INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL
ISSN 1841-9836, e-ISSN 1841-9844, 14(3), 375-387, June 2019.
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals
M. Miranda, R. Salinas, U. Raff, O. Magna
Michael Miranda*
Department of Informatic Engineering
Metropolitan University of Technology, Chile
Jose Pedro Alessandri 1242, Nunoa, Santiago, Chile
*Corresponding author: michael.miranda@utem.cl
Renato Salinas
Department of Mechanical Engineering
University of Santiago, Chile
Av. Libertador Bernardo O’Higgins 3363, Santiago, Chile.
renato.salinas@usach.cl
Ulrich Raff
Department of Physics
University of Santiago, Chile
Av. Libertador Bernardo O’Higgins 3363, Santiago, Chile.
ulrich.raff@usach.cl
Oscar Magna
Department of Informatic Engineering
Metropolitan University of Technology, Chile
Jose Pedro Alessandri 1242, Nunoa, Santiago, Chile
omagna@utem.cl
Abstract: The blinking of an eye can be detected in electroencephalographic (EEG)
recordings and can be understood as a useful control signal in some information
processing tasks. The detection of a specific pattern associated with the blinking
of an eye in real time using EEG signals of a single channel has been analyzed.
This study considers both theoretical and practical principles enabling the design
and implementation of a system capable of precise real-time detection of eye blinks
within the EEG signal. This signal or pattern is subject to considerable scale changes
and multiple incidences. In our proposed approach, a new wavelet was designed
to improve the detection and localization of the eye blinking signal. The detection
of multiple occurrences of the blinking perturbation in the recordings performed in
real-time operation is achieved with a window giving a time-limited projection of an
ongoing analysis of the sampled EEG signal.
Keywords: Biological signals, electroencephalogram, brain computer interface, eye
blink detection, pattern recognition, wavelet design.
1 Introduction
The electroencephalogram was designed to record the brain activity of a living being, specif-
ically by sensors, with which electrical signals from the brain are captured. Any activity that
does not come from the brain, that is, noise, is called an artifact. Depending on the origin, they
can be divided into physiological and extra-physiological artifacts. The first ones are generated
by the patient, on the other hand, extra-physiological artifacts arise from sources external to the
individual, that is to say from the environment. Blinking of eyes is considered an ocular artifact,
which is captured in the frontal zones Fp1-Fp2 of the international system 10-20 [10].
Copyright ©2019 CC BY-NC
376 M. Miranda, R. Salinas, U. Raff, O. Magna
The eyeball acts as a dipole, with a positive pole oriented anteriorly (cornea) and a negative
pole oriented posteriorly (retina). A blinking of eyes causes the positive pole to approach the
fronto-polar electrodes Fp1-Fp2, producing symmetrical descending deflections [15]. The EEG
records are manifested with periodic and unpredictable oscillations, having a greater spectral
amplitude in certain frequency bands, which are divided into: 0.5 − 4 Hertz (delta band),
4−8 Hertz (theta band), 8−12 Hertz (alpha band), 12−30 Hertz (beta band) and greater
than 30 Hertz (gamma band) [4].
The extraction of characteristics is an important process in the classification of EEG signals,
and additionally, it is also possible to relate patterns with a defined intentionality on the part
of the individual. However, the relationship between the electrical signal and the intention is
diffuse, besides it is necessary to filter the artifacts, to obtain a signal without noise, so as not
to disturb the results. One of the artifacts that must be filtered is the eye blinking, but before
filtering it must be detected. The blinking of eyes could be considered, in itself, a control signal,
since in general an individual can generate voluntary blinks, being able to increase the frequency
and / or amplitude, which in turn can be associated with machine instructions for a computer.
From the previous conceptualization, it is possible to devise a brain-machine interface or BCI,
which uses eye blinking as support data. A brain-machine interface or BCI, is defined as the
technology that allows capturing brain waves to be processed by a computer with the intention
of obtaining information about a state or cognitive process of the person. For example, in Dzitac
et al. [7] changes in amplitude are studied in the different frequency bands, specifically the events
of desynchronization (or event-related ERD) and their application to BCI.
