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2011 4th International Conference on Biomedical Engineering and Informatics (BMEI)

Extracting of the Ultrasound Fetal Heart Rate Signal Based on Wavelet Packet Mix Node Threshold

Mingquan Wang, Wanli Zhu, Shi Zhang, Zijing Wang

College of Information Science and Engineering Northeastern University

Shenyang, China wangmingquan@ise.neu.edu.cn

Abstract—Clinically, fetal heart rate, to a certain extent, reflects the health of the fetus. Therefore, how to extract the fetal heart rate signals in ultrasound fetal heart rate signal processing has been a key issue. In this paper, a new wavelet packet mix node threshold (WPMNT) denoising algorithm based on the maximum wavelet packet energy entropy is proposed. Moreover, based on the threshold given by the new algorithm, a new wavelet packet threshold function is constructed for ultrasound fetal heart rate signal denoising. Experimental results show that this algorithm gives better signal noise ratio (SNR) gains and mean square error (MSE) performance than traditional algorithms.

Keywords-FHR; wavelet packet; energy entropy; threshold function

I. INTRODUCTION Ultrasound Doppler fetal heart rate monitor is a kind of

important equipment for fetus monitoring. It can detect the fetal earliest stages hypoxia by showing the fetal heart rate. The information of fetal heart rate is obtained by measurement of the ultrasound doppler signal shift caused by the movement of the fetus heart [1]. Because of the influence of fetal and maternal breathing, blood flowing, and other factors, ultrasound doppler fetal heart rate signal takes along with a lot of noise, so it is necessary to extract ultrasound doppler fetal heart rate signal from the ultrasonic echo signal. The traditional filter method can filter out the higher than cutoff frequency of the signal, but cannot extract fetal heart rate signal.

In recent years, the wavelet transform has been considered as the powerful technique for time-scale analysis of a signal and has shown potential in biomedical signal processing [2]. Wavelet threshold denoising methods have attracted much attention because of its excellent multi-scale decomposition and multi-resolution analysis capacities in time and frequency domain. Now, the wavelet hard threshold and the soft threshold proposed by D.L.Donoho and I.M.Johnstone [3, 4] are also widely used in signal denoising. However, the hard threshold function has discontinuous threshold point, and the soft threshold function exists a constant deviation, which influences fetal heart rate signal accurately detecting. So the traditional hard threshold and soft threshold are not suitable for extracting of the ultrasound fetal heart rate signal.

This paper proposes the wavelet packet mix node threshold algorithm based on the maximum wavelet packet energy

entropy to calculate threshold in the wavelet packet space, and a new threshold function. Experimental results show that this algorithm gives better signal noise ratio (SNR) gains and mean square error (MSE) performance than the traditional hard threshold and soft threshold wavelet and wavelet packet.

The remaining sections of this paper are organized as follows: section II gives a detailed description of the proposed extracting algorithm in detail; experimental results and analysis are presented in the section III; finally, section IV concludes the whole paper.

II. ALGORITHM

A. Wavelet Packet and Wavelet Packet Transform

In )(2 RL space, the wavelet transform of a signal )(tf at the scale a and position translation τ is computed by the following equation:

.)()(1

)(),(),(

*

,

dta

ttfa

ttfaWT

R

af

∫−=

=

τψ

ψτ τ (1)

It is obvious that the Wavelet Transform has a shortcoming, which is its poor high frequency resolution [5]. Because the high frequency of ultrasound fetal heart rate signal also has some active principle, the wavelet transform for extracting of the ultrasound fetal heart rate signal can not perform very well. However, the wavelet packet further subdivides the high frequency and the low frequency, it can generate the higher spectral in extracting of the ultrasound fetal heart rate signal. The wavelet packet function can be obtained by

),2(2)(

),2(2)(

112

02

ktht

ktht

Zknkn

Zknkn

−=

−=

∑

∑

∈−

∈

ωω

ωω (2)

where )(tω is usually called mother wavelet function; kh0

and kh1 are the filters' coefficients defined by the following equations:

750

).2(2)(

),2(2)(

1

0

ktht

ktht

kk

kk

−=

−=

∑

∑

ψψ

φφ (3)

The iteration relations between the j level and the 1+j level are

.

,

,)2(1

12,1

,)2(0

2,1

∑

∑

−++

−+

=

=

l

njlkl

njk

l

njlkl

njk

dhd

dhd (4)

In this paper, we utilize a suitable threshold for coefficients of the last level wavelet packet.

