Electroencephalogram denoising using discrete wavelet transform and adaptive noise cancellation based on information theory

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 14, No. 1, February 2025, pp. 769~779
ISSN: 2252-8938, DOI: 10.11591/ijai.v14.i1.pp769-779  769
Journal homepage: http://ijai.iaescore.com
Electroencephalogram denoising using discrete wavelet
transform and adaptive noise cancellation based on information
theory
Hashem Abdolahniya1
, Ali Akbar Khazaei1
, Mahdi Azarnoosh2
, Seyed Ehsan Razavi1
1
Department of Electrical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2
Department of Biomedical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Article Info ABSTRACT
Article history:
Received Jan 23, 2024
Revised Sep 17, 2024
Accepted Sep 30, 2024
One of the most frequently used techniques for removing background noise
from electroencephalogram (EEG) data is adaptive noise cancellation (ANC).
Nonetheless, there exist two primary disadvantages associated with the
adaptive noise reduction of EEG signals: the adaptive filter, which is supposed
to be an approximation of contaminated noise, lacks the reference signal. The
mean squared error (MSE) criterion is frequently employed to achieve this
goal in adaptive filters. The MSE criterion, which only considers second-order
errors, cannot be used since neither the EEG signal nor the EOG artifact are
Gaussian. In this work, we employ an ANC system, deriving an estimate of
EOG noise with a discrete wavelet transform (DWT) and input this signal into
the reference of the ANC system. The entropy-based error metric is used to
reduce the error signal instead of the MSE. Results from computer simulations
demonstrate that the suggested system outperforms competing methods with
respect to root-mean-square-error, signal-to-noise ratio, and coherence
measurements.
Keywords:
Adaptive noise cancellation
Discrete wavelet transform
Error entropy
Information theory
Mean squared error
Noise reduction
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ali Akbar Khazaei
Department of Electrical Engineering, Mashhad Branch, Islamic Azad University
Mashhad, Iran
Email: khazaei@mshdiau.ac.ir
1. INTRODUCTION
Electroencephalogram (EEG) signal is referred to as measurements of electrical activity of the brain,
which is performed by electrodes placed over the scalp. Blinking or moving the head while recording the EEG
signal can lead to contamination of the signal with the electrooculogram (EOG) artifact. In many applications
used in EEG, like the brain-computer interface (BCI), the existence of artifacts within the EEG signal
diminishes the efficiency of the system [1]. Therefore, the elimination of artifacts is crucial in EEG signal
analysis.
Regression-based techniques find applications in two distinct domains, time and frequency [2], [3],
for omitting EOG artifact of EEG signal, which is recorded for likely provoked studies. In these methods, we
can use EEG data which is graded for different causes for obtaining the mean coefficients of transmission
within each EEG channel and EOG. However, within the process, the mean transfer coefficients for removing
EOG from real-time EEG signals is insufficient because EOG and EEG signals exhibit dynamic characteristics.
Hence, the necessity for adaptive filters arises in order to monitor the dynamic alterations in the signal [4].
The utilization of adaptive noise cancellation (ANC) in biomedical signals is extensive [5]–[8].
Nevertheless, these methods typically presuppose the availability of a referenced signal for ANC. An
alternative approach employs an adaptive noise reduction method with self-contained component analysis [9].

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This involves the application of independent component analysis (ICA) on EEG signals proximate to the eye
(F_p1 or F_p2) to derive active noise cancellation basis signals. It should be noted that this method can be
applied solely to multiple-electrode EEG signal analysis so, as e result may not suitable for portable devices.
The local singular spectrum analysis (SSA) method [10], [11] has found application in the elimination
of high-level EOG artifacts from single-channel EEG signals [12], [13]. Through the proposed method, vectors
of feature are generated through sorting of delayed signals, followed by clustering using the K-means algorithm
[14]. Additionally, in the process of singular value decomposition, we calculate the eigenvectors and eigenvalues
of the covariance matrix for each category. The minimum description length (MDL) metric [15] quantifies the
data necessary for estimating EOG signal, considering the dimension of signal subcategory or the number of
eigenvectors. It's important to emphasize that achieving an accurate estimate of the signal subcategory requires
creating sufficient separation among the eigenvalues that define EEG and EOG signals [10].