The work that will be presented in this publication, shows the research results related to
the automatic detection of eye blinking by designing an ad-hoc mother wavelet, which allows the
analysis in the time domain.
2 Materials and methods
2.1 Creation of an EEG signal database
The design of a mother wavelet requires experimental data and validation, from which it
is possible to extract the representative pattern present in the study signal. For this reason, a
free access database of EEG signals was consulted to obtain experimental data. Subsequently,
a software based on Matlab and Java was developed for obtaining in real time experimental
validation samples, recording the EEG signal and the video of the face of the individual with
the same time-base, this way to correlate the video with the EEG signal and clearly define the
occurrence of the blinks.
2.2 Obtaining experimental data
To verify the main hypotheses of this work, the available data is located in www.physionet.org,
specifically the PhysioBank database. This is a database of high-growth physiological digital
signals, with good foundation in data related to the biomedical research community. Polysomno-
graphic record signals, of multiple parameters, are included in this database including cardiopul-
monary, neural and other fields of biomedicine. The records correspond to both healthy individu-
als and patients with a wide variety of conditions that concern different pathological implications,
such as sudden cardiac death, failure congestive heart, epilepsy, motor disorders, sleep apnea and
senility. This database is freely accessible via web and tends to cooperative activities, that is
providing data for research and requesting the submission of results for its feedback. The Phys-
ioBank collections are organized in more than 50 databases, each with a number of records, and
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals 377
each record contains information collected from a single subject.
2.3 Obtaining validation data
Validation data were obtained from a continuous EEG measurement with the biosensor
consisting of a band designed by Neurosky MindWave TM, being one of the first to enter the
market of EEG amplifiers for use in non-invasive BCI. Mindwave is very economical due to the
simplicity that characterizes it, having one electrode in position FP1 and has the option of being
compatible with both iOs and Android [13].
Figure 1: Video recording module, status indicator module and real-time software-oscilloscope
module
The state of the eye blink was detected through a video camera during the EEG measure-
ment, subsequently and then manually added to the file after analyzing the video frames. Where
"1" indicates the closed eye state and "0" the state of the eye open. All the values are in chrono-
logical order with the first value measured in the top of the data. The platform developed is
called "EEG Studio" and is composed of three modules:
1. Oscilloscope that works in real time.
2. Video recording: records the face of the individual in real time.
3. Status Indicator: indicates the correct functioning of the different modules.
3 Wavelet transform
Wavelets are functions that satisfy certain mathematical requirements and are used for the
representation of data or other functions. Wavelets are very suitable for data approximation
of signals with abrupt discontinuities. The fundamental idea behind wavelets is to analyze
functions according to scales. In wavelet analysis, the scale used to analyze the data plays a
special role. Algorithms that use wavelets process data at different scales or resolutions. If a
signal or function is observed using a wide "window", the small details are not observed; On
the other hand, if the "window" used is narrow, then they can be observed. In wavelet analysis,
378 M. Miranda, R. Salinas, U. Raff, O. Magna
these windows are automatically adjusted when changing resolution, usually referred to as multi-
resolution analysis. This makes wavelets a useful and interesting tool. The general procedure of
the analysis using wavelets is to adopt a "prototype" function, generally called mother wavelet.
The temporal analysis is then carried out using dilatations and translations of said function.
The original signal can then be represented as a linear combination of the original function and
its translated and dilated ones. This procedure is called a wavelet expansion. The choice of the
mother wavelet [13] (and thus the base or the wavelet frame) is not unique and depends on the
type of functions or data to analyze. The multi-resolution analysis of the wavelets, makes it a
very powerful tool for the study of EEG signals. An example of the EEG artifact and pattern of
blinking of eyes is seen in Fig. 2.