B. Wavelet Packet Energy Entropy (WPEE) In the information theory, the entropy shows uncertainty of

measurement. For the coefficients of each wavelet packet node signal, they can be averagely divided into T parts whose length is W. Sometimes we select the W is as power of 2. Every part can be considered independent each other. The total energy of each part is defined as:

,1

2,, ∑

==

W

inink dE (5)

where n is the nth node in the last level; k stands that the current part is the kth part of the nth node. Continue to divide each part into 2 segments. So each segment's energy can be defined as:

).2,1(2

1

2,,,,, ==∑

=jdE

W

inkjinkj

(6)

The proportion of each segment relative to their part is

.,

,,,,

nk

nkjnkj E

Ep = (7)

Equation (7) represents the wavelet packet energy distribution in the relevant wavelet packet node. It is obvious that the nkjp ,, will change with the signal changing.

According to the definition of Shannon entropy, the wavelet packet energy entropy can be defined as follows:

.1log,,

101

,,, ⎟⎟⎠

⎞⎜⎜⎝

⎛=∑

= nkj

V

jnkjnk p

pEntropy (8)

When the energy of signal is distributed with equal probability, the energy entropy obtains maximum.

C. Wavelet Packet Mix Node Threshold (WPMNT) The traditional wavelet packet threshold which is proposed

by D. L. Donoho is expressed as follows [6]:

,)ln(2 NLthr σ= (9)

where NL is the sampling length of signal; σ, which is equal

to 6745.0)( idMedian , is the standard deviation of zero-mean

additive white Gaussian noise estimated by Donoho and Johnston. (.)Median is a medium function. id is the high frequency coefficients of first level. This traditional wavelet packet threshold is the global threshold. It is obvious that the global threshold is not suitable for extracting of the ultrasound fetal heart rate signal. According to the entropy theory, the signal's entropy will get the maximum value when the probability distribution is same. We can consider that the noise's probability distribution is same in different frequency range. However, the probability distribution of ultrasound fetal heart rate signal is not same. For the different part described in section 2.2, if the main component is noise, the corresponding entropy should be maximum value. So we choose the middle value of the wavelet packet coefficients in the maximum value part as this node's standard deviation, recorded as nσ . According to (9), we can get the node threshold

)ln(2 NLthr nn σ= . As we all know, in wavelet packet low frequency coefficients, the ultrasound fetal heart rate signal is the main part, but the noise is secondary. We assume that the number of the last level of the wavelet packet transform is N (N is power of 2). According to the above analysis, we propose a new rule to choose the node threshold. The rule is shown as follows:

1) Calculate the traditional standard deviation σ . 2) Calculate the traditional wavelet packet threshold thr. 3) Calculate the new standard deviation nσ . 4) Calculate the new wavelet packet threshold nthr . 5) When 2

Nn > ( N is the sum number of the last level

wavelet packet nodes), choose nthr as the nth node threshold

nodenthr , . When 2Nn ≤ , choose the minimum value between

thr and nthr as the nth node threshold nodenthr , . So we call this new threshold wavelet packet mix node

threshold (WPMNT).

D. New Wavelet Packet Threshold Function Denoising Wavelet packet threshold denoising can be implemented

through the following three steps:

1) Decompose the wavelet packet of the signal )(kf , and archive the wavelet packet coefficients.

751

2) Dispose the wavelet packet coefficients using the wavelet packet threshold. Two ways are usually used, which are hard threshold function and soft threshold function:

.0 ,

,,, thrd

thrddd

ni

ninini <

≥

⎩⎨⎧

= (10)

.0

))((

,

,,,, thrd

thrdthrddsigndni

nininini <

≥

⎪⎩

⎪⎨⎧ −= (11)

Equation (10) is the hard threshold function and (11) is the soft threshold function. (.)sign in the (11) is a sign function, which is equal to 1, 0 or -1 when x is respectively greater than 0 or equal to 0 or less than 0.

3) Reconstruct signal with wavelet packet inverse transformation based on new wavelet coefficients.

However, both hard threshold function and soft threshold function have disadvantages. Hard threshold function is not continuous, soft thresholding function makes the wavelet packet coefficients to be constant deviation [7].

Threshold function is very important for denoising. In this paper, a new wavelet packet threshold function is proposed as follows:

,0

*)(,

,,, thrd

thrddmdfdsignd

ni

ninini <

≥

⎪⎩

⎪⎨⎧

= (12)

in which, df is equal to threthrthrd ni *)1(*)tanh( 2, +−− ,

and dm is equal to )tanh(*1 ,*2 ,

nid

dthrthreni

++ .

