## 3 Proposed CPDAE
### Decoder Layer  
The decoder layer is almost inversely symmetrical to the encoder part. Seven decoders are mapped to the high-dimensional features from the code \(\mathbf{z}\), as illustrated in Figure 5. Except for the last layer (decoder 7), the input of each decoder is the sum of both the skip connection and the output of the upper decoder layer, calculated through element-wise addition. Each decoder reconstructs the features from \(\mathbf{a}^{n}\) by using the 1D residual block. Subsequently, the point-wise convolution (PW Conv) increases two times the channels that are required before up-sampling the 1D FS operation, and the features (\(\mathbf{a}^{n+1}\)) are rearranged to be the output features in the decoder layer, as illustrated in Figure 8. With the same configuration as the encoder layer, the kernel size of the 1D convolution in the 1D residual block is set to 5, and that of the point-wise convolution in the encoder layer is set to 1.  
Figure 6: Layer structure of encoders 1–7; C and N are the numbers of input channels and features, respectively.  
Figure 7: Channel-wise average pooling layer structure and point-wise convolution operation.  
After passing through decoders 1-7, the features of the clean ECG are distributed in 32 channels, where the features are mapped from low dimensions to high dimensions. The reconstructed ECG signal (\(\mathbf{\tilde{x}}\)) is obtained after the data pass through the output layer, which diminishes the 32 channels into 1 channel by convolution operations.  
The detailed layer information of the proposed regular model and its submodule is listed in Tables 2 and 3, respectively. Initially, the noisy ECG with the size of 1 \(\times\) 1024 is fed into the Input Layer. Then, the ECG signal is extracted by 7 layers of the Encoder, and it is further compressed into the Code z with the size of 32 \(\times\) 8. Subsequently, the clean ECG can be reconstructed by 7 layers of the Decoder and an Output Layer. In addition, to enhance the quality of the reconstructed signal, the key features are transmitted by 6 layers of CWAP inserting between Encoder Layers 1-6 and Decoder Layers 1-6. The total number of parameters of CPDAERegular is 194,753, and the proposed model can be real-time run on certain low-cost CUDA devices. The number of encoders and decoders in the proposed model can be arbitrarily increased or decreased as long as the number of the feature code z is a natural number.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Execution Order-** \\ **Annotation** \\ \end{tabular} } & \multirow{2}{*}{**Type**} & \multirow{2}{*}{**1D NN Layer Name**} & \multicolumn{2}{c}{**No. Filter**} & \multirow{2}{*}{**Paddings**} & \multirow{2}{*}{**Region/Unit**} & \multirow{2}{*}{***}{***} & \multirow{2}{*}{***}{**’AF**} & \multirow{2}{*}{**Toinable**} \\  & & & & & & & & **Size** \\ \hline \multirow{2}{*}{\begin{tabular}{c} **0-Input (\(\mathbf{\tilde{x}}\))** \\ 1 \\ 2 \\ 3 \\ 4 \\ \end{tabular} } & \multirow{2}{*}{**Noisy ECG**} & \multirow{2}{*}{\begin{tabular}{c} Convolution \\ Res. 32 \(\times\) 5 \\ 32 \\ 4 \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} 32 \(\times\) 1024 \\ 32 \(\times\) 1024 \\ 32 \(\times\) 1024 \\ 32 \(\times\) 5 \\ \end{tabular} } \\  & & & & & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} 3 \\ 5 \\ 7 \\ 9 \\ 11 \\ 13 \\ 15 \\ 16 \\ 17 \\ 18 \\ 19 \\ 19 \\ 20 \\ 21 \\ 22 \\ 23 \\ 24 \\ \end{tabular} } & \multicolumn{2}{c}{**No. Filter**} & \multirow{2}{*}{**Paddings**} & \multirow{2}{*}{**Region/Unit**} & \multirow{2}{*}{***}{***} & \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Output**} \\  & & & & & & & **Size** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} **0-Input (\(\mathbf{\tilde{x}}\))** \\ 1 \\ 2 \\ 3 \\ 4 \\ \end{tabular} } & \multirow{2}{*}{**Noisy ECG**} & \multirow{2}{*}{
\begin{tabular}{c} Convolution \\ Res. 32 \(\