was set to
0 for all simulations (µ
b
= 0 s). Standard deviation σ
b
controls the time positions of simulated blink peaks
and thus is responsible for the duration of simulated
eyeblink artifact. Relation between defined parame-
ters and morphology of simulated artifact is presented
in Fig. 4.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
[s]
-150
-100
-50
0
50
100
150
200
[ V]
Figure 3: Real EEG signal contaminated by eye blink arti-
fact (Binias et al., 2016a) (own source).
-N
0
/2 -2
b 0
2
b
N
0
/2
-w
b
w
b
Figure 4: Time course of simulated eye blink artifact (own
source).
According to experimental work, such artifacts
can be divided into three categories basing on their
length: short blinks (71 100 ms), medium blinks
(101 170 ms) and long blinks (171 300 ms)
(Benedetto et al., 2011). Therefore, parameter σ
b
was
randomly selected from uniform distribution ranged
σ
b
< 0.035 s; 0.085 s > that corresponds with short
blink duration. U
f
is introduced as a normaliza-
tion operator of function f. As a result its applica-
tion range of function is normalized to range f <
1;1 >. The amplitude of simulated artifact was
controlled by parameter w
b
which was randomly se-
lected from uniform distribution w
b
< 70 µV;110
µV > (based on (Binias et al., 2015)). Obtained sim-
ulated eye blink was ten amplified and added to orig-
inal, uncontaminated EEG signal s(n) as in (3). The
scaling coefficientw
m
was selected randomly for each
test from uniform distribution ranged from 0.8 to 1.0
(w
m
< 0.8;1.0 >). The introduction of scaling of
b(n) signals originates from biophysical aspect of the
problem. The bioelectrical source of eye blink arti-
facts is located closer to position of electrode record-
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
442
ing reference signal than to EEG measurement loca-
tions. Therefore, amplitudes of such artifacts will be,
in general, lower in EEG channels than in EOG. A
model of additive source mixing and linear scaling is
commonly accepted among researchers (Nunez et al.,
1997; Pfurtscheller and Da Silva, 1999; Blankertz
et al., 2008)
x(n) = s(n) + w
m
b(n). (3)
All simulation parameters used in this work were
selected on the basis of literature review (Binias et al.,
2015; Benedetto et al., 2011). That way the most real-
istic characteristics of simulated time series could be
ensured. Time course of simulated EEG signal with
eye blink artifact contamination and overlapped refer-
ential EOG recording are presented in Fig. 5. The ref-
erential EOG signal that was provided with the sim-
ulated data was obtained from adding a pink noise to
the b(n).
0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4
[s]
-80
-60
-40
-20
0
20
40
60
80
100
[ V]
EEG
EOG
Figure 5: Time courses of simulated EEG signal with eye
blink artifact contamination and referential EOG recording
(own source).
3 METHODS
3.1 Nonlinear Projective Filtering
A discrete time series s(n) R
N
can be represented
as a trajectory in a D-dimensional phase space with
Takens Method using time delay coordinates s
n
=
s
n
,s
n + τ
,. .. ,s
n + (D 1)τ

(D denotes the
embedding dimension, τ is a delay time) (Takens,
1981). For deterministic dynamical systems the phase
trajectory is frequently confined to a set of points in
state space, referred to as the attractor. Simplest ap-
proach to the problem of denoising or filtering of the
contaminated signals in the phase space can be re-
duced to the following steps (Kantz and Schreiber,
1998; Schreiber and Kantz, 1998):
1. obtain a referential, desired trajectory, which is a
low dimensional approximation of the attractor;
2. project each point in the trajectory of the contam-
inated signal s(n) orthogonally on to the approxi-
mation of the attractor to produce a trajectory vec-
tor of cleaned time series ˆs(n);
3. convert the filtered phase space trajectory ˆs(n) to
the scalar time domain to produce a denoised time
series ˆs(n).
The described Nonlinear Projective Filtering algo-
rithm was designed for the filtering of various types
of noise contamination present in deterministically
chaotic systems.
