The wearable device has been widely studied in recent years. In the related researches, it is essential to monitor the cardiac and physical activities in users with congestive heart issues at home. The electrocardiogram (ECG) is an important signal in monitoring the cardiac activity. A Holter ECG device is frequently applied to record long-term ECG signals and helps to find arrhythmic heartbeats within twenty-four hours [1
]. Another apparatus is called an Event Recorder that is able to record one-minute ECG signals when a user feels uncomfortable on the chest region [2
]. Currently, the commercial Holter ECG apparatus or Event Recorder only record the ECG signals, and is lacking in the real time analysis of the ECG signals. Moreover, the user has been encouraged to neither do any severe exercises nor take a shower, because these two kinds of devices do not have a high ingress protection rating.
An ECG patch is a wearable device, which not only records ECG signal, but also shows some cardiac information on the smart phone in real time [3
]. However, its function for the arrhythmic beat detection is not better than the ECG Holter analysis. The problem is that the ECG patch is used under a body-motion condition, which is easily coupled with some noise, like motion artifact and electromyogram (EMG). Therefore, how to cancel the noise in real time would help to develop the applications of ECG patch. In the measurement of ECG signals, it is vulnerable to various noises and interferences, such as the EMG, 50 or 60Hz power line noise (PLn), baseline drift and measurement noise and so on. In [4
], it was found that for complex QRS wave of a standard ECG signal, its power is within the frequencies lower than 30Hz, and its peak power is within the range between 4 Hz and 12 Hz. Generally, the high frequencies in the PLn and EMG noise are able to cover up the characteristic of an ECG signal such that the QRS wave group cannot be located accurately [5
]. Besides, it is known that ECG signals affected by noises will lead to erroneous diagnosis by physicians. Therefore, it is crucial to remove the PLn and EMG noise in the ECG monitoring and clinical diagnosis.
Traditionally, ECG noise cancellation methods applied a low-pass filter [6
] to remove the high-frequency components in noise while a high-pass filter and adaptive filter are used to rid of low-frequency vibrations, such as baseline drift [7
] and respiratory interference [9
]. Since most of the noises in ECG signals are distributed at the high-frequency components, and the traditional low-pass filters cannot solve the problem that signal and noise co-exist within the same bandwidth. Augustyniak [10
] used the time-frequency transform to rescale the ECG coupled with different noises and then eliminated the noises to enhance the signal noise ratio. Rundo et al. [11
] applied the bio-inspired nonlinear system to cancel the noise in an ECG signal and then to align the ECG and pulse wave. Some ECG denoising methods employ the frequency decomposition technique, such as the wavelet transform [12
], the empirical mode decomposition (EMD) [13
] and the ensemble empirical mode decomposition (EEMD) [14
]. The EMD is a pre-processing algorithm of Hilbert-Huang Transform (HHT) which was introduced by Huang et al. [15
] with a capability to perform time-frequency transformation for non-linear and non-stationary signals. In recent years, the EMD has been widely applied in biomedical signal processing, such as ECG [13
], EMG [16
] and blood pressure waves [17
The basic idea for ECG noise cancellation consists of two main stages. First, an ECG signal is decomposed by the EMD into a set of IMFs through which the noisy IMFs are discriminated and discarded. Second, the ECG is reconstructed by the retained IMFs. By this doing, the noise in the ECG signal is reduced or cancelled. To be successful in the EMD-based noise cancellation, a fundamental problem is to estimate the noise energy appropriately in each IMF. In addition, the problem of mode mixing occurs during the EMD decomposition. The problem of mode mixing comes from either an IMF mingled with signals of different scales or other IMF appeared in the combination of other components. To overcome the mode mixing problem in the EMD, the EEMD [18
] was proposed with an additive white noise into the ECG signal. The EEMD is able to reduce the mode mixing effect on the next IMF scale. The EEMD has been widely applied in noise cancellation. For example, Chang et al. presented a scheme to cancel the white noise in ECG signals where noisy low-order IMFs were removed by a predefined threshold [12
]. Jenitta et al. used the zero-crossing ratio of adjacent IMFs to discriminate noisy IMFs by its noise energy [19
]. Yannis et al. proposed a scheme according to the energy of the first-order IMF through which noise cancellation was performed among IMFs for ECG signals [20
]. Kumaravel et al. presented a genetic algorithm to determine the noise energy threshold in the first-order IMF for the PLn cancellation in ECG signals [21
The methods described above generally deal with white noise and the PLn only. Besides, All of them estimates the noise energy in the first-order IMF. However, only considering the noise energy in the first-order IMF might not be appropriate especially when the signal energy of the related IMF is high. This will lead to over-cancellation and result in distortion in the reconstructed ECG signal. Consequently, this paper considers noise energies in every IMFs through the noise magnitude spectrum.
