## 5 Denoising Experiments
### Simulation Results  
We evaluate the denoising performance of our method in this section. To perform a comprehensive study of the proposed method, we consider different numbers of ECG data. We also study the performance of the BP-ADMM algorithm according to SNR and MSE in order to demonstrate its ability. The first group of ECG data in the MIT-BIH arrhythmia database is recorded in file No. 100. The data in this group of data contain little noise and abnormal heart beats. This group of ECG data is preprocessed to obtain the first length 3000 pure ECG signal \(x\) in Figure 2(a), which is linearly superimposed with the first baseline wandering noise in the BW file to obtain a noisy ECG signal \(y\) in Figure 2(c). Figure 3: Mixed ECG signal. The blue line represents the noisy signal, and the solid red line represents the signal after filtering the baseline wander noise and Gaussian white noise in Figure 4. It can be seen from the figure that after the algorithm filtering in this paper, the ECG signal that initially deviated from the baseline level returns to the baseline level, and the Gaussian white noise is effectively removed, which proves that the BP-ADMM algorithm can effectively remove baseline wander noise and Gaussian white noise. Before denoising, due to the large amount of white noise and baseline drift in the initial signal, the waveform diagram basically does not show the original characteristics of the ECG signal. However, after processing by the proposed algorithm, the waveform characteristics of pulse signals can be easily seen. In order to further verify the effect of denoising, the values of the SNR before and after denoising of the pulse signal are calculated, respectively. The calculation results are shown in Table 1.  
Table 1 is a comparison of SNR and MSE after filtering with wavelet, mean, and total variation (TV) noise reduction algorithms. In Table 1, the wavelet transform and the mean \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MIT-BIH No.** & & & **100** & **103** & **213** \\ \hline BP-ADMM & 5 dB & SNR & 14.71 & 14.86 & 13.92 \\  & & MSE & 0.003 & 0.004 & 0.024 \\  & 15 dB & SNR & 15.13 & 16.02 & 14.37 \\  & & MSE & 0.002 & 0.002 & 0.003 \\ Wavelet & 5 dB & SNR & 5.3124 & 4.85 & 7.49 \\  & & MSE & 0.0248 & 0.086 & 0.127 \\  & 15 dB & SNR & 9.7863 & 5.14 & 8.22 \\  & & MSE & 0.1002 & 0.082 & 0.107 \\ Average & 5 dB & SNR & 2.3397 & 2.3837 & 3.0389 \\  & & MSE & 0.5093 & 0.5177 & 1.1896 \\  & 15 dB & SNR & 2.3219 & 3.3011 & 3.4347 \\  & & MSE & 0.2667 & 0.3071 & 0.9611 \\ TV & 5 dB & SNR & 4.6338 & 4.8580 & 9.2792 \\  & & MSE & 0.3025 & 0.3064 & 0.2838 \\  & 15 dB & SNR & 10.7101 & 11.2702 & 12.7509 \\  & & MSE & 0.0481 & 0.0483 & 0.0706 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: (Signal-to-noise ratio) SNR and mean square error (MSE) comparison results. Figure 4: MIT-BIH no.105 denoising and reconstruction. value method are not very effective in filtering Gaussian white noise, but the TV transform shows a good denoising effect. Even so, the denoising effect of the algorithm proposed in this article is still better than the three denoising algorithms mentioned above. The data in Table 1 show that the signal-to-noise ratio after denoising has been significantly improved compared to the ratio before denoising. The larger the value of the signal-to-noise ratio, the better the denoising effect, which indicates that the algorithm in this paper can effectively suppress a variety of noises and achieve a good denoising effect. We calculate the mean SNR of the above 28 pieces of ECG data shown in Table 2. Among them, the mean SNR of BP-ADMM is 7.129 which is the biggest among the four methods. This experiment is performed under the noise data input 5 dB. In order to verify the effectiveness of the noise reduction algorithm proposed in this paper, we compare it with TV, wavelet, and mean filtering methods with different SNR noises. Figures 5 and 6 show the results.