Effectiveness of the local SSA approach primarily lies in its capability to clean frontal EEG signals
from EOG interference, in situations characterized by a substantial rise in EOG amplitude within the EEG. In
contrast, EEG signals are typically most reliable at channels C3 and C4 [10], and due to the spatial separation
between the electrodes and the eye, there isn't a substantial magnitude contrast among the eigenvalues
presenting EEG and EOG signals. Consequently, MDL criterion may fall short in accurately estimating the
true dimension for the signal subcategory, leading to residual EOG artifacts in the denoised EEG signal.
An adaptive line enhancer (ALE) was employed for separating the electrocardiogram (ECG) and
electromyogram (EMG) based on the principles of SSA [16]. In this approach, the ALE is designed to
exclusively eliminate the interference signal by utilizing the cyclic nature of the artifact and its delayed version,
with the delay determined according to the periodicity of the corrupted signal. Nonetheless, given that EEG
and EOG signals are inherently dynamic, the presented approach demonstrates limited effectiveness in the
elimination of EOG artifacts from EEG signals.
Combination of discrete wavelet transform (DWT), and ANC has been used to cut out EOG artifact
from EEG signals [17]. Through the method, the DWT is applied to the EEG signal to obtain the EOG basis
signal, then the EOG artifact is dynamically deleted from the EEG signal. It is quite clear that the type of
wavelet function and figure of disintegration levels are important for a good estimate of the reference signal.
The efficiency of this method primarily relies on estimation of the reference signal.
The majority of algorithms employed for error reduction in adaptive filters rely on the mean squared
error (MSE) measure. However, it's important to note that the MSE criterion is primarily suitable for Gaussian
and stationary signals as it solely takes into account the mean and variance of the error distribution. This
criterion may not yield an optimal response for signals that exhibit non-Gaussian characteristics or contain
significant information in their higher-order statistics [3].
If the probability density function (PDF) of the error is non-Gaussian, then an appropriate cost
function for the adaptive filter must be used. Erdogmus and Principe [18] have used the error entropy criterion
in a non-linear adaptive system. So far, many algorithms like minimum error entropy with stochastic
information gradient (MEE-SIG) [19], minimum error entropy with self adjusting step-size (MEE-SAS) [20],
and normalized minimum error entropy (NMEE) [21], have been presented based on this criterion. When the
goal of adaptation is to remove uncertainty from the error signal as much as feasible, the error entropy criterion
is preferable to the MSE criterion [3].
Algorithms that operate on the principle of error entropy tend to exhibit high resilience against
outliers, non-Gaussian, and non-stationary noise sources. Consequently, these algorithms prove to be
particularly well-suited for effectively eliminating EOG artifacts from EEG signals, as both the EEG signal
and EOG artifact exhibit characteristics that are neither Gaussian nor stationary. Also, the entropy-based error
criterion considers the higher-order statistical conduct of the systems and signals [3].
In the proposed approach, we introduce the DWT-MEE algorithm for removing EOG artifacts from
EEG signals. Conventional least mean squares (LMS) algorithm may not possess the optimal capability to
accurately track EOG artifacts due to their non-Gaussian characteristics. Furthermore, minimum error entropy
(MEE) method represents a substantial improvement over the LMS algorithm, primarily because it constrains
error entropy rather than solely focusing on mean and variance considerations [3].
In the suggested approach, an estimation of the EOG interference is derived as the basis signal through
the application of DWT on the EEG signal contaminated by artifacts. The signal is given to the ANC reference
input. Since this EOG artifact is not regenerated well [22], the explicit diminution of this predicted signal from
the EEG signal does not result in removal of all of the EOG elements from the corrupted EEG signal. To
eliminate any remaining traces of EOG artifact, DWT is united with MEE. Finally, the MEE-based ANC
accomplishes the removal of the EOG artifact through continuous adaptation of filter coefficients.
The structure of ANC, DWT, and the entropy-based error metric are elaborated upon in the second
part of this study. Detailed description about the proposed method is provided in section 3. The analysis of
simulations is provided in section 4. Finally, the conclusion is in section 5.

Int J Artif Intell ISSN: 2252-8938 
Electroencephalogram denoising using discrete wavelet transform and adaptive … (Hashem Abdolahniya)
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2. METHOD
In this section, the proposed method for EEG signal noise cancelation has been introduced. In this
section, the structure of the adaptive noise cancelation is introduced and input-output signals are specified.