The new wavelet packet threshold function is continuous just like soft threshold function. What is more, because it takes nini dd ,, = as its asymptote, it overcomes the constant deviation of the soft threshold function.

Fig. 1 shows the diagram of hard threshold function, soft threshold function and this new threshold function. The new threshold function overcomes the disadvantages of hard threshold function and soft threshold function.

III. EXPERIMENT AND ANALYSIS In order to prove the effectiveness of the new algorithm

proposed by this paper, we select the ultrasound fetal heart rate signal which is gathered from the Chinese medical university second affiliated hospital ultrasound fetal heart rate signal database and add 6db Gaussian white noise. In this paper, the software platform is MATLAB2009A. At the same time, the

quantities of SNR and MSE are introduced to judge the denoising effectiveness.

Figure 1. Diagram of hard threshold function, soft threshold function and the new threshold function

( )

( ) ( )[ ] ⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−=

∑

∑

=

=N

n

N

n

nynx

nySNR

1

2

1

2

10log10 (13)

( ) ( )[ ]∑=

−=N

nnynx

NMSE

1

21 (14)

Fig. 2 shows the results of the experiment with noisy fetal heart rate signal using wavelet hard threshold, wavelet soft threshold, wavelet packet hard threshold, wavelet packet soft threshold and the new method. All these methods' mother function select DB8 and decomposing level is 5. Table 1 lists the SNR and MSE of these five methods.

(a)

(b)

752

(c)

(d)

(e)

(f)

(g)

Figure 2. Experiment with noisy fetal rate signal: (a) the original signal, (b) the original signal with 6db Gaussian white noise, (c) wavelet hard threshold,

(d) wavelet soft threshold, (e) wavelet packet hard threshold, (f) wavelet packet soft threshold, (g) our new algorithm

Noting the experimental results, the wavelet hard threshold cannot remove noise in the signal. Also, wavelet hard threshold and wavelet soft threshold lose the useful fetal heart rate signal, which will directly impact the extracting of fetal heart rate

signal. The wavelet packet hard threshold and wavelet packet soft threshold is better than wavelet hard threshold and wavelet soft threshold, but still cannot accurately extract fetal heart rate signal. However, our new algorithm performs effectively. From the Fig. 2, we can see that the energy is mainly distributed around the useful fetal heart rate signal, which make for extracting signal. Table I shows that this algorithm gives better SNR gains and MSE performance than the hard-threshold and the soft-threshold wavelet and wavelet packet.

TABLE I. SNR AND MSE OF THE EXPERIMENT WITH NOISY FETAL RATE SIGNAL

Algorithm SNR MSE

wavelet soft 5.7240 896.3106

wavelet hard 8.9581 1887.4

wavelet packet soft 9.5904 774.8613

wavelet packet hard 11.8018 465.6855

new algorithm 12.1172 433.0562

IV. CONCLUSION In this paper, a new wavelet packet mix node threshold

denoising algorithm based on the maximum wavelet packet energy entropy is proposed. Moreover, based on the threshold given by the new algorithm, a new wavelet packet threshold function is constructed for ultrasound fetal heart rate signal denoising. Experimental results show that this algorithm gives better SNR gains and MSE performance than traditional algorithms.

REFERENCES [1] Xiao Hua, Luo Kaiqing, Zhang Zhenxi. A New Algorithm for Detecting

Fetal Heart Rate using Ultrasound Doppler signals, ULTRASONICS 2005, pp. 399-403.

[2] B. Natwong, P. Sooraksa, C. Pintavirooj, S. Bunluechokchai, W. Ussawawongaraya. Wavelet Entropy Analysis of the High Resolution ECG, IEEE Industrial Electronics and Applications, 2006, pp. 24-26.

[3] D L Donoho, De-noising by Soft-thresholding, IEEE. Trans Inform Theory, 1995, pp. 613-627.

[4] D L Donoho, I M Johnstone. Adaptive to Unknown Smoothness Via Wavelet Shrinkage, Journal of American Stat. Assoc, 1995, pp. 1200-1224.

[5] Lisha Sun, Guoliang Chang, Hongrong Tang. Wavelet Packet Entropy in the Analysis of EEG Signals, IEEE Signal Processing, 2006, pp. 16-20.

[6] Donoho, D.L., Johnston, I.M., Ideal spatial adaptive via wavelet shrinkage, Biometrika, vol.81, 1994, pp. 425–455.

[7] Zhao Xiu-min, Cao Gui-tao. A Novel De-noising Method for Heart Sound Signal Using Improved Thresholding Function in Wavelet Domain, IEEE International Conference on Future BioMedical Information Engineering, 2009, pp. 65-68.