## 4 Experiments
### Experimental Results and Analysis

Table 2: PNSR(dB) results of two methods on 10 commonly used images with various noise levels. Figure 10: Some representative images in the Urban100 database. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Images** & **Barbara** & **Boat** & **Cameraman** & **Couple** & **Hill** & **House** & **Lena** & **Man** & **Monarch** & **Peppers** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=10\)} \\ \hline DIP & 0.9754 & 0.9775 & 0.9511 & 0.9802 & 0.9750 & 0.9520 & 0.9482 & 0.9537 & 0.9765 & 0.9747 \\ \hline Proposed & **0.9825** & **0.9873** & **0.9653** & **0.9868** & **0.9813** & **0.9583** & **0.9857** & **0.9843** & **0.9642** & **0.9668** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=20\)} \\ \hline DIP & 0.9478 & 0.9525 & 0.9249 & 0.9645 & 0.9462 & 0.9262 & 0.9072 & 0.9251 & 0.9490 & 0.9495 \\ \hline Proposed & **0.9760** & **0.9741** & **0.9379** & **0.9739** & **0.9695** & **0.9429** & **0.9767** & **0.9703** & **0.9468** & **0.9472** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=30\)} \\ \hline DIP & 0.9261 & 0.9277 & 0.9024 & 0.9488 & 0.9227 & 0.9065 & 0.8793 & 0.9036 & 0.9256 & 0.9272 \\ \hline Proposed & **0.9630** & **0.9580** & **0.9161** & **0.9574** & **0.9536** & **0.9260** & **0.9671** & **0.9529** & **0.9315** & **0.9312** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=40\)} \\ \hline DIP & 0.8968 & 0.9088 & 0.8809 & 0.9349 & 0.9073 & 0.8912 & 0.8589 & 0.8878 & 0.9045 & 0.9058 \\ \hline Proposed & **0.9501** & **0.9416** & **0.8837** & **0.9398** & **0.9368** & **0.9145** & **0.9567** & **0.9365** & **0.9172** & **0.9168** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=50\)} \\ \hline DIP & 0.9033 & 0.8903 & 0.8633 & 0.9166 & 0.8886 & 0.8735 & 0.8375 & 0.8671 & 0.8826 & 0.8946 \\ \hline Proposed & **0.9377** & **0.9274** & **0.8779** & **0.9237** & **0.9228** & **0.9017** & **0.9459** & **0.9199** & **0.9070** & **0.8900** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=60\)} \\ \hline DIP & 0.8850 & 0.8737 & 0.8494 & 0.9075 & 0.8690 & 0.8615 & 0.8195 & 0.8534 & 0.8654 & 0.8750 \\ \hline Proposed & **0.9249** & **0.9131** & **0.8496** & **0.9112** & **0.9089** & **0.8963** & **0.9373** & **0.9048** & **0.8936** & **0.8899** \\ \hline \end{tabular}
\end{table} 
Table 3: SSIM results of two methods on 10 commonly used images with various noise levels. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Images** & **[PERSON]** & **Boat** & **Cameraman** & **Couple** & **[PERSON]** & **[PERSON]** & **[PERSON]** & **Man** & **Monarch** & **Peppers** \\ \hline Noise Level & \multicolumn{8}{c}{\(\sigma=10\)} \\ \hline DIP & 0.9754 & 0.9775 & 0.9511 & 0.9802 & 0.9750 & 0.9520 & 0.9482 & 0.9537 & 0.9765 & 0.9747 \\ \hline Proposed & **0.9825** & **0.9873** & **0.9653** & **0.9868** & **0.9813** & **0.9583** & **0.9857** & **0.9843** & **Moreover, we present the average PSNR, SSIM, and FSIM results of the eight other denoising methods on the 10 commonly used images for noise levels \(\sigma\in\) [10, 20, 30, 40, 50, 60] in Tables 6-8, respectively. From Table 6, we can draw the following conclusions. First, although the original DIP method is more flexible, its overall denoising effect is inferior to the mainstream denoising methods. Second, our method surpassed the other mainstream denoising methods and obtained the highest average PSNR results. Specifically, it outperformed the deep learning-based method FFDNet by 0.48 to 1.23 dB. Table 7 shows that the original DIP method was the second best method and achieved impressive SSIM results at noise levels \(\sigma\in\) [10, 20, 30, 40, 50]. However, the SSIM results of our method were higher than DIP and improved the SSIM values by 0.0184 to 0.0901. Further, from Table 8, it can be seen that the proposed method also achieved the highest FSIM results in all cases. To test the robustness of the proposed method, we conducted experiments using the BSD dataset in which the texture of the images is more complex, making the task of image denoising more difficult.