3.2 Adaptive Nonlinear Projective
Filtering
The goal of proposed, novel algorithm is the elim-
ination of eye-blink related artifacts from EEG sig-
nals. Although in this application the eye-blink com-
ponent b(n) is a disturbance, from the signal-to-noise
ratio perspective it is much easier to solve the inverse
problem. Therefore, the proposed ANPF will first try
to find the estimate of eye-blink component in con-
taminated EEG signal
ˆ
b(n) w
m
b(n) by filtering out
all EEG related components. The difference e(n) be-
tween recorded, noisy EEG signal x(n) and filtered
eye-blink artifact
ˆ
b(n) will be an estimate of clear, un-
contaminated signal s(n). Mathematically, this can be
described as in (4)
e(n) = x(n)
ˆ
b(n),
e(n) = s(n) + w
m
b(n)
ˆ
b(n),
e(n) s(n).
(4)
For the ANPF algorithm to work properly a reli-
able low dimensional approximation to the attractor
must be provide. This approximation will be also re-
ferred to as a reference trajectory. Together with EEG,
the EOG signals are often recorded. These signals are
measured from locations that lay close to location of
bioelectrical sources of eye blink and movement re-
lated artifacts (i.e. eyes). EOG is commonly used as
a secondary noise input for the adaptive noise can-
celling algorithms (Binias et al., 2015; Binias et al.,
2016b). The reconstructed state space trajectory of
simulated EOG signal b
r
(n) will be used as the refer-
ential approximation of the attractor in this work.
Considering the presented assumptions and con-
siderations, the ANPF algorithm can be realized in
following steps:
Adaptive Nonlinear Projective Filtering - Application to Filtering of Artifacts in EEG Signals
443
1. create a state space representation of contami-
nated EEG signal x(n) and reference EOG trajec-
tory b
r
(n);
2. for each every point in contaminated trajectory
find closest point of reference trajectory;
3. replace a corrected point from contaminated tra-
jectory with its closest point from reference tra-
jectory to produce a cleaned vector
ˆ
b(n);
4. convert the cleaned trajectory of
ˆ
b(n) to scalar
time domain.
5. subtract cleaned reference trajectory
ˆ
b(n) from
contaminated signal x(n) in time domain to obtain
a filtered EEG signal e(n).
In Fig. 6 presented are exemplary state space tra-
jectories of simulated signals obtained for embedding
dimension D = 2 and delay time τ = 5 samples.
3.3 Adaptive Nonlinear Projective
Filtering - Real-Time
Implementation
It must be noted that ANPF algorithm, as described in
Sec. 3.2 is implementable only for off-line process-
ing of EEG signals. In many practical applications,
such as BCI systems, it is required for all utilized al-
gorithms to be causal and realizable in real time (or
at least with as short phase delay introduced as pos-
sible). Therefore, in this research an implementation
of ANPF allowing a causal processing with negligi-
ble delay is proposed and validated. This modifica-
tion will be referred to as ANPF
RT
. For that pur-
pose ANPF algorithm is applied to overlapping seg-
ments of analysed signal x(n), each of length M. For
each discrete time index n filtered output is calcu-
lated only from segment x
m
(n) = [x(n M),x(n
M + 1),. ..,x(n)]. Resulting, filtered signal e(n) will
be delayed for M samples. Described modification of
algorithm can be implemented in following steps:
1. for analyzed discrete time index n create a seg-
ment x
m
(n) = [x(n M),x(n M + 1),. .. ,x(n)]
from past M 1 samples of contaminated EEG
recording x(n) and current sample;
2. for analyzed discrete time index n create a ref-
erence segment b
rm
(n) = [b
r
(nM),b
r
(nM +
1),. ..,b
r
(n)] from past M 1 samples of refer-
ence signal b
r
(n) and current sample;
3. apply ANPF algorithm to x
m
(n) with b
rm
(n) serv-
ing as reference to obtain its filtered output e
n
R
M
;
4. filtered output of x(n) at discrete time index n is a
first sample of e
n
: e(n) = e
n
(0).
3.4 Normalized Least Means Squares
Adaptive Filter
An adaptive noise cancelling filter based on NLMS
algorithm served as a reference method for validation
of ANPF. If b
rm
(n) R
M
is a signal segment extracted
from referential EOG recording at time index n con-
sisting of M in a same manner as described in Sec.
