Variation of Wavelet Entropy inElectroencephalogram Signal during

Neurofeedback Training

MAJID GHOSHUNI,1 MOHAMMAD FIROOZABADI,2 MOHAMMAD ALI KHALILZADEH3

AND MOHAMMAD REZA HASHEMI GOLPAYEGANI41Department of Biomedical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;

2Medical Physics Department, Tarbiat Modares University, Tehran, Iran; 3Department of

Biomedical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran; and 4Department of

Biomedical Engineering, Amir Kabir University of Technology, Tehran, Iran

Received November 15, 2011; revised March 30, 2012; accepted August 9, 2012

Neurofeedback training (NFT) has an important role in improvement of cognitive functions in both clinical and

healthy individuals. In this study, variation of wavelet entropy during low beta NFTwas investigated. To investigate

the effect of low beta NFTon wavelet entropy, correlation between the change in low beta activity and the change in

wavelet entropy was computed. The results revealed that there is a highly significant negative correlation between

the change in low beta activity and wavelet entropy. The given outcome suggests that enhancing low beta activity

through NFT associated with decrements in wavelet entropy. Furthermore, we discuss a new implementation of

NFT, based on wavelet entropy for future research. � 2012 Wiley Periodicals, Inc. Complexity 00: 000–000, 2012

Key Words: low beta activity; neurofeedback; wavelet entropy

1. INTRODUCTION

Neurofeedback is the use of instruments to mirror the

brain’s electrical activity which the individual is not

normally aware and would be brought under volun-

tary control. In a neurofeedback session, as the person

alters his/her own mental state a change in the amplitude

of various brain wave frequencies is observed. This change

is detected by the individual as it is displayed on the

monitor screen; therefore, he/she makes an attempt to al-

ter brain patterns to achieve a predefined goal. In this

manner, the client learns to self-regulate their brain

patterns [1].

Neurofeedback training (NFT) has been applied for

treatment of substance abuse [2], attention deficit

hyperactivity disorder (ADHD) [3], epilepsy[4], and

autism [5]. In addition, NFT has been used in healthy

individuals to enhance cognitive performance, such as

improving attention [6,7], memory [8,9], and mood [10].

Correspondence to: Majid Ghoshuni, Department of Bio-

medical Engineering, Science and Research Branch, Islamic

Azad University, Tehran, Iran (e-mail: ghoshuni@gmail.com)

Q 2012 Wiley Periodicals, Inc., Vol. 00, No. 00 C O M P L E X I T Y 1

DOI 10.1002/cplx.21423Published online in Wiley Online Library(wileyonlinelibrary.com)

On the other hand, beta activity is associated with

active, busy, or anxious thinking and active concentra-

tion [11]. Enhancement of beta activity through NFT

has been widely used to treat patients with ADHD [3].

Moreover, beta NFT has been used to improve cognitive

function [12] and memory performance [8] in healthy

subjects.

There is some evidence that electroencephalogram

(EEG) signal has a dynamical complexity and nonlinear

methods must be applied for EEG analysis [13]. There are

few studies exploring the variation of dynamical com-

plexity in EEG signal during NFT. Fell et al. [14] investi-

gated the variation of spectral entropy during auditory

alpha NFT in healthy subjects. They found that alpha

power amplification was significantly correlated with a

decrease in spectral entropy within the alpha range. In

another study, Zhao et al. [15] investigated the effect of

NFT on approximate entropy in six patients with intracta-

ble epilepsy. The patients were trained to enhance senso-

rimotor rhythm (SMR) activity (12–15Hz) and decrease

theta (4–9 Hz) activity through neurofeedback. The

results showed that after the end of neurofeedback ses-

sions, there appeared an increase in SMR/theta compared

to before the NFT. The approximate entropy also

increased from before to after NFT simultaneously. How-

ever, in Zhao et al. [15] study, correlation between the

change in SMR/theta and the change in approximate en-

tropy was not investigated. It is possible that the change

in approximate entropy be the result of NFT, but it can-

not be ruled out that this change is caused by some other

factors.

Although in previous studies [14,15], the variation of

approximate entropy and spectral entropy in EEG signal

during the NFT has been investigated, there are some lim-

itations as follows: approximate entropy is defined in time

domain and is sensitive to variations in embedding dimen-

sion, number of data points, and noise level [16]. Further-

more, long time recordings are required for estimation of

approximate entropy [15,16]. On the other hand, spectral

entropy is based on power spectrum analysis [17], which

needs the stationarity assumption of brain electrical signal,

whereas EEG signal is highly nonstationary signal. Further-

more, spectral entropy only measures sharpening of the

frequency distribution within a particular frequency range

[17,18].

