# A Triple Deep Image Prior Model for Image Denoising Based on Mixed Priors and Noise Learning
## 5 Conclusions  
In this study, we proposed a novel denoising model called TripleDIP using the strategies of internal and external mixed priors and two-branch independent noise learning. Compared with the DIP which only uses internal prior information, we utilized the Restormer model to generate external priors before denoising, and the introduction of internal and external mixed priors significantly improved the quality of the target image. Additionally, Restormer, a supervised model based on the Transformer, has excellent general denoising capabilities, while DIP as an unsupervised model, can restore local details of a particular image well. Mixed priors enhance the denoising performance of the model in a complementary manner. For two-branch noise learning, the designed loss function realizes the independent generation of noise towards the same target, ensuring the stability of noise learning while enhancing the constraints on the content learning branch. The automatic stopping criterion we proposed effectively prevents overfitting and improves the execution efficiency. The experimental results demonstrate that the proposed TripleDIP method is far superior to the original DIP method, outperforms the mainstream unsupervised denoising models, and even surpasses the recently proposed supervised models on the two synthetic datasets, thus demonstrating the efficacy of internal and external mixed priors and two-branch noise learning.  
Although the denoising performance of TripleDIP has been significantly improved over the original DIP model, it still endures long execution time and high computational load due to the simultaneous operation of three DIP subnetworks. The on-line training method is not suitable for some time-critical applications. There are two possible directions for future research: (1) Utilizing the model agnostic meta-learning method (MAML) [52] to compress execution time without losing the effectiveness. The network parameters of TripleDIP produced by random initialization require several thousand iterations to obtain desirable results. We can utilize the MAML to get a better initialization. In this way, TripleDIP can significantly reduce the required number of iterations. (2) Finding better stopping criterions. As can be seen from Figure 3, the stopping criterion can not only prevent overfitting but also effectively reduce the number of iterations. We can combine this with other methods such as the early stopping (ES) method [38] to optimize execution efficiency.  
Conceptualization, Y.H. ([PERSON]) and S.X.; methodology, S.X.; software, X.C.; validation, [PERSON] ([PERSON]), C.Z. and [PERSON]. ([PERSON]); formal analysis, [PERSON] ([PERSON]) and S.X.; investigation, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); resources, S.X. and Y.H. ([PERSON]); data curation, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); writing initial draft preparation, [PERSON] ([PERSON]); review and editing, [PERSON] ([PERSON]), X.C. and S.X.; visualization, X.C. and Y.H. ([PERSON]); supervision, S.X. and Y.H. ([PERSON]); project administration, S.X.; funding acquisition, S.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of China, grant number 62162043; Jiangxi Postgraduate Innovation Special Fund Project, grant number YC2022-s033.  
Not applicable.  
After our paper was published, we will provide the data and material upon request to allow the reported experiments to be more easily reproduced.  
The authors would like to acknowledge the reviewers and AE for their constructive comments and suggestions that helped to improve the paper's quality.  
The authors declare no conflict of interest.