3.3, then the output of an adaptive filter at discrete
moment n can be calculated as in (5)
y(n) = b
rm
(n)
T
w(n). (5)
The coefficients w(n) R
M
of the filter are be-
ing adaptively updated for each new sample. Because
of the lack of correlation between desired component
s(n) and the reference signal b
r
(n) the output y(n) will
be fitted to noise component b(n) of x(n). As a re-
sult the difference between the filter output at sample
n and contaminated signal will be an estimate of de-
sired, uncontaminated signal s(n) as presented in (6)
e = x(n) y(n). (6)
The formula for updating the filter coefficients for n+
1 sample with NLMS algorithm is presented in (7)
w(n+ 1) = w(n) + µ(n)e(n)b
rm
(n). (7)
The adaptation step in NLMS is normalised with
the power of input signal as presented in (8). The
purpose of γ parameter is to prevent situations where
the denominator of that expression approaches 0
µ(n) =
µ
0
γ+ b
T
rm
(n)b
rm
(n)
. (8)
3.5 Testing Procedure
The effectiveness of artifact filtering and correction
was evaluated using NMSE measure. Since the data
used in this work were simulated, the desired, uncon-
taminated signal s(n) was available for comparison
with filtered discrete time course e(n). The NMSE
was calculated for each test as presented in (9).
NMSE
s(n),e(n)
=
1
N
0
N
0
n=1
s(n) e(n)
2
N
0
n=1
s
2
(n)
(9)
To properly evaluate the effectiveness of proposed
ANPF algorithm, assess its advantages and compare it
with referential NLMS approach, following tests were
designed and performed:
Test 1 Sensitivity analysis of ANPF to embedding di-
mension D from 1 to 12, with fixed delay time
τ = 10 samples
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
444
-100 0 100
b(n)
-100
0
100
b(n-5)
a.
-100 0 100
b
r
(n)
-100
0
100
b
r
(n-5)
b.
-100 0 100
s(n)
-100
-50
0
50
100
s(n-5)
c.
-100 0 100
x(n)
-100
-50
0
50
100
x(n-5)
d.
Figure 6: Exemplary state space trajectories of simulated signals: a. eye-blink component; b. reference signal; c. desired
EEG component; d. contaminated EEG recording (own source).
Test 2 Sensitivity analysis of ANPF to delay time τ
{1,2,.. .,40} with embedding dimension D fixed
at best value of that parameter selected in Test 1
Test 3 Sensitivity analysis of NLMS to µ
0
in range
{0.0001,0.0002,. . .,2.5} with fixed M = 15 and
γ = 0.01.
Test 4 Sensitivity analysis of NLMS to M in range
{1,2,.. .,30} with fixed µ
0
at best value from Test
3 and γ = 0.01.
Test 5 Comparison between performance of ANPF,
ANPF
RT
and NLMS with parameters ensuring
best performance of each method. Range of
parameters searched for the best performance
of ANPF/ANPF
RT
: τ {1,2,. ..,40}, D
{1,2,.. .,12}, M {1, 2, ... , 30}. Range of pa-
rameters searched for best performanceof NLMS:
µ
0
{0.0001,0.0002, ...,2.5}, M {1,2,.. ., 30}
and γ = 0.01.
All of the performed tests consisted of 500 itera-
tions. During each iteration a new, random EEG time
course was simulated accordingly to parameters de-
scribed in Sec. 2. It must be noted, that delay in-
troduced by ANPF
RT
implementation had to be cor-
rected, so that results obtained with NMSE would re-
main reliable. However, said correction was imple-
mented during the offline processing. Therefore, it
must be taken into account that tests of ANPF
RT
im-
plementation provide an overviewof its correction ca-
pabilities rather than real time performance. It must
be however noted that the maximal delay that could
result from ANPF
RT
in this research did not exceed
150 ms. The statistical significances of achieved re-
sults were evaluated using adequate tests and pre-
sented in Sec. 4. To test the differences between mean
performances achieved for different configurations of
parameters inside each test the one-way analysis of
variance (ANOVA) were performed. In such tests
the null hypothesis states that samples from differ-
ent groups are drawn from populations with the same
mean against the alternative hypothesis that the popu-
lation means are not all the same. In this research the
grouping is attributed to different parameters in spe-
cific sensitivity tests. The desired threshold α value
was set to 0.01.