In contrast, wavelet entropy is defined according to a

time–frequency representation of the signal as provided

by the wavelet transform and it does not need any statio-

narity assumptions of EEG signal [19]. In addition, short

duration EEG signal is sufficient for wavelet entropy

estimation, and any other parameter was not needed for

estimation of wavelet entropy [19]. These advantages of

wavelet entropy make it appropriate for using in NFT

applications.

In this article, the variation of wavelet entropy in EEG

signal during low beta NFT was investigated. Our hypothe-

sis is that low beta NFT can affect the wavelet entropy of

EEG signal, and, therefore, wavelet entropy can be imple-

mented for NFT in future researches.

2. MATERIALS AND METHODS

2.1. ParticipantsTen undergraduate students (five males and five females,

aged 22–23-years old: Mean 5 22.30, SD 5 0.48) partici-

pated in this study. All subjects had no history of neuro-

logical or psychiatric disorders. The experiment was

approved by Mashhad University of Medical Sciences

Ethics Committee.

2.2. Neurofeedback TrainingIn this study, we used individual low beta frequency band

which spanned about 3 Hz and was immediately above

the alpha range. Additionally, occipital (Oz) and frontal

(Fz) electrodes were used here for NFT. Local synchrony in

occipital and frontal brain regions can be monitored in

this way [8].

NFT was conducted over a period of 4 weeks, with each

subject receiving two training sessions per week. The sub-

jects underwent training to enhance their individual low

beta activity on Oz and Fz electrodes simultaneously. EEG

was recorded and the individual low beta activity was

extracted and fed back, using an audio–visual online feed-

back loop in the form of a video game. The threshold was

set manually to the low beta activity which would be sur-

passed 60% of the time during the preceding 30-sec win-

dow. The low beta activity was calculated on a moving av-

erage window of 30 sec that was updated continuously.

Moreover, when the participant had an eye movement or

other muscle activity which caused EEG fluctuations, the

feedback was suspended according to artifact rejection

thresholds.

2.3. EEG RecordingTo extract individual low beta frequency band, all the

subjects participated in an EEG recording session before

the first neurofeedback session. In the EEG recording ses-

sion, a 2-minute EEG baseline with open eyes and a 2-

minute EEG baseline with closed eyes were recorded

from each subject. The EEG signal was recorded from

two electrodes attached to the scalp of the subject, one

on the Oz position and the other on Fz position, accord-

ing to the international 10–20 system. A ground electrode

was placed on FCz (between Fz and Cz electrodes) and

both earlobes were connected together using two 1 kX

resistors and then the middle of the resistors (average of

two earlobes) was used as the reference electrode. The

2 C O M P L E X I T Y Q 2012 Wiley Periodicals, Inc.DOI 10.1002/cplx

electrode impedances were also kept below 10 kX. For

EEG recording, the FlexComp (Thought Technology Ltd.)

differential amplifier was used. Acquired signal was

amplified and filtered with an analog elliptic band pass

filter ranging from 0.1 to 64 Hz. Furthermore, a 50-Hz

notch filter was enabled. Sampling frequency was 256 Hz

and A to D precision was 14 bit.

2.4. ProcedureThe subjects first participated in an EEG recording session

through which their individual low beta frequency band

was extracted. On the next level, they completed eight

NFT sessions over a 4-week period. Each NFT session con-

sisted of three 5-minute segments of NFT, while each seg-

ment was followed by a 2-minute ‘‘blink break.’’

2.5. EEG Analysis

2.5.1. Power Spectrum Density

The power spectrum density (PSD) of EEG baselines was

estimated from each subject to extract individual low beta

band. The PSD of EEG signals was approximated by means

of Welch’s averaged modified periodogram [20] with 2-sec

epochs (0.5-Hz frequency resolution), 50% overlap, and a

Hanning window. The PSD of EEG baselines in both open

and closed-eye conditions were computed. Then, individ-

ual alpha peak (IAP) frequency was calculated for each

subject according to the formula:

