## 4 Results and Discussions
### Experimental Results
#### 4.3.3 Statistical Analysis  
To further verify the robustness of the algorithm, we set up 100 experiments with different noise distributions to test the model, in which each group of experiments had the same noise graph, and we used the standard deviation and mean value to verify the stability and denoising performance of the algorithm, respectively. As shown in Table 7, the mean values and standard deviations of different models with a noise intensity of 15, 25, and 50 are respectively shown. It can be clearly seen that the standard deviation of DRFENet is generally low, which indicates that the algorithm performance is improved while maintaining high algorithm stability.  
We also used the analysis of variance (ANOVA) to test the significance of the difference in means between the models. When the significance level \(\alpha=0.05\), the ANOVA showed  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Methods** & & **DnCNN** & **IRCNN** & **ECNDNet** & **ADNet** & **BRDNet** & **Ours** \\ \hline \multirow{2}{*}{\(\sigma=15\)} & Mean & 32.88 & 32.66 & 32.88 & 32.89 & 32.87 & 32.95 \\ \cline{2-7}  & Std & 0.000120 & 0.000122 & 0.000129 & 0.000116 & 0.000135 & 0.000119 \\ \hline \multirow{2}{*}{\(\sigma=25\)} & Mean & 30.45 & 30.23 & 30.45 & 30.48 & 30.49 & 30.53 \\ \cline{2-7}  & Std & 0.000153 & 0.00018 & 0.000176 & 0.000214 & 0.000156 & 0.000175 \\ \hline \multirow{2}{*}{\(\sigma=50\)} & Mean & 27.20 & 26.97 & 27.13 & 27.26 & 27.28 & 27.32 \\ \cline{2-7}  & Std & 0.000402 & 0.000362 & 0.000435 & 0.000341 & 0.000406 & 0.000387 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The average PSNR(dB) results of 100 experiments and the standard deviations between each result were obtained from different methods in the Set12 dataset with noise level of 25.  
Figure 4: Noise images processed in ADNet and in DRFENet have noise levels of 15, 35, and 75, respectively. (**a**) Original image, (**b**) (\(\sigma=15\)) noisy image, (**c**) (\(\sigma=15\)) ADNet/PSNR = 42.13 dB, (**d**) DRFENet/PSNR = 42.25 dB, (**e**) (\(\sigma=35\)) Noisy image, (**f**) (\(\sigma=35\)) ADNet/PSNR = 38.44 dB, (**g**) DRFENet/PSNR = 38.46 dB, (**h**) (\(\sigma=75\)) Noisy image, (**i**) (\(\sigma=75\)) ADNet/PSNR = 34.66 dB, (**j**) DRFENet/PSNR = 34.92 dB.  
that the significance (P value) was less than 0.001 when the noise intensity was 15, 25, and 50, indicating a significant difference between DRFENet and other algorithms. The 95% confidence interval showed no overlap in the PSNR value of the noise reduction performance under the same noise intensity. This indicates that DRFENet has an advantage in any noise distribution environment.  
The [PERSON] t-test formula is shown in Equations (14) and (15). The [PERSON] t-test formula was used to test the difference between the experimental group and the control group.  
\[S_{w}^{2}=MSE\bigg{(}\frac{1}{n_{i}}+\frac{1}{n_{0}}\bigg{)} \tag{14}\]  
\[Dunnett^{\prime}t=\frac{\overline{X}_{i}-\overline{X}_{0}}{S_{w}} \tag{15}\]  
where \(n_{i}\) represents the data volume of group \(i\), \(n_{0}\) represents the data volume of the control group, \(\overline{X}_{i}\) represents the mean value of group \(i\), \(\overline{X}_{0}\) represents the mean value of the control group, and MSE represents the mean square error.  
We compared DRFENet as a control group with the other five models. According to the Dunnett t-test, none of the horizontal mean values include 0 value, and DRFENet is significantly different from the mean values of other models. The Dunnett t-test and 95% confidence interval at a noise level of 25 are shown in Figure 5.