Figure 2: EEG signal with two artifacts produced by blinking eyes. The artifacts are indicated
with two light gray time intervals
3.1 Continuous wavelet transform
The continuous Wavelet transform allows the analysis of a signal in a segment located in
it and consists in expressing a continuous signal as an expansion of terms or coefficients of the
internal product between the signal and a Mother Wavelet function. A Mother Wavelet is a
localized function, belonging to space L2(R), that contains all functions with finite energy and
square integrable functions defined:
f ∈ L2 ⇒
∫
|f(t)|2 dt = E < ∞ (1)
In this way we have a single modulated window and from this a complete family of elementary
functions is generated by dilatations or contractions and translations in time Ψa,b(t), called
wavelet daughters that meet all the conditions of the form:
Ψa,b(t) =
1
√
a
Ψ
(
t− b
a
)
(a,b) � R, a 6= 0. (2)
The Mother Wavelet must comply with the eligibility condition:
CΨ(t) =
∫ ∞
0
|Ψ(ω)|2
ω
dω < ∞ (3)
Which means that the function is well localized in time, that is, the function oscillates around
an axis and its average is zero and that the Fourier transform is a continuous band-pass filter,
with rapid decrease towards infinity and toward ω = 0. The Wavelet transform of a function at
a given scale and position, is calculated by the correlation of the form:
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals 379
CWT (a,b) =
1
√
a
∫ ∞
−∞
x(t)Ψ
(
t− b
a
)
dt (4)
3.2 Wavelet pattern design applied in CWT
When searching a defined pattern it is possible to apply two different techniques to perform
multiresolution analysis. The first technique includes the use of an existent wavelet family trying
to find whatever fits best the detection of the pattern, i.e. trial and error technique [16]. In
reference [16] the biorthogonal wavelet was used. The other alternative consists in designing
or building a wavelet starting with the pattern that is asked to be detected. This process can
obviously decrease the time to approach the desired goal while improving the detection of the
blinking artifact. This approach will work as long as the characteristics of the designed wavelet
are close enough to the characteristics of the recorded pattern. Based on a given function f with
compact support and finite energy, we may consider the construction of a wavelet usable with
CWT while approximating this function in the least square sense. Various construction methods
are possible, and since we have numerical sampling of our pattern over a given interval [a,b], we
used the method described by Misiti [14]. Let us consider a finite set of values:
(tk,yk)k=1, ... , K , such that : a ≤ tk ≤ b and yk ≈ f(tk) (5)
Consider a family F = ρiNi=1 of linearly independent functions in L
2(a,b), where L2 is the
space of square integrable functions over R, and denote by V the vector space spanning F . For-
mulated for this finite set of pairs, the problem consists of seeking coefficients α = αiNi=1 in R
N,
where:
ψ =
N∑
i=1
αiρi (6)
such that:
K∑
k=1
[ψ (tk) −yk]
2
=
Min
β�RN
{
K∑
k=1
[vβ (tk) −yk]
2
}
(7)
such that: ∫ b
a
vβ (t) dt = 0 (8)
where for β in RN:
vβ =
N∑
i=1
βiρi (9)
It is thus a problem of least squares sense minimization with a constraint. The vector α
and the Lagrange multiplier λ associated with the constraint are obtained by solving the linear
system: [
G Mt
M 0
][
α
λ
]
=
[
B
0
]
(10)
with G, M and B defined by:
Gi,j =
K∑
k=1
ρi (tk) ·ρj (tk) (11)
380 M. Miranda, R. Salinas, U. Raff, O. Magna
Mi =
∫ b
a
ρi (t) dt (12)
Bi =
K∑
k=1
yk ·ρj (tk) (13)
The wavelet ψ(t), must satisfy conditions of admissibility and regularity. Regularity is
defined as the capability of a given wavelet to reconstruct a signal from the coefficients computed
during the transformation process [11]. In other words, a function is regular if it can be locally
approximated by a polynomial. According to Lipschitz’s definition of regularity [12], a function
f is pointwise Lipschitz α ≥ 0 at υ, if there exist C > 0, and a polynomial ρυ of degree m = [α],
such that:
∀t � R , |f (t) −ρυ(t)| ≤ C · |t−υ|α (14)
A function f is uniformely Lipschitz α over [a,b] if it satisfies for all υ � [a,b], with a constant
C that is independent of υ. The Lipschitz regularity of f at υ or over [a,b] is the supremum of
the α such that f is Lipschitz α. On the other hand, admissibility [11] is defined by the following
conditions:
∫ ∞
−∞
ψ (t) dt = 0 (15)
∫ ∞
−∞
|ψ (t) |2dt < ∞ (16)
That is, function ψ(t) must be localized in a bounded time interval, having oscillations
around time axis, so its average be zero.