Then, the weight updating algorithm for adaptive filter, based on the error entropy minimization is introduced
that called MEE algorithm. Also, the mathematical equations of updating the weights are expressed. After that,
the DWT transformation and its mathematical relationships are examined. Finally, the structure of the proposed
method named DWT-ANC-MEE and how it works will be described.
2.1. Adaptive noise cancellation
The primary elements of ANC consist of blocks responsible for weight updates and filtering, as
illustrated in Figure 1. Various algorithms, such as LMS, recursive least squares (RLS), or MEE, can be
employed to update the weights. In our proposed approach, we opt for MEE owing to its exceptional capability
to effectively track non-Gaussian and non-stationary noise, while also leveraging higher-degree statistical
analysis. Using the presented method, the filter coefficients reach their optimum values with a reduced number
of iterations in comparison to alternative techniques [3].
Figure 1. Overview of ANC configuration
2.2. Minimum error entropy method
The measure of average data content within a specific data arrangement is commonly referred to as
the concept of entropy. Indeed, MSE represents a specific instance of entropy, as MSE exclusively deals with
the second-order statistics of the error PDF, whereas entropy encompasses the entirety of the PDF of the error
distribution. In fact, when entropy is minimized, all the moments of error distribution are minimized, not just
the second moment. Therefore, the entropy criterion can be chosen as a better alternative to MSE. In this study,
we employ the following extended definitions of entropy to offer versatility within a parametric set, with
Shannon's concepts serving as the specific situation when the parameter 'a' equals 1. The Renyi entropy of 'e,'
with order 'a,' is defined as (1) [18]:
Hα(e) =
1
1−α
log ∫ fα (e) de (1)
Here, f(e) represents error random variable’s PDF. In the present research, we have opted for Second-order
Renyi’s entropy denoted as 𝛼 = 2, which is expressed as (2):
H2(e) = − log ∫ f2 (e) de (2)
As evident from (1) and (2), the computation of entropy necessitates knowledge of the PDF of a
random variable. Consequently, in this study, the Parzen windowing method is employed for the estimation of
this PDF. The Parzen windowing technique is represented by (3):
f
̂(e) =
1
N
∑ kσ
N
i=1 (e − e(i)) (3)
Here, k(e) represents the Kernel function, σ denotes the Kernel size, and {{e(1), e(2), … , e(N)} represents the
error data points. While various kernel functions can be employed for the Parzen window, in this study, we
utilize a multidimensional Gaussian distribution function with a radially symmetrical variance of σ2
.
Consequently, the estimation of Renyi's quadratic entropy for error samples is calculated as follows:

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H
̂2(e) = − log ∫ (
1
N
∑ Gσ(e − e(i))
N
i=1 )2
de
+∞
−∞
H
̂2(e) = − log
1
N2 ∫ (∑ ∑ Gσ(e − e(j))Gσ(e − e(i))
N
j=1 ) de
N
i=1
+∞
−∞
H
̂2(e) = − log
1
N2 (∑ ∑ ∫ Gσ(e − e(j))Gσ(e − e(i))
+∞
−∞
N
j=1 ) de
N
i=1 (4)
H
̂2(e) = − log (
1
N2
∑ ∑ Gσ√2(e(j) − e(i))
N
j=1
N
i=1 ) (5)
In (4) and (5), Gσ(. ) represents the kernel function with a Gaussian core. The term enclosed within the
logarithmic function, often referred to as information potential (IP), is presented as (6):
V
̂2(e) =
1
N2
∑ ∑ Gσ√2(e(j) − e(i))
N
j=1
N
i=1 (6)
Hence, the entropy equation for the error random variable can be expressed as (7):
H
̂2(e) = − log ( V
̂2(e)) (7)
As the logarithm function is a monotonic transformation, it may be deduced that the lowest entropy corresponds
to the highest IP. Then, the cost function J(e) for the MEE criterion can be defined as (8):
JMEE(e) = V(e)
w
max
(8)
In online training scenarios, the stochastic information gradient (SIG) can be employed to estimate
the IP, as depicted in (9). As a common result, the stochastic gradient of information is derived, computed as
the summation of L new samples at time n.
V
̂2(e(n)) ≈
1
L
∑ Gσ√2(e(n) − e(i))
n−1
i=n−L (9)
By implementing the MEE-SIG method for coefficient updates, as described in [21], the aim is to reduce the
signal e(n) entropy within the adaptive filter illustrated in Figure 1.
