# An ECG Signal De-Noising Approach Based on Wavelet Energy and Sub-Band Smoothing Filter
## 4 Results and Discussion
### Quantitative Comparison  
In this paper, the performance of de-noising signal is analyzed by SNR, MSE and PRD, and the quality of reconstructed signal is studied. The SNR can be divided into output SNR and improved SNR. The output SNR formula is defined as follows:  
\[SNR_{out}=10 lg\left[\frac{\sum_{i=1}^{L}x^{2}\left(i\right)}{\sum_{i=1}^{L} \left(s\left(i\right)-x\left(i\right)\right)^{2}}\right] \tag{21}\]  
Figure 8: The de-noising results after adding 15 dB WGN to the synthetic ECG: (**a**) The original signal. (**b**) The signal after adding WGN. (**c–f**) De-noised signals using wavelet soft threshold, EMD, EMD soft threshold, proposed method. Figure 7: The de-noising results after adding EMG noise to No. 115 record of the MIT-BIH database: (**a**) The original signal. (**b**) The signal after adding EMG noise. (**c–f**) De-noised signals using wavelet soft threshold, EMD, EMD soft threshold, proposed method. The formula of improved SNR is defined as follows:  
\[SNR_{imp}=10 lg\left[\frac{\sum_{i=1}^{L}\left(y\left(i\right)-x\left(i\right) \right)^{2}}{\sum_{i=1}^{L}\left(s\left(i\right)-x\left(i\right)\right)^{2}}\right] \tag{22}\]  
The MSE is used to measure the deviation between the original signal and the de-noised signal. The formula is given as follows:  
\[MSE=\frac{1}{L}\sum_{i=1}^{L}\left(x\left(i\right)-s\left(i\right)\right)^{2} \tag{23}\]  
The percent root mean square difference is defined as follows:  
\[PRD=\sqrt{\frac{\sum_{i=1}^{L}\left(x\left(i\right)-s\left(i\right)\right)^{2} }{\sum_{i=1}^{L}x^{2}\left(i\right)}}\times 100 \tag{24}\]  
where \(x\left(i\right)\) is the original signals, \(y\left(i\right)\) is the signal after adding noise, \(s\left(i\right)\) is the final de-noised and smoothed signal, and \(L\) is the signal length. The experimental comparison shows that the de-noising effect is better when the wavelet basis of DB family is used for wavelet transform. In order to compare with the traditional wavelet-based ECG de-noising scheme, we tested the traditional wavelet-based ECG de-noising scheme (WT), multi-adaptive bionic wavelet transform (MABWT) and our proposed method in MIT-BIH arrhythmia database [28]. Table 2 (Soft Threshold) and Table 3 (Hard Threshold) respectively show the improved SNR results of ECG signals de-noising with WGN (5 dB) added. It can be seen that compared with the traditional wavelet-based de-noising scheme and multi-adaptive bionic wavelet transform, the method proposed in this paper has a higher SNR improvement whether it uses soft threshold or hard threshold. \begin{table}
\begin{tabular}{c c c c} \hline
**ECG Signals** & **WT** & **MABWT** & **Proposed Method** \\ \hline
100 & 6.5 & 7.8 & 7.1 \\
103 & 6.1 & 7.7 & 7.9 \\
105 & 6.0 & 8.1 & 9.4 \\
115 & 6.6 & 7.8 & 8.0 \\
215 & 6.1 & 7.4 & 8.6 \\
113 & 6.2 & 7.9 & 7.7 \\
117 & 6.0 & 7.9 & 8.0 \\
119 & 5.8 & 7.6 & 7.8 \\
122 & 5.6 & 6 Tables 4-6 shows the results of quantitative comparison with several other methods after adding different noise to the 115 th record for denoising, namely,the parallel-type fractional zero-phase filtering (FZP), zero-phase Butterworth filter (BZP) [29], the Riemann Liouville (RL) integrator [30] and the proposed method. We select record 115 because the record is relatively clean and suitable for observing the de-noising effect of the algorithm on different types of noise. Table 4 gives a comparison of power line interference (50 Hz), with an amplitude of 0.15 mv. In Table 5, EMG interference is compared and these noises are simulated using random noise. Table 6 gives the comparison results in the case of synthetic interference. These noises are simulated using WGN with an input signal-to-noise ratio of 15 dB. Tables 4-6 shows that the proposed algorithm provides better de-noising results and has smaller deviation compared with the original ECG signal. The ability of the algorithm in tracking signal and removing noise is proved. Table 7 and Figure 10 show the comparison of the proposed method with EMD soft threshold [4], wavelet soft threshold [12] and EMD-wavelet [13].