# A Triple Deep Image Prior Model for Image Denoising Based on Mixed Priors and Noise Learning
## 1 Introduction
[33] proposed the Neighbor2 Neighbor denoising model, which introduced the strategy of a random neighbor sub-sampler to produce noisy image pairs for training. Thus, Neighbor2 Neighbor further decreases the acquisition difficulty of training images in the unsupervised model. However, the sampling operation will reduce the image resolution, and result in the degradation of the denoising effect. Meanwhile, Neighbor2 Neighbor is also unsuitable for dealing with spatially-correlated noise and extremely dark images. Although the unsupervised methods no longer depend on numerous distortion-free images compared with the supervised approach, they still require several noisy images pairs for training to achieve desired denoising performance. Therefore, these methods still have significant limitations in practical application. Compared to most learning-based methods that learn realistic image priors from numerous data, the deep image prior (DIP) presented by [PERSON] et al. [34] has shown that plenty of image statistics can be implicitly captured by a suitable network architecture like U-Net [35]. Therefore, the DIP can be trained using a single degraded image with random initialization of the parameters through gradient descent, significantly decreasing the requirements on massive training data. However, there is still a gap regarding the DIP's denoising performance. This can be attributed to the substantial reliance on internal priors, insufficient constraints, and a fixed number of stopped iterations. First, reliance only on the internal priors results in the model's denoising performance depend on the target image's quality. When confronted with poor self-similarity or high-noise images, DIP cannot fully exploit its advantages. Second, DIP only uses a mean square error (MSE) between network output and noisy image to optimize the network parameters, which cannot adequately guide the model's denoising process. Finally, most of the DIP's iterations are based on empirical values obtained from extensive experiments, which cannot accurately determine when the model's iterative process stops. To address the above issues, we propose a Triple Deep Image Prior model for image denoising based on internal and external mixed priors and two-branch independent noise learning, called TripleDIP. Specifically, we first utilize the effective and efficient Restformer model to obtain the preprocessed image with rich external priors. Subsequently, we introduce a DIP branch to learn the image content and two DIP branches to learn the image noise independently. To evaluate the proposed TripleDIP, we experimented with two common datasets. The experimental results demonstrate that the denoising effect of our TripleDIP significantly outperforms the original DIP model, and the unsupervised models and exceeds that of some efficient supervised models. The main contributions of this study are as follows:  
(1) We construct a novel triple branch network architecture to improve the denoising performance of DIP. Regarding single branch image content learning, random initialization and single constraint usually result in low quality in the DIP's output. Therefore, we introduce noise learning to maintain the structural information of the images and provide more noise detail. We caused the learned noise to be more stable by utilizing two branches to generate noise independently. Thus, TripleDIP can generate rich noise components more stably and produce satisfying output with content learning. (2) Based on the supervised denoising model, we introduce high-quality preprocessed images as external prior. The introduction of external priors limits the range of network output solutions and effectively prevents DIP from overfitting noisy images. In addition, the internal and external mixed priors compensates for the lack of perception of general image information in traditional DIP while preventing model performance from being constrained by the low-quality target image. This significantly enhances the denoising effect of DIP.