𝑊(𝑛 + 1) = 𝑊(𝑛) + 𝜇. ∇𝑉(𝑒(𝑛)) (10)
In this context, the gradient is calculated as (11):
∇𝑉(𝑒(𝑛)) =
1
2𝜎2𝐿
∑ 𝐺𝜎√2(𝑒(𝑛) − 𝑒(𝑖))
𝑛−1
𝑖=𝑛−𝐿 {𝑒(𝑛) − 𝑒(𝑖)} {𝑋(𝑛) − 𝑋(𝑖)} (11)
2.3. Discrete wavelet transform
The wavelet analysis is among the most powerful tools for capturing both temporal and spectral
information within a signal. It excels in providing enhanced temporal resolution for segments with higher
frequencies and improved frequency resolution for components with lower frequencies. The signal, denoted as
y(t), could be expressed through a wavelet analysis as outlined in [23].
𝑦(𝑡) = ∑ 𝑎𝑀𝑚 ϕ𝑀𝑚
𝑚 + ∑ ∑ 𝑑𝑙𝑚𝜑𝑙𝑚(𝑡)
𝑚
𝑀
𝑙−1 (12)
Where 𝑎𝑀𝑚 is the proximate and 𝑑𝑙𝑚 are the coefficients detail. To reconstruct the primary signal y(t) at
presented decomposition level (e.g., M), the process is as (13):
𝑦(𝑡) = 𝐴𝑀(𝑡) + ∑ 𝐷𝑙(𝑡)
𝑀
𝑙=1 (13)
2.4. Proposed discrete wavelet transform-adaptive noise cancellation-minimum error entropy technique
Figure 2 depicts the process of EOG artifact cancellation using the DWT-MEE technique. The
corrupted EEG signal 𝑦(𝑛), obtained as the sum of the EEG signal 𝑠(𝑛) and a constant ratio (𝑝) of the EOG
signal 𝑟1(𝑛), is the input. To generate the reference signal required for the ANC, the DWT is employed on the
signal vector 𝑦 = [𝑦(1), 𝑦(2), … , 𝑦(𝑁)], which is held in a buffer of size n. The subsequent subsections will
detail the primary steps involved in creating the source signal for ANC.

773
Figure 2. DWT-MEE method block diagram
2.4.1. Extraction the source signal for adaptive noise cancellation using discrete wavelet transform
In this study, we have conducted a multi-level wavelet decomposition using DWT up to level 8.
This process enables the precise identification of wavelet coefficients associated with the EOG artifact,
taking into consideration the effective factors such as eye movement (0-7 Hz) and blinking (8-13 Hz)
(level 8: 0.25-0.5 Hz, level 7: 0.5-1 Hz, level 6: 1-2 Hz, level 5: 2-4 Hz, level 4: 4-8 Hz, level 3: 8-16 Hz, level
2: 16-32 Hz, and level 1: 32-64 Hz). Thresholding has been applied to the detail coefficients from level 8 down
to level 3 for EOG denoising. Decomposing the EEG signal to level 3 provides the essential ocular-related
wavelet coefficients necessary for noise reduction, as indicated in [24]. To obtain the reference signal, we apply
the DWT to the noisy signal, resulting in the EOG signal vector, denoted as 𝑟2, which serves as the primary
input for the ANC system.
2.4.2. Discrete wavelet transform-minimum error entropy
In the DWT-MEE method proposed, the ANC system takes as its initial and source inputs the
contaminated EEG signal vector (𝑦) and the elicited EOG signal vector (𝑟2,), respectively. By renewing the
coefficients of the filter using the MEE method, an estimate of the signal 𝑟̂1(𝑛) is obtained from the signal 𝑟2.
To obtain a clean EEG signal, in each block of data, the estimated signal 𝑟̂1(𝑛) is deducted from the corrupted
EEG signal y(n). The time required to derive the corrected EEG signal for each block matches the combined
computing durations of the serial-to-parallel converter, the DWT process, parallel-to-serial converter, and the
ANC operation. This method is particularly advantageous as the computational time to obtain the accurate
EEG signal is shorter than the sampling interval of the EEG signal.
