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 ﬁlter 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

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 (13−29 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

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

is the

pseudorandomly generated initial phase of k-th fre-

quency component of s(n), n is a discrete time index

and w

(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=1

(k)sin(2π f

n+ φ

). (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

of the individual frequency com-

ponents can be approximated by normal distribution

with mean value randomly selected from alpha wave

range µ

= 8 −12 Hz and standard deviation σ

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]

[ 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

[ 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

[ 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



√

2π

−

(

n−µ

)



. (2)

In formula (2) n ∈< −N

/2;N

/2 > is a discrete time

variable. If total duration of simulation is denoted by

and sampling frequency is represented by f

, then

= f

= 1 s and f

= 200 Hz in this work).

Mean of Gaussian distribution function µ

was set to

0 for all simulations (µ

= 0 s). Standard deviation σ

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

100

150

200

[ V]

Figure 3: Real EEG signal contaminated by eye blink arti-

fact (Binias et al., 2016a) (own source).

-N

/2 -2

b 0

-w

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

was

randomly selected from uniform distribution ranged

∈< 0.035 s; 0.085 s > that corresponds with short

blink duration. U





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

which was randomly se-

lected from uniform distribution w

∈< 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

was selected randomly for each

test from uniform distribution ranged from 0.8 to 1.0

∈< 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

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

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

can be represented

as a trajectory in a D-dimensional phase space with

Takens Method using time delay coordinates 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

b(n) ≃ w

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

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) −

b(n),

e(n) = s(n) + w

b(n) −

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

(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

(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

b(n);

4. convert the cleaned trajectory of

b(n) to scalar

time domain.

5. subtract cleaned reference trajectory

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

. 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

(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

(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

(n) = [b

(n−M),b

(n−M +

1),. ..,b

(n)] from past M −1 samples of refer-

ence signal b

(n) and current sample;

3. apply ANPF algorithm to x

(n) with b

(n) serv-

ing as reference to obtain its ﬁltered output e

∈

;

4. ﬁltered output of x(n) at discrete time index n is a

ﬁrst sample of e

: e(n) = e

(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

(n) ∈R

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

(n)

w(n). (5)

The coefﬁcients w(n) ∈ R

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

(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

(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) =

γ+ b

(n)b

(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)



∑

n=1



s(n) −e(n)



∑

n=1

(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

100

b(n-5)

-100 0 100

(n)

-100

100

(n-5)

-100 0 100

s(n)

-100

-50

100

s(n-5)

-100 0 100

x(n)

-100

-50

100

x(n-5)

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

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

at best value from Test

3 and γ = 0.01.

Test 5 Comparison between performance of ANPF,

ANPF

and NLMS with parameters ensuring

best performance of each method. Range of

parameters searched for the best performance

of ANPF/ANPF

: τ ∈ {1,2,. ..,40}, D ∈

{1,2,.. .,12}, M ∈ {1, 2, ... , 30}. Range of pa-

rameters searched for best performanceof NLMS:

∈{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

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

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

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)

algorithm’s performance begins to downgrade.

1 2 3 4 5 6 7 8 9 10 11 12

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

0.01

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

= 0.1 (marked with green colour in

Fig. 7). Visual inspection of result reveals the pos-

sibility of means being equal in two groups: µ

0.0001÷0.001 and µ

= 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

. Then, for a great range of µ

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

> 2.0 were

not included. In other words, best µ

value needs to

be individually selected for each speciﬁc case as it is

not related to neither high nor low values of µ

. This

observation corresponds well with general knowledge

about characteristics of adaptive ﬁlters (Haykin and

Widrow, 2003).

0.2

0.4

0.6

0.8

NMSE

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

1.3

1.6

1.9

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

(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

obtained

median NMSE score ANPF

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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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

NMSE

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.

ANPF

NLMS

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Figure 11: Comparison between ﬁne-tuned ANPF,

ANPF

(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

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

. The best performance of ANPF

was

achieved with relatively low delay of 150 ms. Ad-

ditionally, the NLMS based approach outperformed

ANPF

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)

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