# A Triple Deep Image Prior Model for Image Denoising Based on Mixed Priors and Noise Learning
## 4 Experiments
### Ablation Experiment  
The DIP model has excellent ability to restore specific local regions, but its overall performance on the whole image still lags behind that of supervised state-of-the-art counterparts. This is because supervised models can handle the generic image content of most regions well from massive training data, which indicates that supervised and unsupervised models can be complementary for denoising. We expect to select a model complementary to DIP as the generator of the external prior image (i.e., the second target image) to maximize the performance of the internal and external mixed priors. Therefore, we conducted ablation experiments on the Set12 benchmark dataset with a noise level of 25 to analyze the effect of different preprocessed images. Table 2 shows the PSNR values of denoising results under distinct preprocessing image generators (i.e., N2V, IRCNN, DnCNN, DeamNet, DAGL, SwinIR, Restormer). As Table 2 shows, the denoising performance of N2V is unimpressive compared with other methods, and its PSNR is 30.62 dB. Regardless of the strict assumptions of the model, the reason may be that using only a single image for denoising in N2V cannot effectively provide high-quality external priors for TripleDIP. The PSNR value increases significantly regarding IRCNN and DnCNN are used as generators (i.e., 0.62 dB, 0.72 dB, respectively). It can be attributed that supervised methods can learn richer details from massive data. Compared to DnCNN, the PSNR values of DeamNet, DAGL, SwinIR, and Restormer are further improved after the introduction of the attention mechanism (i.e., 0.16 dB, 0.24 dB, 0.34 dB, 0.36 dB, respectively), where DeamNet and DAGL use the DEAM module and graph attention respectively to capture cross-scale features and dynamic non-local property. Therefore, they can supplement the TripleDIP with external priors distinct from internal priors. The Transformer-based model SwinIR and Restormer disregard the limitations of the local receptive field and can perceive more structural similarities from large areas. Therefore, compared with the CNN method, they are more suitable for generating complementary prior information with DIP. Considering Restormer can exploit distant image context without disintegrating them into local windows like SwinIR, we finally selected Restormer as the model's second target image generator. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Generator** & **N2V** & **IRCNN** & **DnCNN** & **DeamNet** & **DAGL** & **SwinIR** & **Restormer** \\ \hline PSNR & 30.62 & 31.24 & 31.34 & 31.50 & 31.58 & 31.68 & 31.70 \\ \hline \end{tabular}
\end{table} 
Table 2: The average PSNR results for different preprocessed images. The loss function drives independent noise learning and mixed prior perception; furthermore, the different weight parameters of the loss function are among the determinants of model performance. In this study, the \(Loss_{Internal}\), \(Loss_{External}\), \(Loss_{Mixed}\), and \(Loss_{Stability}\), as a constraint of the model, are considered to perform an equally important role; therefore, their weight is set to one (i.e., \(\alpha=\beta=\gamma=\eta=1\)). We conducted ablation experiments primarily on the weight \(\omega\) of the initial \(Loss_{DIP}\), which measures the MSE between the output of DIP1 and the noisy image. \(Loss_{DIP}\) is unconducive to learning image content when encountering heavily polluted noisy images. In addition, higher \(\omega\) values may weaken the constraining effect of other loss functions. As indicated in Table 3, we track the value of \(\omega\) with an interval of 0.1 from 0.1 to 0.6, and calculate the PSNR value of the corresponding denoised image. The results demonstrate that the PSNR rises with the increase of \(\omega\) from 0.1 to 0.4 and reaches the maximum of 31.70 dB at \(\omega\) equal to 0.4; subsequently, the PSNR value slowly decreases to 31.51 dB with the increase of \(\omega\) from 0.4 to 0.6. Therefore, 0.4 is selected as the weight parameter of the loss function \(Loss_{DIP}\).