# A Triple Deep Image Prior Model for Image Denoising Based on Mixed Priors and Noise Learning
## 4 Experiments
### Experimental Results  
#### 4.3.1 Grayscale Images Denoising  
To comprehensively verify the denoising effect of TripleDIP model, we conducted comparative experiments on Set12 and BSD68 grayscale image datasets, where we added Gaussian noise with a noise level of 12, 25 and 50. The two highest PSNR values and SSIM values are expressed in bold respectively. Table 5 lists the average PSNR and SSIM values of comparison methods on the Set12 dataset. Table 6 shows the PSNR and SSIM values on the BSD68 dataset. In addition, we use bar charts in Figures 5 and 6 to present the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Structure**} & \multicolumn{5}{c}{**Loss Function**} & \multicolumn{3}{c}{**Noisy Branch Input**} & \multirow{2}{*}{**Avg (dB)**} \\  & \(L_{DIP}\) & \(L_{Extenal}\) & \(L_{Internal}\) & \(L_{Mixed}\) & \(L_{Stability}\) & \(I_{Noisy}\) & \(z_{1}\) \\ \hline SingleDIP & ✓ & ✓ & & & & & & 31.56 \\ DoubleDIP1 & ✓ & ✓ & ✓ & & & & ✓ & 31.52 \\ DoubleDIP2 & ✓ & ✓ & ✓ & & & ✓ & & 31.53 \\ TripleDIP1 & ✓ & ✓ & ✓ & ✓ & ✓ & & ✓ & 31.53 \\ TripleDIP2 & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & & 31.55 \\ TripleDIP & ✓ & ✓ & ✓ & ✓ & ✓ & ✓ & & 31.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average PSNR results for different network structures. The checkmark means it was used in the loss function or network input. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\omega\) & **0.1** & **0.2** & **0.3** & **0.4** & **0.5** & **0.6** \\ \hline PSNR & 31.32 & 31.40 & 31.61 & 31.70 & 31.63 & 31.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average PSNR results for different weights of \(Loss_{DIP}\). results more intuitively. As shown in Table 5, our TripleDIP outperforms all the methods listed. Compared with BM3D and WNNM methods that only utilize internal image priors for denoising, TripleDIP improves the PSNR values by an average of 1.72 dB and 1.44 dB. Our method outperforms unsupervised methods such as DIP and N2V by an average of 2.79 dB and 2.68 dB. The unsupervised method utilizes only internal priors, whereas TripleDIP uses both internal and external priors to perform denoising. For the latest efficient denoising methods such as WINNet [45], BCDNet [46] and TripleDIP can show significant improvement by an average of 1.13 dB and 0.92 dB. Although SwinIR and Restormer have achieved SOTA results for many image tasks as an efficient Transformer-based model, TripleDIP is still superior to them by an average of 0.63 dB and 0.59 dB. From the observation of SSIM values, we can note the same improvement effect (i.e., better than BM3D, WNNM, and DIP by an average of 0.02, 0.01, and  
Compared with Set12, the BSD68 dataset contains more texture details, which is suitable for further verifying the model's robustness. As shown in Table 6, all denoising results have decreased to varying degrees. However, our model still achieved an apparent improvement over others. Specifically, the PSNR and SSIM values of our model outperform BM3D by 1.36 dB and 0.03, DIP by 2.54 dB and 0.04, N2V by 2.27 dB and 0.1, WINNet by 0.68 dB, BCDNet by 0.57 dB, SwinIR by 0.53 dB and 0.01, and Restormer by 0.53 dB respectively on average, which demonstrates that our model can significantly improve the overall reconstruction quality and structural similarity of images. We demonstrated that TripleDIP outperforms the currently popular SOTA model through experiments on two representative datasets. Compared with the unsupervised model, TripleDIP strengthens the model's capacity to repair most generic image contents by introducing external priors. For an efficient Transformer-based model, TripleDIP has a better complex detailed maintenance effect through DIP's image-specific network structure. Furthermore, two-branch noise learning enriches the learned noise while stabilizing the