## 4 Experiments
### Experimental Results and Analysis  
In this subsection, we present the PSNR results of the proposed method and the original DIP method on 10 commonly used test images. Table 2 shows the results with noise levels of \(\sigma\in[10,\,20,\,30,\,40,\,50,\,60]\). The highest PSNR values for each noise level are highlighted in bold. According to the PSNR results shown in Table 2, it can be observed that our approach achieved better performance in all cases compared with the original DIP method. In particular, the processing result of the Barbara image at noise level \(\sigma=30\) is notable. Even though the Barbara image has abundant texture details and is complex, our proposed method increased the PSNR result by 4.35 dB. The reason for this is that our proposed method is especially suited to denoising images with complex textures because it utilizes two target images of high quality. Additionally, the minimum increase in the PSNR value was observed on the Hill image with the noise level \(\sigma=10\), which reached 1.15 dB. The SSIM and FSIM indexes of the two methods on the 10 commonly used test images were also computed and are shown in Tables 3 and 4, respectively. These results show that the proposed method surpassed the DIP method in both SSIM and FSIM, which confirms that our method significantly improved the local structure preservation and global brightness consistency. We also performed experiments to compare the time efficiency of the two methods. In Table 5, the PSNR value in the second column is the best result that the original DIP method can achieve. The following rows list the number of iterations and time required for DIP and our method to achieve the value, respectively. We can observe that compared with the original DIP method, the proposed method requires less time to reach the PSNR value, which shows that the proposed method surpasses the original DIP method not only in denoising performance but also in time efficiency. Figure 8: Some representative images in the BSD database. Figure 9: Some representative images in the Flickr1024 database. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Images** & **[PERSON]** & **Boat** & **Cameraman** & **Couple** & **[PERSON]** & **House** & **[PERSON]** & **[PERSON]** & **Monarch** & **Peppers** \\ \hline Noise Level & & & & & & \(\sigma=10\) & & & & \\ \hline DIP & 32.06 & 33.36 & 32.86 & 32.97 & 32.84 & 35.46 & 35.36 & 32.71 & 33.00 & 33.77 \\ \hline Proposed & **33.79** & **35.25** & **35.50** & **34.80** & **34.00** & **37.36** & **36.97** & **34.27** & **35.01** & **36.44** \\ \hline Noise Level & & & & & \(\sigma=20\) & & & & \\ \hline DIP & 27.87 & 30.04 & 29.35 & 29.57 & 29.87 & 32.68 & 32.47 & 29.57 & 29.68 & 30.48 \\ \hline Proposed & **32.18** & **32.87** & **32.01** & **32.49** & **32.30** & **35.01** & **35.00** & **32.20** & **32.24** & **33.12** \\ \hline Noise Level & & & & & \(\sigma=30\) & & & & \\ \hline DIP & 25.76 & 28.14 & 27.31 & 27.73 & 28.36 & 31.04 & 30.80 & 28.03 & 27.91 & 28.50 \\ \hline Proposed & **30.11** & **30.91** & **30.03** & **30.49** & **30.62** & **33.62** & **33.31** & **30.31** & **30.28** & **31.17** \\ \hline Noise Level & & & & & \(\sigma=40\) & & & & \\ \hline DIP & 24.26 & 26.91 & 25.69 & 26.28 & 27.35 & 29.43 & 29.43 & 26.95 & 26.48 & 27.13 \\ \hline Proposed & **28.29** & **29.49** & **28.56** & **29.11** & **29.46** & **32.54** & **31.95** & **29.03** & **28.96** & **29.69** \\ \hline Noise Level & & & & & \(\sigma=50\) & & & & \\ \hline DIP & 23.29 & 25.75 & 24.52 & 25.20 & 26.34 & 28.51 & 28.27 & 26.05 & 25.37 & 26.04 \\ \hline Proposed & **26.91** & **28.33** & **27.49** & **27.94** & **28.58** & **31.48** & **30.84** & **28.11** & **27.88** & **28.56** \\ \hline Noise Level & & & & & \(\sigma=60\) & & & & \\ \hline DIP & 22.76 & 24.96 & 23.26 & 24.44 & 25.49 & 27.40 & 27.06 & 25.23 & 24.48 & 24.68 \\ \hline Proposed & **25.79** & **27.44** & **26.54** & **27.14** & **27.82** & **30.65** & **30.00** & **27.36** & **26.82** & **27.55** \\ \hline \hline \end{tabular}
\end{table}