## 4 Experiments
### Ablation Studies
In the testing stage, the clean DIOR-R testing set, and the Gaussian-noise-added DIOR-R testing set were selected as test datasets to evaluate ResNet-50 and WDARFNet, respectively. The corresponding ablation study results are presented in Table 3. The ablation study results show that after adding Gaussian noise with a mean (\(\mu\)) of 0 and a standard deviation (\(\sigma\)) of 10 to the testing set, the mAP using ResNet50 as the backbone network drastically fell to 46.52%, which is a significant decrease of 13.80% compared to the results on the clean test set. When using the WDARFNet backbone network, the mAP fell to 56.61%, which is only a decrease of 8.72% compared to that on the clean test set. After adding Gaussian noise with \(\mu=0\) and \(\sigma=25\) to the test set, the mAP using ResNet50 as the backbone network drastically fell to 31.18%, whereas the mAP using WDARFNet as the backbone network is 48.19%. This indicates that WDARFNet can effectively maintain object structure and suppress noise during network inference. Figure 8 presents two examples of the heatmaps for the well-trained ResNet50 and WDARFNet models, using noisy images as input. The first row displays the clean image and the heatmaps of ResNet50 and WDARFNet. The second and third rows show the images with added Gaussian noise (\(\mu=0\), \(\sigma=10\)) and (\(\mu=0\), \(\sigma=25\)), respectively, along with the heatmaps generated by the two networks. These two examples demonstrate that the original CNN has difficulty suppressing noise, whereas WDARFNet can effectively suppress noise and concentrates its attention primarily on or around the object during the inference process. Consequently, WDARFNet achieves superior detection accuracy in various challenging situations. **Selection of Wavelet Domain sub-bands after 2D Discrete Wavelet Transform. ** Figure 3 illustrates the sub-bands resulting from the 2-D Discrete Wavelet Transform. The four components decomposed after the wavelet transform are the low-frequency component \(A\), the horizontal high-frequency component \(H\), the vertical high-frequency component \(V\), and the diagonal high-frequency component \(D\). It is readily apparent that the low-frequency component primarily preserves the core structural information of the image, \begin{table}
\begin{tabular}{l c} \hline \hline
**Method** & **mAP** \\ \hline O-RCNN (ResNet50) & 62.09 \\ O-RCNN (WDCSM) & 63.56 \\ O-RCNN (WDSSM) & 64.15 \\ O-RCNN (WDCSM+WDSSM) & 65.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: An ablation study was conducted to evaluate the effectiveness of the proposed WDCSM and WDSSM modules. The DIOR-R dataset was utilized in this experiment. filtering out random noise and redundant information. The high-frequency components harbor more detailed information and noise, where the diagonal high-frequency component \(D\) exhibits lower information content and is predominantly composed of noise signals. Thus, selecting appropriate sub-bands significantly influences network performance. We conducted experiments to determine the optimal selection of frequency domain sub-bands, and the corresponding ablation study results are presented in Table 4. The results of the ablation studies indicate that the combination pattern of \(\{A+H\}\) and \(\{A+V\}\) both improve network performance; however, the combination pattern \(\{A+D\}\) reduces network performance, as \(D\) is primarily composed of noise signals, and noise has a marked effect on network performance. When the combination pattern of (A+H+V) is selected, the test results reach the optimum. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**mAP**} \\ \cline{2-4}
**Method** & **Original** & \
\begin{tabular}{c} **Gaussian – Noise** \\ **(\(\mathbf{\mu}\)=0,\(\sigma\)=10)** \\ \end{tabular} &
\begin{tabular}{c} **Gaussian – Noise** \\ **(\(\mathbf{\mu}\)=0,\(\sigma\)=25)** \\ \end{tabular} \\ \hline
**O-RCNN (ResNet50)** & 60.32 & 46.52 & 31.18 \\
**O-RCNN (WDARFNet)** & 65.33 & 56.61 & 48.19 \\ \hline \hline \end{tabular}
\end{table}