4 RESULTS
In Fig. 7 presented are box-plots achieved from Test
1. The lowest median NMSE score was obtained for
D = 8 (marked with green colour in Fig. 7). How-
Adaptive Nonlinear Projective Filtering - Application to Filtering of Artifacts in EEG Signals
445
ever, the one-way ANOVA test performed on the val-
ues of this parameter in range from 1 to 9 returned a
p-value p = 0.4442. Therefore, it can be concluded
that for this range of D parameter no significant dif-
ferences between mean NMSE occurred. After some
threshold value is exceeded (in this work for D
lim
= 9)
algorithms performance begins to downgrade.
1 2 3 4 5 6 7 8 9 10 11 12
D
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
NMSE
Figure 7: Analysis of ANPF algorithm’s sensitivity to em-
bedding dimension D parameter (own source).
Presented in Fig. 8 are box-plots achieved from
Test 2. To ensure a clear overview of performed test
only selected values of τ were included. The low-
est median NMSE score was obtained for τ = 10
(marked with green colour in Fig. 8). The one-way
ANOVA test performed for τ {1,2,... ,11} returned
a p = 0.1138, which is higher than desired α = 0.01.
Therefore, it can be concluded that for lower values of
τ differences in performance are not significant. Simi-
lar behaviour can be observed for τ {19, 20,. ..,40}.
The p-value obtained for that group was also greater
than 0.01 (p = 0.4167). It can be observed that as
τ exceeds some limit the performance start to de-
crease and then stabilizes at steady level, where it is
1 2 3 4 5 6 7 8 9 10 11 12 13 16 19 22 25 28 31 34 37 40
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
NMSE
Figure 8: Analysis of ANPF algorithm’s sensitivity to delay
time τ (own source).
no longer affected by increases of τ.
In Fig. 9 presented are selected box-plotsachieved
from Test 3. The lowest median NMSE score was
obtained for µ
0
= 0.1 (marked with green colour in
Fig. 7). Visual inspection of result reveals the pos-
sibility of means being equal in two groups: µ
0
=
0.0001÷0.001 and µ
0
= 0.1÷1.9. One-way ANOVA
tests of each group returned respectively p = 0.3196
and p = 0.1365. According to achieved results over-
all mean NMSE tends to decrease with the increase
of µ
0
. Then, for a great range of µ
0
values the NMSE
remains stable until a value is reached when the fil-
tering error becomes very high. To maintain the clar-
ity of a data presentation, results for µ
0
> 2.0 were
not included. In other words, best µ
0
value needs to
be individually selected for each specific case as it is
not related to neither high nor low values of µ
0
. This
observation corresponds well with general knowledge
about characteristics of adaptive filters (Haykin and
Widrow, 2003).
0
0.2
0.4
0.6
0.8
1
NMSE
0
0.0001
0.0004
0.0007
0.001
0.002
0.003
0.005
0.007
0.01
0.03
0.05
0.07
0.1
0.4
0.7
1
1.3
1.6
1.9
2
Figure 9: Analysis of NLMS algorithm’s sensitivity to
adaptation step µ (own source).
In Fig. 10 presented are box-plots achieved from
Test 4. The lowest median NMSE score was obtained
for M = 2 (marked with green colour in Fig. 10). For
M = 13÷30 calculated p-value (p = 0.0456) exceeds
desired α which indicates that NLMS is not sensitive
to changes of that parameter in that range in described
case. It is worth noting that for lower values of M a
better performance was achieved.
Fig. 11 presents the comparison between fine-
tuned off-line ANPF, ANPF
RT
(with delay correc-
tion) and NLMS. Lowest median of NMSE for all
test repetitions ANPF
med
= 0.0025 was achieved for
ANPF with embedding dimension D = 8 and delay
τ = 10. Real time implementation ANPF
RT
obtained
median NMSE score ANPF
RT
med
= 0.0043 for param-
eters D = 2, τ = 1 and M = 30. Referential method
based on NLMS adaptive filter algorithm allowed to
achieve median NMSE NLMS
med
= 0.004. Since
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446
Figure 10: Analysis of NLMS algorithm’s sensitivity to fil-
ter length M (own source).
differences between performances of methods were
compared with one-vs-onestrategy, one-way ANOVA
tests have been replaced with two sample t-tests. All
differences revealed to be statistically significant (p-
values of e 09 range). Therefore, it can be con-
cluded that correction quality of proposed ANPF al-
gorithm significantly outperforms referential NLMS
algorithm. Additionally, it can be observed that real
time implementation of ANPF downgrades its per-
formance, event with the correction of phase delay.