3. RESULTS AND DISCUSSION
Deleting the EOG artifact from live EEG data allows researchers to test how well the proposed
approach works. Even more so at frontal sites, the EEG signal might be contaminated by EOG artifact. Careful
instructions can reduce the severity of the problem, but they rarely eliminate it entirely. Figure 3 shows a
sample of experimental signals obtained from BCI competition dataset that used in the expriments. As can be
seen the original EEG data shows in Figure 3(a). Also Figure 3(b) displays EOG artifact and Figure 3(c)
represent signal contaminated with noise. A clean EEG signal, EOG artifact, and an EEG signal corrupted with
EOG artifact can be seen in this figure. Also, in order to see the frequency spectrum of the clean signal, the
EOG artifact and the corrupted EEG signal with the EOG artifact, their power spectral density (PSD) are shown
in Figures 4(a) to 4(c) respectively. In this figure, the horizontal axis represents frequency and the vertical axis
represents PSD.
Multiple EEG signal recordings covering a wide variety of wave shapes have been used to validate the
proposed technique in the 2008 BCI competition dataset [25]. We have employed real-world EOG signal
artifacts from a database utilized in the BCI competition in order to assess the enhancement performance within
a dynamic environment. BCI datasets typically consist of three EOG channels and twenty-two EEG monopolar
channels. All signals were bandpass filtered between 0.5 and 100 Hz and captured at 250 Hz. Additionally, a
notch filter with a frequency of 50 Hz was used on this data set. Nine healthy volunteers were used to collect
EEG data over the course of two sessions. Each session begins with three tasks: one with eyes closed, one with
eyes open, and one including eye movements [25]. Compared to Croft's intended strategy [26], the electrode
placement for the EOG signals in this data set is unique. All EEG signals were also filtered with a low-pass filter
set at 45 Hz for this study. To avoid confounding the EEG readings, a low-pass filter set at 20 Hz is used to the
EOG readings in this method [26]. Figure 3(b) depicts an EOG artifact, which we used as the model's reference
signal x(n). The input to an adaptive filter is an EEG signal that has been contaminated by EOG artifacts. In the

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suggested technique, the PSD, coherence examination and signal-to-noise ratio (SNR) were used to assess the
quality of noisy EEG signals. The equation for enhancing the quality of an EEG signal is as (14):
𝑆𝑁𝑅 = 10 log10
𝑉𝑎𝑟(𝑒𝑒𝑔𝑐(𝑛))
𝑉𝑎𝑟(𝑒𝑒𝑔𝑐(𝑛)−𝑒𝑒𝑔
̂ 𝑡(𝑛))
(14)
The variance operator is denoted by var, and the real 𝑒𝑒𝑔𝑐(𝑛) signal, and the true EEG signal 𝑒𝑒𝑔
̂ 𝑡(𝑛) which
is estimated using the adaptive filter, respectively.
samples
(a)
samples
(b)
(c)
Figure 3. A sample of experimental signals from BCI competition dataset (a) EEG without noise,
(b) EOG artifact, and (c) signal contaminated with noise
Frequency (Hz)
(a)
Frequency (Hz)
(b)
(c)
Figure 4. PSD of experimental signals (a) EEG signal, (b) EOG, and (c) EEG contaminated by EOG

775
Since the EEG signal is not constant, this article employs Welch's approach to estimate the power
component using a Hamming-window of 1024 data points of 1 second duration with 50% overlap. We assessed
spectral coherence between denoised and clean EEG signals as a numerical measurement for the proposed
efficient denoising approach at the target frequency. The following is the consistency equation between the
𝑒𝑒𝑔
̂ 𝑡(𝑓) signal and the 𝑒𝑒𝑔𝑐(𝑓) signal.
𝐶𝑜ℎ(𝑓) =
|𝑃𝑒𝑒𝑔𝑐𝑒𝑒𝑔
̂𝑡
(𝑓)|
2
𝑃𝑒𝑒𝑔𝑐
(𝑓) 𝑃𝑒𝑒𝑔
̂𝑡
(𝑓)
(15)
The cross-spectral density between signals 𝑒𝑒𝑔𝑐(𝑓) and 𝑒𝑒𝑔
̂ 𝑡(𝑓) is represented by 𝑃𝑒𝑒𝑔𝑐𝑒𝑒𝑔
̂ 𝑡
(𝑓), where
𝑃𝑒𝑒𝑔𝑐
(𝑓) and 𝑃𝑒𝑒𝑔
̂ 𝑡
(𝑓) are the corresponding auto spectra.
