Discrete Wavelet Soft Threshold Denoise Processing for ECG Signal

Qi P Haibing1, P LiuP Xiongfei2, Pan Chao P

1P

(1.School of Electric and Electronic Information Engineering, Huangshi Institute of Technology, Huangshi 435003, China 2. School of Physics Science and Technology, Central South University of Technology, Changsha 410083, China )

qhbcs@yahoo.com.cn

Abstract—Electrocardiogram (ECG) is an essential method for the clinical diagnosis of cardiovascular diseases. The weak biomedical signal buried in all kinds of noise will result in the useful information lost or false information on the wavelet decomposition. According to the characteristics of ECG signal and wavelet transform, a discrete wavelet soft threshold denoise processing method is used to remove the interference of electrical power frequency, electromyography and baseline drift, and a favorable effect is obtained through the simulation.

Keywords-ECG signal; discrete wavelet; soft threshold; denoise processing

I. INTRODUCTION ECG (electrocardiogram) is an important method for the

diagnosis of cardiovascular diseases. In the process of ECG signal detection, some special signal or some characteristic parameters of a signal are utilized to denote the measured physical parameters [1]. However, the detected biomedical is too weak to directly provide the useful information, it need to be extracted from the noise interference with signal processing methods.

Usually, the frequency spectrum range of normal ECG signal is 0.01Hz to 100Hz and 90% spectral energy of the signal focus on 0.25Hz to 35Hz. These interferences may cover up the subtle variable of original ECG waveform, and result in the total ECG is difficult to identify and diagnosis. There are several kinds of noise in the process of collecting ECG signal mainly including electrical power frequency interference, which is caused by the electric power system. The interference frequency is composed of 50Hz and its harmonic frequency. Next is electromyography, which is caused by irregular frequency interference generated by the activity muscle tension, usually including the single fiber muscle signal (500 ~10 KHz), drive unit signals (5~10Hz), and surface muscle signal (0.01 ~ 500Hz). The last is baseline drift, which is induced by the undesirable contact of electrode, the changes of skin resistance, breathing and the other movement of body, the frequency range of this interference is 0.05Hz to 2Hz and is close to the frequency component Q wave and ST segment of ECG signal. As the Q wave and ST segment detection is the main judgment of myocardial infarction and myocardial ischemia, the noise of baseline drift should be reduced, the American heart association (AHA) suggested that the high-pass filter cutoff frequency to remove the composition of ECG dc should not

exceed 0.05Hz, and less than 0.8Hz to keep the linear phase [2]. According to the characteristics of ECG signal and wavelet transform, a discrete wavelet soft threshold denoise processing method is used to remove the interference of electrical power frequency, electromyography and baseline drift in this paper.

II. PRINCIPLE OF WAVELET SOFT THRESHOLD DENOISE PROCESSING

A. The basic principle of wavelet denoise processing Wavelet transform, especially the orthogonal wavelet

transform has the character of strong decorrelation, which can make the transformed signal energy concentrate in the larger wavelet coefficients in the wavelet domain, and the energy of noise distribute in the whole wavelet domain. Therefore, the wavelet coefficients of useful signal is larger than that of noise through the wavelet decomposition, and then the wavelet transform can be regarded as a filter processing.

For an actual one-dimensional input signal, it can be expressed as

1,....,2,1),()()( −=⋅+= niieifis σ (1) where f(i) is the useful signal, s(i) is the input signal, σ is the RMS (Root-Mean-Square) of the noise, e(i) is the noise.

When the noise e(i) is Gaussian white noise and high frequency, the useful signal is low frequency and smoothly signal, an one-dimensional signal denoise processing can be generally divided into three steps [3], the first step is wavelet decomposition. It need to choose a wavelet and make sure the decomposition hierarchy N of the wavelet. The second is threshold quantification of wavelet coefficients. The quantitative disposal on the each high frequency coefficient from the first layer to N layers is processed by selecting a threshold value. The last step is reconstruction of one-dimensional wavelet. Based on the wavelet decomposed N-th low-frequency coefficients and high-frequency coefficients from the first layer to N layers, one dimensional wavelet can be reconstructed.

How to select the threshold and how to quantize the threshold of quantification is the key factor in the above three steps, they are directly related to ECG signal denoise processing quality.

2010 International Conference on Intelligent Computation Technology and Automation

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DOI 10.1109/ICICTA.2010.404

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(a) Original input signal (b) hard threshold (c) soft threshold

Fig.1 The method of threshold processing B. The method of threshold processing

Too small threshold will result in the useful information signal loss. However, excessive threshold will not obtain the satisfying filter effect. There are four kinds of rules to select threshold such as VisuShrink rule, RigrSURE rule, HeurSURE rule and RiskShrink rule. A threshold method “Wavelet Shrinkage” to select the appropriate threshold proposed by Donoho and Johnstone [4] in 1992 now has extensive influence.