IAP ¼

Pf 2

f¼f 1

Pðf Þ3f

Pf 2

f¼f 1

Pðf Þ(1)

where P(f) is the PSD estimate of closed eyes EEG baseline

at frequency f and the index of summation is in the range

of f1–f2. The frequency window f1–f2 was the range of

alpha peak which was determined individually for each

subject. For determining the frequency window f1–f2, the

PSD of EEG baseline was plotted with open and closed

eyes together. By visual inspection, the bandwidth of the

frequency window f1–f2 was determined. f1 marks the be-

ginning of the ‘‘ascent’’ and f2 the end of the ‘‘descent’’ of

the alpha peak for closed eyes PSD, compared to open

eyes PSD. After computing IAP for each subject, we

defined IAP-2 Hz to IAP12 Hz as an individual alpha fre-

quency band and IAP12 Hz to IAP15 Hz as an individual

low beta frequency band. These definitions were used

because in traditional EEG frequency bands, low beta (12–

15 Hz) frequency band mostly lies after alpha (8–12 Hz)

frequency band.

Amplitude of EEG signal recorded in a particular sub-

ject depends on many factors including neurophysiologi-

cal, anatomical, and physical properties of the brain, sur-

rounding tissues, and electrode impedances [21]. These

parameters vary from one subject to another and resulted

in large variations in absolute PSD of EEG signal. To com-

pensate for these variations, relative EEG power was com-

puted and used in subsequent analysis. Relative power

was computed based on the following formula:

Prðf Þ ¼ Paðf ÞPPaðfiÞ

(2)

where Pr(f) is a relative power at frequency f, Pa(f) is an

absolute PSD at the same frequency, andP

is a sum of

the power over the all bandwidth.

2.5.2. Wavelet Entropy

Wavelet entropy is defined according to a time–frequency

representation of the signal as provided by the wavelet

transform [19]. In this study, a multiresolution decomposi-

tion [22] was performed by applying a discrete wavelet

transform (DWT). Quadratic B-Spline function was used as

a mother wavelet. In the previous studies [23–26], this

function has been used for short duration brain electrical

signals.

The algorithm, which was used for estimating wavelet

entropy, closely resembled the algorithm used in the study

of Rosso et al. [19]. The EEG signal of three 5-minute seg-

ments in each NFT session was decomposed into five lev-

els by DWT. Six sets of coefficients (including residual

scale) within the following frequency bands were obtained;

64–128 Hz (j 5 21), 32–64 Hz (j 5 22), 16–32 Hz (j 5

23), 8–16 Hz (j 5 24), 4–8 Hz (j 5 25), and the residues

in the 0.1–4 Hz (r 5 25). To simplify the notation, we rep-

resent the coefficients of the residue by j 5 26 instead of

r 5 25. The coefficients within 64–128 Hz (j 5 21) has

been removed in the subsequent analysis, because the

coefficients within this range have been filtered and do

not have any useful information. After decomposing the

EEG signal, the coefficients of each resolution level j were

divided in nonoverlapping temporal windows of length

equal to 1 sec of the EEG signal. The mean wavelet energy

at resolution level j for each time window i was computed

according to the formula:

EðiÞj ¼ 1

Nj

Xi:Nj

k¼ði�1ÞNjþ1

CjðkÞ�� ��2 i ¼ 1; 2; . . . ;NT (3)

where Cj represents wavelet coefficients at resolution level

j, Nj represents the number of wavelet coefficients at reso-

Q 2012 Wiley Periodicals, Inc. C O M P L E X I T Y 3

DOI 10.1002/cplx

lution level j included in the time interval i, and NT repre-

sents the number of time windows. Then, the total mean

energy at this time window would be:

EðiÞtot ¼

X

j<0

EðiÞj (4)

The time evolution of the relative wavelet energy was

computed as:

pðiÞj ¼

EðiÞj

EðiÞtot

(5)

and the time evolution of wavelet entropy would be given

by:

WEðiÞ ¼ �X

j<0

pðiÞj lnðpðiÞ

j Þ (6)

To obtain a quantifier for the whole time period, the tem-

poral average was evaluated. The temporal average of

wavelet entropy was given by:

WEh i ¼ 1

NT

XNT

i¼1

WEðiÞ (7)

3. RESULTSThe mean IAP for all subjects was obtained 9.89 6 0.46

Hz. Therefore, the mean value of individual low beta fre-

quency band was 11.89–14.89 Hz. To see whether NFT has

been successful in increasing low beta band amplitudes,

the average relative low beta power of three 5-minute

segments in the first and last neurofeedback sessions were

computed. Two-way repeated measures analysis of var-

iance (ANOVA) was performed using two within subject

factors: ‘‘Electrode’’ (two levels: Fz/Oz) and ‘‘Session’’ (two

levels: first neurofeedback session/last neurofeedback ses-

sion). Results showed a significant main effect of Electrode

(F(1,29) 5 10.33, P < 0.01), Session (F(1,29) 5 5.87, P <

0.05) and Electrode 3 Session interaction (F(1,29) 5 5.75,

P < 0.05). In Figure 1, relative low beta power of the first

and last neurofeedback sessions on Fz and Oz electrodes

was shown. As can be seen from Figure 1, relative low

beta power was increased from the first to the last session

especially on Fz electrode.

