## 4 Experimental Results
### Experimental Results and Comparison  
The artificial intelligence framework of this study was PyTorch 1.9, and the adopted CPU, RAM, and GPU in our experiment were an AMD R9-5950x, 96 GB, and Nvidia RTX3090 24 GB, respectively. To train the models efficiently, suitable hyperparameters were selected and set to accelerate the training convergence speed. Table 4 demonstrates the six hyperparameters used in this study. The cost function using MSE was the same as in previous studies [21-24,28]. The epochs were set to 1000 to ensure that each model would converge during the training phase. The learning rate was set to \(10^{-4}\) and decayed by one-half every 200 epochs. This implied that the weights could be updated rapidly in the early training stage, and finetuned at the final training stage [51]. For optimization, an Adam optimizer was employed instead of stochastic gradient descent because it could locate the gradient more accurately. To evaluate the denoising performance with various parameters and MACs, we implemented CPDAE,Lite, CPDAE,Regular, and CPDAEFull with different combinations, as displayed in Table 5. CPDAE,Lite is highly suitable for implementation on an embedded platform. CPDAEFull has the highest denoising performance and the greatest number of MACs. This implies that a powerful GPU would be needed to realize this highly complex algorithm. CPDAE,Regular balances denoising performance and lightweight computational capability. For the testing phases of Lite, Regular, and Full versions, the average run-time per frame was 0.1154 ms, 0.1424 ms, and 0.1327 ms, respectively. Conceptually, the MACs can be reduced by decreasing the number of encoder and decoder layers and the \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameters** & **Value** \\ \hline Cost function & Mean-square-error (MSE) \\ Learning Rate (LR) & \(1\times 10^{-4}\) \\ Learning Rate scheduler & Step-LR (\(LR/2^{\lfloor 6\,\sigma\) epoch/\(200\rfloor}\)) \\ Optimizer & Adam \\ Batch size & 32 \\ Epochs & 1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Hyperparameters for the Experiment. number of channels for each layer, but the denoising capability of DAE would drop down. However, deeper layers have the ability to learn data representations with multiple levels of abstraction. This method compensates for the lack of features when a low number of channels in each encoder/decoder layer is used (e.g., \(\text{CPDAE}_{\text{Lite}}\)). By contrast, when more channels are available in each encoder/decoder layer (e.g., \(\text{CPDAE}_{\text{Full}}\)), the denoising performance is not substantially improved by adding more layers. To evaluate the performance of the proposed CPDAE more clearly, the channel numbers were, respectively set to 16, 32, 48, 64, and 128 with the corresponding numbers of layers set to 5, 6, 7, 8, and 9 for the usage of encoder and decoder. Here, the average of \(SNR_{imp}\) was utilized to measure the performance. Figure 9 shows that the more layers, the higher \(SNR_{imp}\) attained under the fixed numbers of channels. In addition, a better average of \(SNR_{imp}\) would be obtained with the adjustment of the numbers of channels and layers. The design goal of \(\text{CPDAE}_{\text{Lite}}\) aims to decrease the number of parameters and achieved performance similar to that of FCN [22]. The desired average of \(SNR_{imp}\) in \(\text{CPDAE}_{\text{Lite}}\) has to be more than 10 dB, so the numbers of channels and layers were set to 16 and 8, respectively. The result with \(\text{CPDAE}_{\text{Regular}}\) attained a curve with the greatest improvement, where the numbers of channels and layers were respectively set to 32 and 7. The model of \(\text{CPDAE}_{\text{Full}}\) achieved the best denoising results, where the numbers of channels and layers were respectively set to 128 and 6. Although each additional encoder and decoder layer could improve the performance slightly, it also led to a significant increase in the number of parameters.