## 4 Results and Analysis  
### Comparison of Training Results Based on Neural Network  
Our model and the model in [20] are both neural networks that are similar to VGG. Both of them evaluate SNR directly rather than denoise. Therefore, the two models are compared and analyzed. Firstly, both of the two are trained in traditional methods. Following this, they were trained in the novel method: (1) the model in [20] was trained in the traditional training method, denoted as Net-1; (2) Net-1-M was the model of Net-1 that was trained in the novel method; (3) our model was trained in the traditional method, denoted as Net-2; and (4) Net-2-M was the model of Net-2 that was trained in the novel method. The root mean square error (RMSE) measures the deviations between the estimated and the true values, which is described as follows:  
\[RMSE=\sqrt[2]{\frac{1}{N}\sum_{k=1}^{N}(\sigma-\sigma_{0})^{2}} \tag{5}\]  
where \(\mathbf{\sigma_{0}}\) is the true noise SD, \(\mathbf{\sigma}\) is the estimated SD, and \(\mathbf{N}\) is the number of \(\mathbf{\sigma}\). The training results are shown in Figure 4.  
Figure 4 shows the training results for the four cases described above. The deviation estimated by Net-1-M (yellow), trained in the multi-branch method, is closer to true value and less than that of Net-1 (blue), trained in the traditional method. Meanwhile, the deviation estimated by Net-2 (green), trained in the traditional method, is also significantly higher than that of Net-2-M (red), trained in the multi-branch method. The comparative experiments show that the multi-branch training could improve the ability of the CNNs that are similar to VGG, and its training effect is higher than that of the traditional training method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Params** & **Size** & **Strip** & **Count** & **Training** & **Inference** \\ \hline Conv 1 & \(3\times 3\) & 1 & 16 & \(\surd\) & \(\surd\) \\ BN & \(16\times 32\times 32\) & – & – & \(\surd\) & \(\surd\) \\ Conv 2 & \(3\times 3\) & 1 & 32 & \(\surd\) & Conv 2,Conv \\ Conv 3 & \(3\times 3\) & 1 & 32 & \(\surd\) & 3 integrated \\ BN & \(32\times 16\times 16\) & – & – & \(\surd\) & \(\surd\) \\ Conv 4 & \(3\times 3\) & 1 & 64 & \(\surd\) & Conv 4,Conv \\ Conv 5 & \(3\times 3\) & 1 & 64 & \(\surd\) & 5 integrated \\ BN & \(64\times 8\times 8\) & – & – & \(\surd\) & \(\surd\) \\ FC 1 & \(64\times 8\times 8\times\) & – & – & \(\surd\) & \(\surd\) \\  & 2 & – & – & \(\surd\) & \(\surd\) \\ BN & 2 & – & – & \(\surd\) & \(\surd\) \\ FC 2 & \(2\times 1\) & – & – & \(\surd\) & \(\surd\) \\ \hline \hline \multicolumn{4}{c}{Activation Function: ReLU} & \multicolumn{4}{c}{Params Updating: Adam} \\ \multicolumn{4}{c}{Initialized Weight: He} & \multicolumn{4}{c}{Learning Rate: 0.0001} \\ \multicolumn{4}{c}{Input Size: 32 \(\times\) 32} & Output: Noise SD \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The weight parameters of training and inference. The parallel multiple convolutions extract different feature maps. Additionally, they are integrated into one feature map. On one hand, integration makes the feature information rich and avoids overfitting to some extent. On the other hand, the upstream gradient is passed to each branch when the gradient is propagated backward. Additionally, the gradient attenuation of each branch is the same, which accelerates the gradient updating and makes the whole of the training process converge fast. After going through many forward and backward propagations, each branch learns different features that tend to express the abstract features of targets. However, CNNs that are similar to VGG and trained in the traditional method need more epoch time or a deeper structure to achieve a better performance. The yellow (Net-1-M) and green (Net-2) curves in Figure 4 illustrate the situation: the results estimated by Net-1-M were close to those of Net-2, which had a deeper network.