# Physics-Based Noise Modeling and Deep Learning for Denoising Permanently Shadowed Lunar Images
## 4 Results
### Experimental Results of Real Images  
Table 2 presents the quantitative denoising results of different methods applied to real images. The evaluation metrics used include IL-NIQE, NRQM, and MUSIQ, with the results reflecting the average values of all processed real images. The best denoising results are emphasized in bold. According to Table 2, the proposed method performs excellently, achieving the lowest IL-NIQE score and the highest NRQM and MUSIQ scores. Specifically, compared to the worst-performing UNet network, the proposed method improves the IL-NIQE, NRQM, and MUSIQ scores by 3.875, 0.122, and 0.987, respectively. Furthermore, when compared to the better-performing AST network, the proposed method improves the IL-NIQE, NRQM, and MUSIQ scores by 0.604, 0.024, and 0.213, respectively. Although our proposed method shows improvements over other networks in these three non-parameter metrics, the differences are relatively small. Therefore, we will also conduct qualitative experiments using real images to compare the denoising results of different networks, in order to provide supplementary insights to the current quantitative findings.  
Figure 11: Denoising results of the simulated images. (**a**) Latitude: \(-72.78^{\circ}\) Longitude: \(310.81^{\circ}\) (**b**) Latitude: \(57.36^{\circ}\) Longitude: \(194.01^{\circ}\) (**c**) Latitude: \(-58.12^{\circ}\) Longitude: \(153.74^{\circ}\) (**d**) Latitude: \(-32.57^{\circ}\) Longitude: \(153.23^{\circ}\).  
Figure 12 shows the results of applying different denoising techniques to real images labeled as a, b, c, and d. By comparing the regions within the red boxes in the figure, the following observations can be made: UNet performs reasonably well on real images, but its robustness is poor, with denoising failure occurring in Figure 12c. While UNet3 Plus demonstrates better denoising performance than UNet, in Figure 12a, the black regions in the noisy image negatively affect the denoising results, leading to the appearance of holes. Additionally, oversmoothing is observed, with significant brightness differences between some regions, particularly in Figure 12b. DRANet, UFormer, and AST perform well in denoising, but as shown in Figure 12c, these networks do not effectively remove vertical stripe noise, leaving it still visible. Furthermore, Figure 12a-c reveal that DRANet introduces stripes at the image edges, while UFormer and AST fail to recover fine texture details in the image. In contrast, the method proposed in this study not only effectively removes a significant amount of noise but also, as shown in Figure 12c, effectively eliminates vertical stripe noise. While maintaining excellent visual quality, it recovers the most texture details and topographical features, preserving the image information after denoising to the greatest extent.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Evaluating Indicator** & **Original Image** & **UNet** & **UNet3 Plus** & **DRANet** & **UFormer** & **AST** & **This Study** \\ \hline IL-NIQE & 143.279 & 97.981 & 95.895 & 97.522 & 97.085 & 94.710 & 94.106 \\ NRQM & 2.762 & 2.946 & 2.969 & 3.015 & 2.988 & 3.044 & 3.068 \\ MUSIQ & 25.272 & 26.791 & 26.810 & 26.134 & 27.203 & 27.565 & 27.778 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Quantitative evaluation results for the real image experiment.  
Figure 12: Denoising result of the real images. (**a**) Latitude: \(-88.13^{\circ}\) Longitude: \(216.34^{\circ}\) (**b**) Latitude: \(-70.26^{\circ}\) Longitude: \(187.91^{\circ}\) (**c**) Latitude: \(-83.63^{\circ}\) Longitude: \(16.12^{\circ}\) (**d**) Latitude: \(-83.52^{\circ}\) Longitude: \(56.23^{\circ}\).