There are two methods in the threshold of quantification including hard and soft threshold. One is the method of hard threshold, comparing the absolute wavelet coefficients with the threshold, the absolute coefficient which is smaller than the given threshold is enforced as zero, and the absolute coefficient which is larger than the given threshold is maintained as the original value. The mathematical expression is

⎪⎩

⎪⎨⎧

<

≥=

0)(,0

)(,)()(

if

thififif (2)

where f(i) is the wavelet coefficient, th is the given threshold.

The other is the method of soft threshold, on the basis of hard threshold, the absolute coefficient which is smaller than the threshold in the soft threshold is treated as that of in the hard threshold. However, the absolute coefficient which is larger than the given threshold is taken as the difference of coefficient and the threshold [5, 6]. The corresponding mathematical expression is

sgn( ( ))* ( ) , ( )( )

0 , ( ) 0

f i f i th f i thf i

f i

⎧ − ≥⎪= ⎨<⎪⎩

(3) where sgn(i) is the Signum function. Normally, the method of hard threshold is the simplest method, but the method of soft threshold can obtain better effect, this reason is that there are discontinuous points at ±th where the absolute coefficients are set as zero for the value is less than the given threshold. However, it is continuous at the points of ±th for the soft threshold.

TFig. 2 the denoise processing with discret wavelet soft threshold method . (a) original input signal, (b) denoise processed signal, (c) residual low frequency components.

III. SIMULATION AND RESULT ANALYSIS Based on the frequency characteristics of ECG signals,

we finally choose Daubechies3 wavelet which is limited support in time domain as mother wavelet for denoise processing. Daubechies (dbN) wavelet [7] has no explicit expression, but the square mode of the conversion function is very obvious, assuming that there

∑−

=

+−=1

0

1)(N

k

kkNk yCyP (4)

And then Daubechies wavelet is defined as

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

2sin

2cos)( 222

0ωωω Pm

N

(5)

where kNkC +−1 is the binomial coefficient,

∑−

=

−=12

00 2

1)(N

k

ikk ehm ωω (6)

Some characteristics of Daubechies are short support in time domain, that is limited length of ( )tψ and its high order original moment

( )∫ == Npdttt p ~0,0ψ (7)

Obviously, the length of ( )tψ is longer with the bigger

value of N. Also, the function of ( )ωψ has N zero points in frequency domain at 0=ω . And it's orthogonal with its integer displacement,

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Fig. 3 Discrete wavelet decomposition for different scales. (a)~(h) are the component for 8-scale to 1-scale, respectively.

Fig.4 denoise processing based on Haar wavelet

( ) ( )∫ =− kdtktt δψψ (8)

The wavelet function Ψ(t) of Daubechies wavelet can be solved by the so-called "scaling function". Scaling function is a low function and limited length, the range of its support domain is 0 to 2N-1.

The T104 from 6:10 to 6:20 of Arrhythmia database in MIT-BIH is used as experimental data. The interferences of the samples are mainly Electromyography interference and Power frequency interference as shown in Fig.2.T the reconstruction of the filtering signal is shown in TFig.2 (b)

TA 8-scale wavelet decomposition is performed on Daubechies3. Fig.3 shows the components in various scales, Thorizontal coordinate isT for signal amplitude, HTTlongitudinal coordinateTH Tis for sampling points. The energy of ECG signal distributed mainly in the scale of T

22 to 42 . Generally, the component of 12 scale is the high frequency induced by electromyography noise, which can be removed directly by filtering. The distributed range of power frequency interference is mainly between 22 and 32 , which can not be filtered completely for its frequency spectrum is superposition to that of ECG, it should adopt softT threshold method and the value of threshold T )ln(21 nT σ= . The component of 42 to 82 scale should be all reserved. The rest components of ECG signal are mainly low-frequency corresponding to the baseline drift, which can be set to zero.T

In order to compare the effect of denoise processing with different wavelet function and different threshold. Fig. 4 show that the filtering effect of Haar wavelet function is relative to the above processing method. The denoise ECG signal of Haar wavelet function have an obvious sawtooth waveform as shown in Fig.4 (a), not only the signal is

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distorted but also the filtering effect is not better. The in-appropriate threshold may also bring about serious distortion. Fig.4 (b) shows that some useful signal is also removed on denoise processing the Electromyography for the different threshold. The un-continuity of signal brought out by the nonlinear processing method of hard threshold will result in the limited filtering effect and no smooth as shown in Fig.4(c).

IV. CONCLUSIONS The ECG signal is denoise processed by the wavelet

decomposition method on the basis of wavelet analysis. It can be concluded that this method have a good and comprehensive filtering effect for the ECG signal interfered by electrical power frequency, electromyography and baseline drift. The introduce of wavelet decomposition method can distinguish the different frequency distribution of the useful and noise signal, and pick up the useful signal clearly from the actual input signal. With regard to the overlapping frequency range of useful signal and the noise signal, which the traditional filtering method can not solve

this problem. We can minimize the useful signal loss through wavelet decomposition. The better optimization method of selecting the threshold and wavelet function is the further research field for better effect of filter.

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