## 4 Experimental Results
### Experimental Results and Comparison
The proposed models were compared with the following four existing approaches: (1) DNN-DAE, (2) CNN-DAE, (3) FCN-DAE [22], and (4) CNN-LSTM-DAE [23]. The DNN-DAE has 10 fully connected layers with 512, 256, 128, 64, 32, 64, 128, 256, 512, and 1024 nodes. The CNN-DAE uses the same structure as the FCN-DAE [22] in layers 1-13, and two fully connected layers are added in layers 14 and 15. Moreover, ReLU and batch normalization are used at the end of each layer. The model architectures of the FCN-DAE [22] and CNN-LSTM-DAE [23] are state-of-the-art. The FCN-DAE [22] has six \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Proposed** & **No. Encoder/** & **No. Channels** & **Kernel Size** & **MACs** & \multicolumn{2}{c}{**Average Run-Time (ms) per Frame**} \\ \cline{5-8}
**Models** & **Decoder Layers** & & & & **Training Phase** & **Testing Phase** \\ \hline \(\text{CPDAE}_{\text{Lite}}\) & 8 & 16 & 5 & 14.69 M & 0.5508 & 0.1154 \\ \(\text{CPDAE}_{\text{Regular}}\) & 7 & 32 & 5 & 56.96 M & 0.6439 & 0.1424 \\ \(\text{CPDAE}_{\text{Full}}\) & 6 & 128 & 5 & 355.01 M & 0.6935 & 0.1327 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Components of the Proposed Models. Figure 9: A performance comparison of CPDAE models with various channels and encoder/decoder layers. convolution layers in the encoder and seven transposed convolutions in the decoder. The CNN-LSTM-DAE [23] uses eight convolution layers and five max-pooling layers to extract the features of the clean ECG in the encoder. In contrast with previous works, LSTM cells at the end of the encoder were added to learn the relevant information in the sequential data. To recover the original clean ECG signal, eight convolution layers, six up-sampling layers, and one fully connected layer are used in the decoder. The average loss curves for various DAEs under the testing and training sets are depicted in Figure 10. In the training phase (Figure 10a), the loss value of every DAE was an obvious decrease in the first 500 epochs, ensuring that all DAEs could effectively obtain the trainable parameters. After the DAEs had been trained over 800 epochs, the trend of the loss curve for all DAEs became flat, so we stopped training at epoch 1000. In the last epoch, DNN-DAE showed the highest loss value; however, the FCN-DAE and CNN-LSTM-DAE had very similar loss values. It is worth noting that the proposed CPDAEFull had the lowest loss value in this experiment, and the loss value almost had no changes after 300 times of epochs. This result shows that the proposed CPDAEFull learns ECG features very well compared with other methods by using fewer training times. In the testing phase, the DNN-DAE had the worst _MSE_. The loss curves of the proposed CPDAE models (Lite, Regular, and Full version) had a significant improvement compared with other approaches. The criteria for the improvement of SNR are reported in Figure 11. We used box plots to display the \(SNR_{imp}\) distribution under certain \(SNR_{in}\). All of the models exhibited favorable improvement in low \(SNR_{in}\) (\(-6\) dB, \(0\) dB, and \(6\) dB). When the \(SNR_{in}\) was \(-6\), the DNN-DAE, CNN-DAE, FCN-DAE, CNN-LSTM-DAE, and CPDAELite exhibited a similar \(SNR_{imp}\) distribution. According to our results, CPDAERegular and CPDAEFull were ranked first (23.68 dB) and second (20.05 dB) in terms of average \(SNR_{imp}\). However, when the \(SNR_{in}\) was increased to 12, 18, and 24 dB, the proposed CPDAE methods were superior to the other approaches. Moreover, because the noise was not always at a high-intensity level, performance had to be tested under low-intensity noise. The state-of-the-art approaches were only tested under the condition of \(SNR_{in}\) > 10 dB; higher \(SNR_{in}\) was essential for validation. The \(SNR_{imp}\) values of the DNN-DAE, CNN-DAE, FCN-DAE, and CNN-LSTM-DAE methods decreased under the conditions of 12, 18, and 24 dB \(SNR_{in}\). Figure 10: The loss curves in training and testing phases: (a) training phase; (b) testing phase.