## 4 Results and Analysis
### Accuracy Validation with Known Noise Levels
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{6}{c}{**Noise Standard Deviation**} \\ \cline{2-7}  & 0.01 & 0.07 & 0.2 & 0.316 & 1.41 & 3.87 \\ \hline LSD & 2.96 & 18.7 & 45.9 & 63 & 75.6 & 63.7 \\ FFT-DC & 2.77 & 5.66 & 2.41 & 1.76 & 1.04 & 1.17 \\ ReSNR & 5.43 & 5.28 & 2.23 & 1.61 & 0.86 & 1.01 \\ DnCNN 1 & 6.98 & 17.9 & 18.7 & 19.2 & 24.3 & 26.8 \\ Net-1 1 & **0.033** & 0.027 & 0.123 & 0.233 & 1.6 & **2.67** \\ Net-2-M 1 & 0.036 & **0.063** & **0.187** & **0.282** & **1.4** & **2.67** \\ \hline
**Method** & \multicolumn{6}{c}{**Root Mean Square Error (RMSE)**} \\ \hline LSD & 2.99 & 18.7 & 45.9 & 62.9 & 74.3 & 67.4 \\ FFT-DC & 2.78 & 6.39 & 2.53 & 1.66 & 0.61 & 2.7 \\ ReSNR & 5.7 & 6.0 & 2.35 & 1.49 & 0.4 & 2.86 \\ DnCNN 1 & 7.11 & 17.8 & 18.5 & 18.9 & 22.91 & 22.88 \\ Net-1 1 & **0.027** & 0.04 & 0.085 & 0.083 & 0.188 & 1.202 \\ Net-2-M 1 & 0.03 & **0.014** & **0.03** & **0.04** & **0.08** & **1.197** \\ \hline \hline \end{tabular}  
* CNN models.  
\end{table} 
Table 4: The noise estimation results of the references and the proposed model. Figure 5: Visualization of Figure 1e under different noise levels. Figure 8: Fitting results of evaluated values and true values for each method. The X-axis represents the true values, and the Y-axis represents the estimated values. “\(\Circarrow\)” represents the input data. The red solid lines are the ideal fitting results. Additionally, R is the correlation coefficient between the estimated values and the true values. The closer R is to 1.0, the higher the correlation. The closer the estimated values are to the true values, the better the performance of the method: (**a**) LSD; (**b**) FFT-DC; (**c**) ReSNR; (**d**) DnCNN; (**e**) Net-1; and (**f**) Net-2-M.  
Figure 6: The results estimated by the three traditional methods in Figure 1 with different noise levels. Each curve represents the noise SD results estimated on different noise levels by an algorithm: (**a**) LSD; (**b**) FFT-DC; and (**c**) ReSNR. Figure 7: Difference between the noise obtained by DnCNN and the truth for Figure 1e: (**a**) Texture structure is left in the noisy image with \(\sigma^{2}\) = 0.04 estimated by DnCNN; (**b**) True noise distribution with \(\sigma^{2}\) = 0.005. To further analyze Figure 8a-c, most of the estimated values are in the upper left, but the noise SDs are not high (<0.5). This is because the traditional methods (a-c) are greatly affected by the uneven ground surfaces. With the noise level increasing up, the estimated values become larger or smaller (black circles gathered at the top right or bottom right), which indicates these methods are affected seriously by noise intensity. Additionally, most of these methods show large errors for the seriously degraded images. For Figure 8d-f, the R values are 0.7205, 0.9733, and 0.98546, respectively. They are closer to 1.0. Meanwhile, our model achieves the best performance: R is 0.98546 in Figure 8f. With respect to Figures 4 and 8 and Table 4, the traditional and CNN-based algorithms comparisons can be drawn, validating our proposed approach: accuracy is increased when training a CNN similar to VGG in a novel method.