Thus, NLMS remains a better choice for real time ap-
plications.
Figure 11: Comparison between fine-tuned ANPF,
ANPF
RT
(with delay correction) and NLMS (own source).
5 CONCLUSIONS
In this work a concept of a novel approach to adaptive
filtering of eye blink related artifacts from EEG sig-
nals was presented and validated. ANPF algorithm
achieved a highly satisfactory performance during
conducted tests. The median NMSE score achieved
by ANPF in described experiment has significantly
outperformed referential method based on NLMS al-
gorithm (0.0025 to 0.004). Additionally, during sen-
sitivity analysis it was revealed that ANPF algorithm
is robust to changes of its parameters, especially in
lower ranges of their values. As a result, utilization of
proposed algorithm for analysis of EEG signals be-
comes easier and less demanding from the parameter
selection perspective. This stands in great contrast to
popularly used adaptive filters based on least mean
squares algorithms. Such algorithms are known to be
highly dependent on their parameters and may even
become unstable due to their poor selection. This
behaviour was observed also in this work. On the
other hand, it should be noted that in case of this
research, performed tests focused on the artifact fil-
tering and correction effectiveness of presented meth-
ods. Since the original form of ANPF is designed for
off-line use and its real time implementation ANPF
RT
required the off-line correction of the phase delay, it
is obvious that they are less suited for real time ap-
plications than NLMS. This conclusion is furtherly
supported by the observed downgrade of ANPF al-
gorithm’s effectiveness in its real time implementa-
tion ANPF
RT
. The best performance of ANPF
RT
was
achieved with relatively low delay of 150 ms. Ad-
ditionally, the NLMS based approach outperformed
ANPF
RT
0.004 to 0.0043 in terms of median NMSE.
Although the difference is not great, it tested to be
statistically significant. However, this fact should not
cover the superiority of generic ANPF algorithm for
off-line filtering of EEG signals.
ACKNOWLEDGEMENTS
This work was supported by Silesian University of
Technology grant no. 02/010/BKM16/0047/31 and
BK/213/RAu1/2016. The research presented here
was funded by the Silesian University of Technol-
ogy grant BK for Institute of Automatic Control (for
both Data Mining and Control and Robotics Groups)
for 2017 year. Moreover, the calculations were per-
formed with the use of IT infrastructure of GeCONiI
Upper Silesian Centre for Computational Science
and Engineering (NCBiR grant no POIG.02.03.01-
24-099/13)
REFERENCES
Benedetto, S., Pedrotti, M., Minin, L., Baccino, T., Re, A.,
and Montanari, R. (2011). Driver workload and eye
Adaptive Nonlinear Projective Filtering - Application to Filtering of Artifacts in EEG Signals
447
blink duration. Transportation Research Rart F: Traf-
fic Psychology and Behaviour, 14(3):199–208.
Binias, B., Myszor, D., Niezabitowski, M., and Cyran,
K. A. (2016a). Evaluation of alertness and mental fa-
tigue among participants of simulated flight sessions.
In Carpathian Control Conference (ICCC), 2016 17th
International, pages 76–81. IEEE.
Binias, B., Palus, H., and Jaskot, K. (2015). Real-time de-
tection and filtering of eye movement and blink related
artifacts in EEG. In 2015 20th International Con-
ference on Methods and Models in Automation and
Robotics (MMAR), pages 903–908. IEEE.
Binias, B., Palus, H., and Jaskot, K. (2016b). Real-time
detection and filtering of eye blink related artifacts
for brain-computer interface applications. In Man–
Machine Interactions 4, pages 281–290. Springer.