3.3 Characteristic pattern detection
Given the waveform pattern associated with eye blinking shown in Figure 2, it is necessary
to design a mother wavelet as close as possible to the recorded pattern. This new wavelet will
be labeled "blinkwave". This designed wavelet can then be used in the CWT analysis because
it fulfills the required wavelet properties using the CWT technique [6].
4 Design and use of the mother wavelet
To design the new wavelet ("blinkwave") it becomes necessary to isolate the EEG Eye
Blinking Pattern. Using this procedure, we obtain a vector or a set of finite number of values in
equation (6). This vector is utilized in the process described by Misiti [14]. Designing the wavelet
process with polynomials of variable grades, we obtain a mother wavelet with best approximation
to the recorded pattern with a polynomial of grade 6, which can be observed in Figure 3.
In this case, the family F = ρiNi=1 used in equations (5) to (13), is the polynomial family of
grade N ≥ 6.
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals 381
Figure 3: Overlay of the waveform produced by eye blinking and the wavelet designed, both
normalized in the range [−1, 1]
4.1 Design of the mother wavelet
According to the method hinted in [18], it is necessary to construct matrices G, M and B,
to fulfill equation (10), and to resolve the following linear system:(
G Mt
M 0
)(
α
λ
)
=
(
B
0
)
⇒ A ·U = B (17)
I.e., solve U as a function of A:
U = A−1 ·B (18)
We take as base the pattern ("blinkwave"), which is defined as an n-component vector:
{yi}mi=1 = y1, y2, . . . , ym (19)
The base pattern is obtained digitizing the continuous signal with a constant sampling
frequency fs which defines the time interval ∆t between samples. The matrix or file vector M,
is built using the formula in equation (12), considering the admissibility restrictions given by
equations (15) and (16), resulting in the following series:
Mi=[1,m] =
∫ b
a
ρi (t) dt =
{
1
i
(bi −ai)
}
i=[1,m]
=
=
[
(b−a) ,
(
b2
2
− a
2
2
)
, . . . ,
(
bN+1
N+1
− a
N+1
N+1
)]
(20)
If one chooses initiating the analysis at the origin, a = 0, then all computations become
simpler, then, recomputing M we obtain:
M =
[
b,
(
b2
2
)
, . . . ,
(
bN+1
N+1
)]
1×(N+1)
(21)
Given M, we must apply the regularity condition indicated in equation (14), to get a new
matrix M, as follows:
382 M. Miranda, R. Salinas, U. Raff, O. Magna
M =
b,
(
b2
2
)
, . . . ,
(
bN+1
N+1
)
1 0 . . . 0
1 b . . . bN
3×(N+1)
(22)
Afterwards, the matrix G is built using equation (11):
G =
b
(
b2
2
)
· · ·
(
bN+1
N+1
)
(
b2
2
) (
b3
3
) ... (bN+2
N+2
)
...
