## 4 Experiments
### Experimental Results and Analysis
The PSNR performance of the nine competitive denoising methods is shown in Table 9. The denoising effects of each method on this dataset showed different degrees of decline compared to the average PSNR results achieved on the first dataset, shown in Table 6. Nevertheless, it is apparent that the PSNR results obtained by our method still outperformed all other methods. Especially when the noise level was set to 10, the improvement was significant (e.g., an average improvement of 3.31 dB over the DIP method). Tables 10 and 11 list the average SSIM and FSIM results for all 10 methods under six different noise levels. We can observe that our method obtained the highest SSIM and FSIM values; additionally, the improvements obtained by our proposed method for both the SSIM and FFIM results are noteworthy. In addition to the traditional databases, we performed experiments on a larger dataset called Flickr1024 with a variety of images. The average PSNR results are shown in Table 12. The PSNR results obtained by our method are clearly superior to those of the other nine methods. Tables 13 and 14 list the average SSIM and FSIM values obtained by 10 methods under six different noise levels. The results show that our method also achieved excellent performance in terms of the values of SSIM and FSIM. Compared to DIP, the proposed method can boost the average SSIM and FSIM values from 0.0607 to 0.1423 and from 0.0144 to 0.0508, respectively. To further evaluate the applicability of our method comprehensively, we randomly selected 10 high-resolution images from Urban100. From Table 15, we can observe that the WNNM method obtains good results when processing high-resolution images. Nevertheless, our method still outperforms it and achieves the highest PSNR results. As shown in Table 16, our method obtained the highest average SSIM results; compared with the other nine methods, the improvement in the values was approximately 0.0104 to 0.1023. Moreover, in Table 17, it can be observed that our method obtained the best average FSIM results. The experimental results clearly show that our proposed approach outperformed the existing state-of-the-art denoising methods on four classical datasets that are highly \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Images** & **Barbara** & **Boat** & **Cameraman** & **Couple** & **Hill** & **House** & **[PERSON]** & **Man** & **Monarch** & **Peppers** \\ \hline PSNR & 25.76 & 28.14 & 27.31 & 27.73 & 28.36 & 31.04 & 30.80 & 28.03 & 27.91 & 28.50 \\ \hline \multicolumn{10}{c}{Number of Iterations} \\ \hline DIP & 3373 & 2505 & 2083 & 2555 & 2774 & 1551 & 2687 & 2655 & 1703 & 1575 \\ \hline Proposed & **2873** & **2488** & **1832** & **2232** & **2529** & **1380** & **2307** & **2334** & **1541** & **1183** \\ \hline \multicolumn{10}{c}{Time} \\ \hline DIP & 43.64 & 31.44 & 27.09 & 33.70 & 37.72 & 21.97 & 38.91 & 39.60 & 26.11 & 24.11 \\ \hline Proposed & **37.04** & **31.41** & **25.00** & **31.33** & **36.78** & **20.75** & **35.45** & **37.16** & **25.44** & **18.02** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Number of iterations and time(s) of two methods on 10 commonly used images with \(\sigma\) = 30.  
representative. In particular, as an improvement of DIP, its denoising effect was notably better than that of the original DIP. It not only retained the flexibility of the original DIP method, but also greatly improved denoising performance. Therefore, it shows promise and adaptability. In the following subsection, we will analyze a visual comparison of images denoised by the different methods, which further supports our conclusion.