# A Masked-Pre-Training-Based Fast Deep Image Prior Denoising Model
## 2 Related Work  
### Deep Image Prior  
To address the limited generalization capabilities in supervised denoising models due to biased data, the DIP denoising model effectively completes the denoising task using only a single noisy image. Leveraging the implicit feature extraction capabilities of deep learning and the prior knowledge embedded in the input noisy image, the DIP model transforms the denoising process into an optimization task focused on finding the optimal network parameters. The DIP model employs an encoder-decoder architecture similar to a U-net, where the input image undergoes multiple downsampling and upsampling operations for feature extraction. The input tensor \(z\) for the DIP model has the same spatial resolution as the output of the network, \(f_{\theta}(z)\), which typically has a fully convolutional architecture. The spatial dimensions of the input are represented as \(R^{\mathbb{C}\times W\times H}\), where \(R\) represents the range of pixel intensity values, \(C\) indicates the number of input channels,and \(W\) and \(H\) correspond to width and height, respectively. Additionally, the network uses skip connections to concatenate features of varying scales before feeding them into the next processing module. It primarily utilizes a residual learning approach, where a residual connection at the end adds the output back to the noisy input image to produce the final denoised image. In terms of the convolutional architecture, the DIP uses various kernel sizes to process the input images through the network, commonly employing sizes such as 3 \(\times\) 3 or 5 \(\times\) 5 depending on the specific layer and setup. This optimization is conducted through an online unsupervised training approach, where the process of optimizing network parameters can be described as follows:  
\[(\hat{\theta})=\arg\min_{\theta}E(f_{\theta}(z);y),\quad\hat{x}=f_{\theta}(z) \tag{1}\]  
where \(\hat{x}\) represents the denoised image, \(y\) denotes the noisy input image, \(\theta\) denotes the network parameters, and \(z\) represents a randomly generated network input; the loss function \(E\) is defined as either the L1 or L2 distance between the network's output image, \(f_{\theta}(z)\), and the noisy image \(y\), which serves as the target image. The denoising process of the DIP model (i.e., the online training process) essentially establishes a complex nonlinear mapping between the random input tensor \(z\) and the target noisy image. Starting with random initialization, the model parameters are iteratively updated via a training method that minimizes the loss function, thereby generating a reconstructed image highly similar to the noisy image. As illustrated in Figure 1, the DIP model typically employs a UNet architecture as its backbone network. Theoretically, after infinite iterations of training, the model's output would converge towards the target image, failing to achieve the denoising task. However, the DIP model, trained in an unsupervised manner, exhibits characteristic noise repulsion. This trait optimizes the model's output (the reconstructed image) to the low-frequency signals of the noisy image. Consequently, by employing the early stopping technique, training is halted after a certain number of iterations, at which point the model's output is considered the denoising result. Compared to mainstream supervised denoising models, the DIP denoising model offers a key advantage with its unsupervised training mode, which allows for precise fine-tuning of the output image. This capability is particularly beneficial in scenarios with limited training data, showcasing a robust generalization ability. However, the  
Figure 1: DIP network architecture. DIP is based on a decoder–encoder architecture, adding skip connections between corresponding layers of the encoder and decoder to minimize losses caused by upsampling and downsampling. In particular, the blue arrows indicate downsampling, the orange arrows represent upsampling, and the yellow arrows denote skip connections.