... · · ·
...(
bN+1
N+1
) (
bN+2
N+2
)
· · ·
(
b2N+1
N+2
)
(N+1)×(N+1)
(23)
Prior to solving the linear system for U, we must generate the column vector B, as described
in equation (13):
B =
(
1
2
)
∑m
i=1 (xi+1 −xi)
(
xi+1·yi+1 + xi ·yi
)∑m
i=1 (xi+1 −xi)(xi+1
2·yi+1 + xi2 ·yi)
...∑m
i=1 (xi+1 −xi)
(
xi+1
N·yi+1 + xiN ·yi
)
(N+1)×1
(24)
Once matrices G and M are generated, it is possible assembling matrix A and proceed
solving equation (17):
U = A−1 ·B ⇒
α1
α2
...
λ1
=
[
G Mt
M 0
].1
· [B] (25)
Mother wavelet ψ(t), is generated using formula in equation (6) replacing the values obtained
for αi
ψ =
N∑
i=1
αi·ρi ⇒ ψ (t) =
N+1∑
i=1
αi·xiN+1−i (26)
Thus, for the numerical pattern shown in Figure 3 (solid line), represented by vector:
y = [0.0, 1.7, 2.0, 1.6, 0.8, 0.0,−0.6,−0.9,−1.1,−1.0,−0.9,−0.7,−0.5,−0.4,−0.3, 0.0] (27)
We obtain the polynomial mother wavelet ψ (t) as follow:
ψ (t) = α1 ·xn + α2 ·xn−1 + . . . + αn ·xn + αn+1 (28)
I.e., the first n numerical coefficients αi are employed, obtained from solving equation (25)
and discarding the Lagrange multipliers λi. These coefficients for the mother wavelet ψ (t), for
the pattern given in equation (27), are shown in equation (29) as follows:
p = [380, −1.2 · 103, 1.3 · 103, −640, 110, 1.2, −2.5 · 10−14] (29)
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals 383
Finally, the polynomial equation for the new mother wavelet ψ (t), is shown graphically in
Figure 3 (dashed line) and it is represented algebraically by equation (30), as follows:
ψ (t) = 380 ·x6 − 1200 ·x5 + 1300 ·x4 − 640·x3 + 110 ·x2 + 1.2 ·x− 02.5 · 10−14 (30)
4.2 Use of the mother wavelet
The new wavelet-blinkwave is used to obtain the coefficients, which will subsequently be
processed to obtain the location of each artifact. Using the signal shown in Figure 3 or the
"blinkwave" mother wavelet for analysis and applying the CWT , we obtain a coefficient matrix
C(a,b) using equation (31), where:
C(a,b) = CWT(”inputsignal”, ”blinkwave”) (31)
C(a,b) is the coefficients matrix and CWT is the continuous wavelet transform, applied to
input signal. The next step includes the detection and duration of the eye blinking from C(a,b).
To improve the analysis, a threshold must be applied to the matrix of wavelet coefficients, as
defined in equation (32).
T (a,b) =
{
0 if C(a,b) < Thresholdfixed
C(a,b) , otherwise
(32)
The dimensions of the matrix depend on the number of samples of the analyzed signal and
the level or number of scales in the decomposition performed by the wavelet transform.
Figure 4: Graphical representation or scalogram to the left image and the thresholded wavelet
coefficient matrix T(a,b) to the right
As can be observed in Figure 4 there is a defined relation between the coefficients and the
searched pattern. In our case, the graphical representations displayed in Figure 4 are used to
support the detection of two blinking artifacts in the EEG recording of Figure 2. A threshold
has been applied to the matrix of wavelet coefficients, as defined in equation (14). With this
numerical relation, it is possible to determine the temporal location and duration of the pattern
in the signal analysis process. In the case studied in this work, the number of samples b is
384 M. Miranda, R. Salinas, U. Raff, O. Magna
256 (analysis window size) and 4 levels of decomposition, which involves obtaining a coefficient
matrix [C] of 4x256 elements. To improve the location of the blinking patterns, the columns of
the coefficient matrix T(a,b) were added as shown in equation (33).
