# A Triple Deep Image Prior Model for Image Denoising Based on Mixed Priors and Noise Learning
## 1 Introduction
[28] proposed a Transformer-based model called SwinIR for image restoration, which achieved local attention and cross-window interaction by introducing the residual Swin Transformer blocks (RSTB) [29]. Moreover, SwinIR achieved satisfying results with fewer parameters through the attention mechanism and network design. Although the Transformer model has a global receptive field, its computational efficiency increases quadratically with the image resolution. To decrease the computational overhead, [PERSON] et al. [30] proposed the Restormer model for multi-scale local-global representation learning. The MDTA (multi-Dconv head transposed attention) applies self-attention layers across channels to create an attention map, significantly reducing the computation cost while maintaining the global learning ability. Meanwhile, the design of the GDFN (gated-Dconv feed-forward network) suppress less informative features and increases the model's denoising efficiency. The combination of MDTA and GDFN allows attention-based denoisers to function sufficiently with high-resolution images. Although the existing supervised learning models exhibit excellent performance in denoising, their performance often deteriorates when processing images distinct from training datasets, and the model's generalization ability still requires improvement. Meanwhile, data dependence problems generally exist in supervised models, which require significant noisy-clean image pairs to enhance their general denoising ability. However, the acquisition of clear images is challenging. In the image acquisition process, noise is usually introduced due to the material characteristics of the sensor; in the transmission process, quality degradation will occur because of transmission media and recording equipment. Furthermore, in medical image denoising, acquiring substantial training images involves exposing the human body to high doses of radiation, which is unethical. In conclusion, data dependence results in training data significantly affecting the denoising performance of supervised models, which causes them to lack robust generalization ability and be unable to repair fine details according to specific images, thus limiting the practicability of supervised models. Considering the dependence of supervised models on massive training data, the unsupervised methods, which use single noisy images for training, are more prevalent in some fields. For instance, [PERSON] et al. [31] introduced a point estimation procedure from a statistical perspective and proposed the Noise2 Noise (N2N) denoising model, which suggested that models can be trained with only the corrupted image pairs for different noise distributions. The N2N significantly reduces the practical training process by mitigating requirements on the availability of clean images. However, the model still requires significant pairs of noisy images to improve its denoising effect, and the collection of noisy image pairs with a constant signal is only feasible for static scenes, which limits the practical application of N2N. Inspired by the N2N, [PERSON] et al. [32] proposed a self-supervised training strategy called Noise2 Void (N2V) that further overcomes the dependence on noisy image pairs. Based on two statistical assumptions: every pixel in the image is conditionally related to adjacent pixels, and the noise is independent of the pixels. [PERSON] et al. innovatively proposed the blind-point network to understand the mapping relationship between the adjacent and center pixels in a pixel block. Considering the center pixel as the model's learning target, the N2V prevents the model from becoming the identical map of a single pixel and reduces the restriction that training images only derive from the same scene in N2N. However, limited by the previous assumptions, the model has unsatisfactory performance on the noisy image where the adjacent pixels and noise are correlated. Subsequently, [PERSON] et al.