## 4 Experiments
### Gray Image Denoising  
The averaged PSNR results of the different metrics on the Set12 and BSD68 datasets are reported in Table 3, and the best three performances are highlighted in boldface. Table 4 also reports the PSNR values of the different methods for 12 Gy images in the Set12 dataset, and the best two performances are highlighted in bold font. Evidently, the proposed method shows a good performance on two datasets with three noise levels. Specifically, the proposed method has an average PSNR gain of approximately 1 dB over BM3D on both Set12 and BSD68 datasets. It also surpasses the DnCNN and the FFDNet by an average PSNR of 0.5 dB on the Set12 dataset and 0.25 dB on the BSD68 dataset. Compared with unsupervised methods DIP and N2V, the PSNR performance of the proposed method is about 2 dB higher than that of DIP and N2V. This is because DIP and N2V utilize only the internal prior, whereas the proposed method can learn both the internal and external priors. Moreover, the proposed method can utilize the uncertainty of the DIP to obtain multiple denoised instances that are complementary to each other so that the fused image can have a better denoising effect. As presented in Table 3, compared with the newly proposed supervised method SwinIR, our method outperforms SwinIR with noise levels of 15 and 25 on both the Set12 and BSD68 datasets. These results indicate that our method can handle more complex corrupted images and achieve better performance than the existing models. It can be seen from Tables 3 and 4 that the proposed method achieves relatively low performance on \"Barbara\", which makes the average PSNR with noise level 50 of the proposed method lower than that of DAGL, DeamNet, DRUNet, and SwinIR. A possible reason is that DIP-based methods are not good at learning non-local self-similarity prior when images at high noise levels contain rich textures and repetitive structures. One possible solution to this problem is to improve the quality of the preliminary image. As discussed in Section 2, the image quality of the DIP learning target can restrict the search space. Using a learning target with better quality can avoid overfitting and help achieve a better denoising result. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Target Image** & **Noisy** & \(p_{i}\) & **Noisy+\(p_{i}\)** \\ \hline
**PSNR** & \(28.92\pm 1.45\) & \(29.02\pm 1.81\) & \(30.56\pm 1.43\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The PSNR (dB) performance of the Set12 dataset while taking different images as the learning target of the DIP optimization process. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Instance** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\
**Numbers** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline
**PSNR** & 30.86 & 30.95 & 31.02 & 31.06 & 31.09 & 31.1 & 31.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Averaged PSNR (dB) of the Set12 dataset while using different numbers of intermediate instances for image fusion. In the proposed method, FFDNet is first employed to preprocess the given noisy image, after which the two-target DIP and unsupervised fusion network are employed to generate the final denoised image. If other supervised denoisers with better denoising performance, such as DRUNet and SwinIR, are utilized to preprocess the given noisy image, the final denoising performance can be further improved. In Table 3, we also compare the performance of two methods proposed in our previous works [31,32]. In [31], we first employed a set of state-of-the-art image denoisers to preprocess the given noisy image and obtain multiple intermediate denoised images. These intermediate denoised images were then concatenated and fed into an unsupervised deep fusion network to generate the final denoised image. In [32], we utilized two state-of-the-art denoisers to generate the preliminary denoised images and proposed an unsupervised fusion network to fuse the two preliminary denoised images into the final denoised image.