Table 1 displays the results of a comparison between LMS-based and MEE-based algorithms applied
to five separate recordings of electroencephalographic (EEG) activity. As can be seen in this table the SNR of
the de-noised EEG signal averages at 3.32 dB when applying the LMS method and rises to 4.72 dB when
utilizing mee method. These results show the significant superiority of the MEE algorithm over the LMS
algorithm in terms of improving the SNR rate.
Table 1. Comparing the SNR between the LMS and the MEE methods
SNR out (dB) RMSE
DWT_LMS DWT_MEE DWT_LMS DWT_MEE
Subject 1 0.42 1.69 0.10 0.09
Subject 2 2.60 2.98 0.15 0.14
Subject 3 5.87 6.52 0.11 0.10
Subject 4 2.27 5.25 0.30 0.21
Subject 5 5.44 7.16 0.15 0.12
Average 3.32 4.72 0.16 0.13
The findings illustrate that the MEE approach surpasses the LMS algorithm in effectively removing
the EOG artifact. Our calculations in this paper are based on a dataset of 2000 EEG samples, employing a step
size coefficient (μ) of 0.01 in LMS and a value of 1 for MEE. Additionally shown are the outcomes of a
simulated EEG with a signal-to-noise ratio of -2 dB due to contamination. Figure 5 displays the effectiveness
of the MEE and LMS algorithms in removing noise. Figure 5(a) shows denoised signal using DWT-LMS
algorithm and Figure 5(b) shows denoised signal using DWT-MEE method. In addition, Figure 6 showcases
the PSD both prior to and following filtration using the LMS and MEE algorithms. Figure 6(a) shows PSD of
contaminated EEG. Also Figure 6(b) represent filtered PSD with LMS, and Figure 6(c) display filtered PSD
using MEE method.
Samples
(a)
(b)
Figure 5. Denoising results: (a) denoised using DWT-LMS algorithm, and (b) denoised using
DWT-MEE method
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-2
-1
0
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a
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-2
-1
0
1
2
b
Amplitude
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 ISSN: 2252-8938
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Frequency (Hz)
(a)
Frequency (Hz)
(b)
(c)
Figure 6. PSD before and after filtration (a) PSD of contaminated EEG, (b) filtered PSD with LMS, and
(c) filtered PSD using MEE method
Figure 7 represents the progression of MEE and LMS techniques as well as the disparities in the the
reconstructed and clean signal. Figure 7(a) displays the outcomes of EOG removal with the LMS algorithm, and
Figure 7(b) shows the outcomes of EOG removal with the MEE method. The results show that the MEE algorithm
outperforms the LMS algorithm at reducing steady-state error. Also coherence of the original and reconstructed
signals employing ANC filter with LMS, and MEE algorithm are displayed in Figures 8(a) and 8(b), respectively.
Substituting the error entropy criterion for the MSE criterion demonstrates a general improvement in coherence
values, particularly in the lower frequency range.
In conclusion, we utilize the relative root mean square error (RRMSE) criterion to assess and compare
the effectiveness of this approach against other recently introduced methods. RRMSE is calculated as (16):
𝑅𝑅𝑀𝑆𝐸 =
𝑅𝑀𝑆(𝑆−𝑆
̂)
𝑅𝑀𝑆(𝑆)
(16)
In the (16), the root mean square of the original signal denoted as RMS(S), while RMS(𝑆
̂) denotes the root
mean square of cleaned EEG signals.
Figure 9 illustrates an effectiveness comparison of proposed approach using SSA-ANC and the
method from [27], DWT-ANC, with regard to the RRMSE metric. In this figure, the horizontal axis shows the
SNR and the vertical axis shows the RRMSE in percent. As can be seen in the figure, the method presented in
this work in all SNRs has a lower RRMSE than other methods, which indicates the better performance of the
method presented in all SNRs. For example, in SNR equal to 2, the RRMSE criterion for the proposed
DWT-ANS-CMEE method is equal to 46, which is 41% superior to the SSA-ANC-RLS algorithm. This shows
the effectiveness of the proposed method in conditions with high noise power (low SNRs).