V (1, 2, . . . , n) =
∑
a
T (a,b) , b = 1, 2, . . . ,n (33)
The vector V obtained gives us the actual location in time of the artifact produced by the
eye blinking. To achieve a tradeoff between data smoothing and real time analysis, a moving
average of a small number of samples with a range of 10[ms] was applied. Applying the system
shown in Figure 1 to the recorded signal displayed in Figure 2 allows overlying the dotted signal
shown in Figure 5, which detects the occurrence of eye blinking and their duration.
Figure 5: Overlay of original EEG signal with the dotted signal highlighting the detected artifacts
and their duration produced by eye blinking
Figure 6: Examples of real-time detection of eye blinking with several analysis windows running
over a 1000[ms] time interval. a) Top: Three eye blinks; b) Bottom: Six eye blinks
Wavelet Design for Automatic Real-Time Eye Blink Detection
and Recognition in EEG Signals 385
5 Results and discussion
Results from this work have been tested with real-time EEG recordings introducing eye-
blinking artifacts with different frequencies and amplitudes. Figure 6 shows two recordings with
three and six eye blinking incidences of variable occurrences within 1000[ms] or one second
time intervals respectively, showing variable amplitudes and duration. This figure proves that
the algorithm is robust enough to filter artifacts produced by other sources that do not share
similarity in shape, as well as detecting a target pattern in its many versions independent of the
number of occurrences regardless of the extent and the level of symmetry in the study window.
Compared to our previous results [16] we have made some major improvements which allowed
robust real-time detection in a given time interval including amplitude and duration of the eye
blinking occurrences. A new mother wavelet has been designed according to the recorded patterns
of the EEG waves displaying eye blinking and the new wavelet decomposition was achieved with
four levels that allowed increasing the number of eye blinking artifacts within a given time
analysis window demonstrated in Figures 6(a) and 6(b).
The use of a designed mother wavelet improved the global detection process of the searched
pattern detection, using different observation periods for analysis, length of patterns, amplitudes
and repetitions. As the relative location was obtained using the "blinkwave" transform wavelet,
the thresholding and the sum of coefficients were simple and allowed quick obtaining of precise
real time results.
6 Conclusions
The use of wavelet transforms in analyzing non-stationary signals, such as electroencephalo-
grams, shows comparative advantages with respect to a conventional Fourier analysis. The design
of a mother wavelet was the main contribution to locate the blinking artifacts in the recorded
EEG signals. The paper shows in detail how to design a mother wavelet for a given case. Among
the advantages of using wavelet signal processing is the multi-resolution analysis, which involves
looking at multiple versions of the blinking patterns. The design of a mother wavelet used in
the context of wavelet analysis incorporates features of shape, amplitude, and phase shift for de-
tecting patterns using one-dimensional wavelet transform thus ensuring a robust detection and
recognition technique of eye blinking phenomena in EEG signals. This work also contributes to
bioengineering with respect to brain computer interfaces or BCI, allowing real-time detection of
eye blinking. Two major applications can be visualized: improvement of current BCI devices and
awareness detection systems. In addition, these eye blinking patterns, generated voluntarily by
the user, can translate into simple commands for helping people with disabilities, e.g., command-
ing a wheelchair in forward or reverse mode. From the results of our work, we conclude that
detection of the eye-blinking artifacts in EEG signals can be very helpful now that the timing
information of occurrence is well defined. It should be noted that although there are alterna-
tive analyses for eye blinking detection from EEG data, those approaches operate off-line, and
our method operates in real time. This approach improves respect previous work, in that there
are fewer processing steps now and increased precision regarding the timing of the eye blinking
events.
Acknowledgment
All authors like to thank the continuous support of the VRAC of the Technologic Metropoli-
tan University of Chile and VRIDEI of the University of Santiago of Chile.
386 M. Miranda, R. Salinas, U. Raff, O. Magna
Author contributions
The authors contributed equally to this work.
Conflict of interest
The authors declare no conflict of interest.
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