## 1 Introduction
The main idea is to collect a large number of noise-clean image pairs, and then train the deep neural network denoiser using end-to-end learning. These methods have significant advantages in accumulating knowledge from big datasets; thus, they can achieve superior denoising performance. In 2017, [PERSON] et al. proposed Deep CNN (DnCNN) [11], which exploited the residual learning strategy to remove noise. They introduced the batch normalization technique as it not only reduced the training time, but also boosted the denoising effect quantitatively and qualitatively. However, it is only effective when the noise level is within a pre-set range. Hence, [PERSON] et al. proposed FFDNet in [12]. FFDNet showed considerable improvement in flexibility and robustness using a single network. Specifically, it was formulated as \(x=F(y,M;\Theta)\), where \(x\) is the expected output, \(y\) is the input noise observation, and \(M\) is a noise level map. In the DnCNN model \(x=F(y;\Theta)\), the parameters \(\Theta\) change with the noise level. As for the FFDNet model, \(M\) is modeled as the input and the hyper-parameters have no relationship to the noise level. Therefore, it could handle different noise levelsin a flexible manner using a single network. The consensus neural network (CsNet) was proposed by [PERSON] et al. [13], and combines multiple relatively weak image denoisers to produce a satisfactory result. CsNet exhibits superior performance in three aspects: solving the noise level mismatch, incorporating denoisers for different image classes, and uniting different denoiser types. In summary, these supervised denoising networks are exceedingly effective when supplied with plenty of noise-clean image pairs for training, but collecting clean images of the ground truth in many real-world scenarios is very difficult. Moreover, if the image priors are significantly different from the image to be denoised, the supervised denoising networks tend to produce hallucination-like effects when handling an unseen noisy image, because the previously learned image statistics cannot handle the untouched image content and noise level well. These networks have strong data dependence [14], leading to a lack of flexibility. To overcome the aforementioned limitations, researchers have focused on training unsupervised denoising networks without training images. Recently, research on generative networks using the deep image prior (DIP) framework [15] demonstrated that even if only the input image itself is used in training, deep convolutional neural networks (CNNs) can still provide superior performance on various inverse problems. No prior training is required, and random noise is used as the network input to generate denoised images. It can be widely used in image noise reduction, super-resolution, and other image restoration problems. Because the hyper-parameters of DIP are determined based on the specific noisy image, it may, in some cases, achieve better denoising results than the supervised denoising models. As shown in Figure 1, although the general denoising performance of DIP is inferior to that of DnCNN, we can still find some local details, such as the magnified part of the images, that DIP can preserve more accurately as compared with DnCNN. The reason is that the prior knowledge captured by DnCNN cannot handle the subtle information that DIP can. DIP performs the inference by stopping the training early. However, in the original DIP model, the early stopping point is set as a fixed number of iterations using experimental data, so the result is not always optimal. Furthermore, the noisy image is used as the target image that provides poor guidance and leads to slow convergence of the generative network. Thus, the denoising performance of DIP is much lower than that of deep learning in some cases, and it still leaves room for improvement.