samples
(a) (b)
Figure 7. The error signals after denoising: (a) the outcomes of EOG removal with the LMS algorithm, and
(b) the outcomes of EOG removal with the MEE method

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Frequency (Hz)
(a)
(b)
Figure 8. The consistency between the primary and recreated signals: (a) outcomes of EOG removal using
the LMS method and (b) outcomes of EOG removal using the MEE method
Figure 9. Evaluation of the SSA-ANC and DWT-ANC methods in relation to RRMSE
It is worth mentioning that this research has investigated simultaneously all the criteria of RRMSE
criteria, output SNR after filtering, error amplitude curve after denoising operation, PSD and coherence
analyses. While previous studies have not investigated the simultaneous effect of all these criteria, and previous
studies have investigated some of these criteria. we found that the output SNR measure were correlated with
the RMSE measure. The proposed method in this study tends to have an extremely low ratio of RMSE
compared to other previous studies which confirms the reduction of filtration error in the proposed method.
Our study suggests that lower RMSE is not associated with poor performance in output SNR. The proposed
method may benefit from RMSE without adversely on output SNR of denoised signal. in this paper a
comprehensive study in EEG signal noise removal with DWT-ANC-MEE algorithm explored. However,
further and in-depth studies may be needed to confirm its effectiveness on more samples of EEG signals. In
0 5 10 15 20 25 30 35 40
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0.5
1
a
Coherence
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0.5
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b
Coherence
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0.5
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 ISSN: 2252-8938
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this study, it was shown that denoising algorithms based on error entropy are more efficient than traditional
methods for denoising the EEG signal. Future studies may investigate more up-to-date adaptive algorithms for
denoising the EEG signal. Recent observations in EEG signal denoising studies show that adaptive filtering
methods can provide aproperiate performance in EEG signal denoising with low error rates. Our findings
provide conclusive evidence that proper updating of the adaptive filter coefficients using the MEE algorithm
can lead to better performance of the ANC system. The results obtained in this work confirm this issue.
4. CONCLUSION
This paper introduces a hybrid approach employing both DWT and ANC for the extraction of EOG
artifacts from EEG signals. The methodology leverages DWT to derive an approximation of the EOG signal,
which serves as the basis input for the adaptive filter. Furthermore, use of the MEE algorithm is advocated for
noise reduction within the adaptive system, particularly for non-Gaussian signals, where it demonstrates
superior suitability compared to MSE-based algorithms. A performance evaluation of the proposed system
against MSE-based algorithms reveals its superior performance in metrics such as RRMSE, SNR of output,
and coherence analyses.
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BIOGRAPHIES OF AUTHORS
Hashem Abdolahniya is a lecturer in the Department of Electrical Engineering at
Azad University of Mashhad. He is currently a Ph.D. student at Mashhad Azad University in
Mashhad. His research interests include signal processing, medical image processing, noise
removal, adaptive filters, and image compression. He can be contacted at email:
hashem.abdolahniya@yahoo.com.
Dr. Ali Akbar Khazaei was born in Mashhad, Iran on May 09, 1969. He received
his B.S. degree in electronics engineering from Ferdowsi University of Mashhad in 1992, his
M.Sc. in communication engineering from Tarbiat Modares University, Tehran, Iran, in 1996
and his Ph.D. in communication engineering from Islamic Azad University, Science and
Research Branch, Tehran, Iran, in 2012 respectively. From 2008 to 2012 he was with the
Satellite Communication Group, Iran Telecommunication Research Center (ITRC), Tehran,
Iran. He has been with the Department of Electrical Engineering of Islamic Azad University,
Mashhad, Iran, as an Assistant Professor from 2012 to now. He can be contacted at email:
khazaei@mshdiau.ac.ir.
Dr. Mahdi Azarnoosh is an Assistant Professor of medical engineering at Islamic
Azad University, Mashhad Branch. He received his doctorate in the field of
medical/bioelectrical engineering at Tehran Islamic Azad University of Science and Research.
His research interests include: acquisition, processing, and analysis of vital signals. He can be
contacted at email: m_azarnoosh@mshdiau.ac.ir.
Dr. Seyed Ehsan Razavi received his B.Sc. in electrical engineering (2006), M.Sc.
in control engineering (2008), and Ph.D. in control engineering (2014). Currently, he is an
Associate Professor at the Department of Electrical Engineering, Islamic Azad University of
Mashhad. His current research interests are control theory, biomedical engineering,
nanoparticles, image processing and hyperthermia. He has authored several book chapters and
published more than 30 papers in journals and conferences. He can be contacted at email:
ehsanrazavi@mshdiau.ac.ir.

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