In the next level, the effect of low beta enhancement

in Fz electrode on variation of wavelet entropy was

investigated. We used paired sample t-test to compare

the temporal average of wavelet entropy of three 5-mi-

nute segments between the first and last neurofeedback

session on Fz electrode. The results showed a signifi-

cant decrease in the temporal average of wavelet en-

tropy on Fz electrode from the first to the last neuro-

feedback session (t(29) 5 4.23, P < 0.001). In Figure 2,

the temporal average of wavelet entropy of the first

and last neurofeedback session on Fz electrode was

shown. Furthermore, to see whether wavelet entropy

decrement was related to low beta enhancing neuro-

feedback or other factors affect it, correlation between

the change in relative low beta power and the change

in temporal average of wavelet entropy was computed.

The results showed a highly significant negative

FIGURE 1

Relative low beta power of the first and last neurofeedbacksession on Fz and Oz electrodes. Error bars represent standarderrors, double asterisks indicate significance level of P < 0.01.

FIGURE 2

Temporal average of wavelet entropy of the first and last neuro-feedback session on Fz electrode. Error bars represent standarderrors, triple asterisks indicate significance level of P < 0.001.

4 C O M P L E X I T Y Q 2012 Wiley Periodicals, Inc.DOI 10.1002/cplx

correlation between the change in relative low beta

power and the change in the temporal average of wave-

let entropy on Fz electrode, r 5 20.72, P < 0.00001

(two-tailed; Figure 3).

Moreover, the training effect over the course of

eight NFT sessions on Fz electrode was investigated. In

Figure 4, the changes in relative low beta power

[Figure 4(A)] and temporal average of wavelet entropy

[Figure 4(B)] on Fz electrode for eight neurofeedback

sessions were plotted. As can be seen in Figure 4, rela-

tive low beta power increased across eight neurofeed-

back sessions, whereas the temporal average of wavelet

entropy decreased. Furthermore, a one-way repeated

measure ANOVA with Session representing a single fac-

tor with eight levels was performed for relative low

beta power and the temporal average of wavelet en-

tropy separately. The results showed a significant main

effect of Session F(7,203) 5 5.54, P < 0.001 for relative

low beta power and a significant main effect of Session

F(7,203) 5 5.92, P < 0.001 for the temporal average of

wavelet entropy.

4. DISCUSSIONIn this study, we showed that the increase in relative low

beta power through NFT was highly significantly correlated

with a decrease in wavelet entropy. Wavelet entropy also

decreased across low beta enhancing neurofeedback ses-

sions [Figure 4(B)].

According to the high correlation between the change

in relative low beta power and the change in wavelet en-

tropy, we suggest a new implementation of neurofeedback

based on wavelet entropy. Applying wavelet entropy for

NFT has the following advantages. First, the time evolution

of frequency patterns can be followed with an optimal

time–frequency resolution [27]. Second, the only input

needed for wavelet entropy estimation is the EEG signal,

and any other parameter was not needed [19]. Third,

wavelet entropy can be estimated from 1-sec brain signal

or shorter [19]. Therefore, the delay time for feedback of

wavelet entropy to the subjects becomes short. Fourth, the

EEG signal is decomposed into several levels by DWT [22].

Thus, to remove high frequency artifacts from the EEG sig-

nal, we can directly remove a set of coefficients in the

level corresponding to the high EEG frequency band;

therefore, no low-pass filter is needed for NFT.

Consequently, in future studies, the neurofeedback

based on wavelet entropy can be implemented, and the

effect of wavelet entropy NFT on patients with various

mental disorders and healthy individuals can be

investigated.

FIGURE 3

Significant negative correlation between the change in relativelow beta power and the change in temporal average of waveletentropy on Fz electrode.

FIGURE 4

The changes of relative low beta power (A) and the temporal aver-age of wavelet entropy (B) over the course of eight neurofeedbacksessions on Fz electrode. Error bars depict standard error of themean.

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