As we know, very few approaches to ECG noise cancellation are based on noise magnitude spectrum. In this paper, two-stage discrimination scheme is proposed to estimate and cancel the PLn and EMG noise in ECG signals according to IMFs’ noise magnitude spectrum where the EMD, the EEMD and the grey spectral noise estimation (GSNE) are employed. In the first stage, the EMD decomposes the input ECG signal into IMFs. Then the GSNE is used to estimate noise in IMFs and calculate the related noise energies through its noise magnitude spectrum. By a user-defined threshold, noisy IMFs are identified and put into the second stage. In the second stage, the noisy IMFs are reconstructed and decomposed by the EEMD. Then the IMFs are rechecked in a similar manner to the first stage. If an IMF is considered as noisy, it is discarded. The procedure is repeated for each IMF. At last, the ECG signal is reconstructed with all retained IMF components. To evaluate the performance, a noise energy ratio in dB () is employed in this paper.
This paper is organized as follows. Section 2
describes the ECG signals with additive noise and the ECG signal decomposition algorithms, the EMD and the EEMD. Section 3
introduces the GSNE based on the first-order grey model of one variable, GM(1,1) model [22
], and then describes how the GSNE is applied to ECG noise cancellation. Next, the proposed GSNC scheme is introduced in Section 4
. In Section 5
, the proposed GSNC scheme is justified by forty-three datasets from the MIT-BIH database [24
]. Discussions about the EMD, the EEMD and the proposed GSNC are given in Section 6
. Finally, the conclusion is given in Section 7
The EMD acts like a filter-bank and has no strict bandwidth restriction with the IMFs. The frequency range of each IMF is adaptive, depending on the original signal content. Generally, the bandwidths of the PLn and EMG noise are assumed in the ranges 59.5–60.5 Hz and 100–500 Hz, respectively. Thus the PLn is considered as a lower frequency noise while the EMG noise is considered as a medium and higher frequency noise. Note that the noise energy is mainly distributed in the low order IMF components after the EMD. Because of different bandwidths, the performance for the EMG noise is better than that for the PLn in the EMD scheme for ECG noise cancellation. As shown in Table 3
and Table 4
, the average
for the PLn is 0.10 dB and 3.52 dB for the EMG noise.
Compared with the EMD, the EEMD has more concentrated band-limit IMF components. With the iterative EMD computation, the average of IMF with the same order yielded a sharper band transition than a single EMD-derived IMF, that is, the transition band overlap between adjacent IMFs is narrower than the EMD result. In other words, with the same filter specification the EEMD acts like a higher-order filter while the EMD works like a lower-order filter. Consequently, the performance of the EEMD scheme is better than the EMD scheme, as shown in Table 3
and Table 4
where the average
for PLn and the EMG noise by the EEMD scheme are 2.20 dB and 3.85 dB, respectively. They are higher than the corresponding
by the EMD scheme. However, the EEMD pays the price of computational complexity, that is, it takes more time to cancel the ECG noise. This hinders the realization in an ECG patch if only the EEMD is applied in the ECG noise cancellation. On contrarily, the proposed GSNC scheme decomposes the input ECG signal by the EMD in the first stage. When
, the proposed GSNC scheme stops further decomposition. This makes the proposed GSNC scheme possible to be embedded in an ECG patch. Moreover, the proposed GSNC scheme employs two-stage discrimination for noisy IMFs while the conventional EMD and EEMD schemes use one-stage discrimination. Thus, the proposed GSNC scheme is expected to have better performance since suspicious IMFs in the first stage can be rechecked in the second stage to avoid mistakes while the one-stage EMD and EEMD scheme fails to.
], Liu et al. showed that the energy of a lower frequency in the EMG noise is found in the first-order IMF component. In other words, the EMD or the EEMD like a filter-bank is able to decompose different intrinsic components in an ECG signal. This is also true for the PLn case. The results. shown in Table 1
and Table 2
have justified the idea where the IMFs for clean and noisy ECG signals can be discriminated in most cases. Another evidence is in Table 3
and Table 4
. The results indicate that the average
are positive. That is, intrinsic noise and additive noise can be dealt and cancelled in the EMD, the EEMD and the proposed GSNC schemes. Among the three schemes, the proposed GSNC scheme has the best performance with the average
3.34 dB for the PLn and 6.14 dB for the EMG noise, as shown in Table 3
and Table 4
, respectively. It implies that the proposed GSNC scheme is able to estimate the noise appropriately and the two-stage discrimination can relieve the over-cancellation problem which generally happens in the one-stage discrimination.
In order to show the proposed GSNC scheme does not affect the morphology of arrhythmic beat, the arrhythmic ECG dataset mitdb/210 is given as an example where two premature ventricular contraction (PVC) beats are within the duration. The denoised results for the PLn and EMG noise (
) by the proposed GSNC scheme are given in Figure 8
. As shown in Figure 8
b,c, the proposed GSNC scheme is able to retain subtle signs in the denoised ECG signal, when compared with Figure 8