## 4 Experimental Results  
### Evaluation Criteria  
In this study, the quantitative performance of the denoising technique was evaluated using _RMSE_, _PRD_, and _SNR\({}_{imp}\)_.  
_SNR\({}_{imp}\)_ compares the SNR between the noisy ECG (_SNR\({}_{in}\)_) and the reconstructed signal (_SNR\({}_{out}\)_). A higher _SNR\({}_{imp}\)_ value indicates superior denoising performance, defined as follows. The aforementioned variables are defined as follows:  
\[SNR_{imp}=SNR_{out}-SNR_{in} \tag{6}\]  
\[SNR_{in}=10\times log_{10}\Bigg{(}\frac{\sum_{i=0}^{M-1}x_{i}^{2}}{\sum_{i=0} ^{M-1}\left(x_{i}-\hat{x}_{i}\right)^{2}}\Bigg{)} \tag{7}\]  
\[SNR_{out}=10\times log_{10}\Bigg{(}\frac{\sum_{i=0}^{M-1}x_{i}^{2}}{\sum_{i=0} ^{M-1}\left(x_{i}-\tilde{x}_{i}\right)^{2}}\Bigg{)} \tag{8}\]  
where \(M\) is the strength of the signal, and \(x_{i}\) is the amplitude of each sampling point in a clean ECG. Similarly, \(\tilde{x}_{i}\) and \(\hat{x}_{i}\) are the amplitudes of the sampling in the reconstructed ECG and noisy ECG, respectively.  
_RMSE_ represents the variance between the reconstructed ECG (\(\widetilde{\textbf{x}}\)) and the clean ECG (**x**). A smaller RMSE value represents a more favorable denoising performance. RMSE is formulated as follows:  
\[RMSE=\sqrt{\frac{1}{M}\times\sum_{i=0}^{M-1}\left(x_{i}-\widetilde{x}_{i} \right)^{2}} \tag{9}\]  
_PRD_ represents the reconstructed signal quality between the clean signal and the reconstructed signal. A lower _PRD_ value, defined in Equation (10), indicates higher quality. Because of the original dc offset that exists in the clean ECG dataset, the mean of the input signal was considered in this work, consistent with the approach in [47].  
\[PRD=\sqrt{\frac{\sum_{i=0}^{M-1}\left(x_{i}-\widetilde{x}_{i}\right)^{2}}{\sum _{i=0}^{M-1}x_{i}^{2}}}\times 100 \tag{10}\]  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline
**Execution Order-** & **1D NN Layer** & **No. Filter \(\times\)** & **Paddings** & **Region/Unit** & *** AF** & **No. Trainable** & **Input Size** & **Output Size** \\
**Annotation** & **Name** & **Kernel Size** & & **Size** & & **10,304** & **32 \(\times\) N** & **32 \(\times\) N** \\ \hline
**Residual Block (Res.)** & & & & & & & \\
1-Conv. & Convolution & \(32\times 5\) & 2 & – & – & 5152 & \(32\times\) N & \(32\times\) N \\
2-Conv. & Convolution & \(32\times 5\) & 2 & – & ReLU & 5152 & \(32\times\) N & \(32\times\) N \\ \hline
**Encoder Layer (Res. + PUS + PW Conv.)** & & & & & & **12,384** & **32 \(\times\) N** & **32 \(\times\) N/2** \\
1-Res. & Residual Block & \(32\times 5\) & 2 & – & ReLU & 10,304 & \(32\times\) N & \(32\times\) N \\
2-PUS & Pixel-UnShuffle & – & – & \(\downarrow\) 2 & – & – & 32 \(\times\) N & \(64\times\) N/2 \\
3-PW Conv. & Convolution & \(32\times 1\) & 0 & – & – & 2080 & \(64\times\) N/2 & \(32\times\) N/2 \\ \hline
**Decoder Layer (Res. + PW Conv. + PS)** & & & & & & **12,416** & **32 \(\times\) N** & **32 \(\times\) N** \\
1-Res. & Residual Block & \(32\times 5\) & 2 & – & – & 10,304 & \(32\times\) N & \(32\times\) N \\
2-PW Conv. & Convolution & \(64\times 1\) & 0 & – & ReLU & 2112 & \(32\times\) N & \(64\times\) N \\
3-PS & Pixel-Shuffle & – & – & \(\uparrow\) 2 & – & – & 64 \(\times\) N & \(32\times\) 2N \\ \hline
**Skip Connection (CWAP + PW Conv.)** & & & & & & **64** & **32 \(\times\) N** & **32 \(\times\) N** \\
1-CWAP & Channel-wise & – & – & \(\downarrow\) 32 & – & – & 32 \(\times\) N & \(1\times\) N \\
2-PW Conv. & Convolution & \(32\times 1\) & 0 & \(\uparrow\) 32 & – & 64 & \(1\times\) N & \(32\times\) N \\ \hline \end{tabular}  
* AF: activation function; \(\downarrow\): down-sampling; \(\uparrow\): up-sampling.  
\end{table}
Table 3: Layer Information of the Submodule for the Regular Version of the Proposed CPDAE.