Blankertz, B., Tomioka, R., Lemm, S., Kawanabe, M., and
Muller, K.-R. (2008). Optimizing spatial filters for ro-
bust EEG single-trial analysis. IEEE Signal Process-
ing Magazine, 25(1):41–56.
Correa, A. G., Laciar, E., Pati˜no, H., and Valentinuzzi,
M. (2007). Artifact removal from EEG signals using
adaptive filters in cascade. 90(1):012081.
Craig, A., Tran, Y., Wijesuriya, N., and Nguyen, H. (2012).
Regional brain wave activity changes associated with
fatigue. Psychophysiology, 49(4):574–582.
da Silva, F. L. (1991). Neural mechanisms underlying
brain waves: from neural membranes to networks.
Electroencephalography and Clinical Neurophysiol-
ogy, 79(2):81–93.
Gao, J., Hu, J., and Tung, W.-w. (2011). Facilitating joint
chaos and fractal analysis of biosignals through non-
linear adaptive filtering. PloS one, 6(9):e24331.
Grunwald, M., Weiss, T., Krause, W., Beyer, L., Rost, R.,
Gutberlet, I., and Gertz, H.-J. (1999). Power of theta
waves in the EEG of human subjects increases dur-
ing recall of haptic information. Neuroscience Letters,
260(3):189–192.
Harezlak, K. (2017). Eye movement dynamics during im-
posed fixations. Information Sciences, 384:249 – 262.
Haykin, S. and Widrow, B. (2003). Least-mean-square
adaptive filters, volume 31. John Wiley & Sons.
Jung, T.-P., Makeig, S., Humphries, C., Lee, T.-W., Mck-
eown, M. J., Iragui, V., and Sejnowski, T. J. (2000).
Removing electroencephalographic artifacts by blind
source separation. Psychophysiology, 37(2):163–178.
Kantz, H. and Schreiber, T. (1998). Nonlinear projective
filtering I: background in chaos theory. arXiv preprint
chao-dyn/9805024.
Kotas, M. (2004). Projective filtering of time-aligned ECG
beats. IEEE Transactions on Biomedical Engineering,
51(7):1129–1139.
Kotas, M. (2009). Nonlinear projective filtering of ECG
signals. INTECH Open Access Publisher.
Makeig, S., Bell, T., Lee, T., Jung, T., Enghoff, S., et al.
(2000). EEGLAB: ICA toolbox for psychophysiolog-
ical research. WWW Site, Swartz Center for Computa-
tional Neuroscience, Institute of Neural Computation,
University of San Diego California.
Nunez, P. L. and Srinivasan, R. (2006). Electric fields of the
brain: the neurophysics of EEG. Oxford university
press.
Nunez, P. L., Srinivasan, R., Westdorp, A. F., Wijesinghe,
R. S., Tucker, D. M., Silberstein, R. B., and Cadusch,
P. J. (1997). EEG coherency: I: statistics, refer-
ence electrode, volume conduction, Laplacians, cor-
tical imaging, and interpretation at multiple scales.
Electroencephalography and Clinical Neurophysiol-
ogy, 103(5):499–515.
P. Berg, M. S. (1991). Dipole models of eye activity and
its application to the removal of eye artifacts from the
EEG ad MEG. Clinical Physics and Physiological
Measurements, 12:49–54.
Pfurtscheller, G. and Da Silva, F. L. (1999). Event-
related EEG/MEG synchronization and desynchro-
nization: basic principles. Clinical Neurophysiology,
110(11):1842–1857.
R. J. Croft, R. J. B. (2000). Removal of ocular artifact from
the EEG: a review. Clinical Neurophysiology, 30:5–
19.
Richter, M., Schreiber, T., and Kaplan, D. T. (1998). Fe-
tal ECG extraction with nonlinear state-space projec-
tions. IEEE Transactions on Biomedical Engineering,
45(1):133–137.
Schreiber, T. and Kantz, H. (1998). Nonlinear projective fil-
tering I: Application to real time series. arXiv preprint
chao-dyn/9805025.
Takens, F. (1981). Detecting strange attractors in turbu-
lence. In Dynamical systems and turbulence, Warwick
1980, pages 366–381. Springer.
Teplan, M. (2002). Fundamentals of EEG measurement.
Measurement Science Review, 2(2):1–11.
ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics
448