# A Masked-Pre-Training-Based Fast Deep Image Prior Denoising Model
## 1 Introduction  
Image noise has a negative impact not only on image quality but also on subsequent high-level visual tasks. These tasks encompass image segmentation [1; 2], classification [3; 4], super-resolution [5; 6], and low-light enhancement [7; 8]. Consequently, researchers have been engaged in addressing the longstanding challenge of image denoising in the field of image processing for decades. Traditional denoising algorithms, such as Block Matching and 3D Filtering (BM3D) [9], Non-Local Mean Filter (NLM) [10], Non-Local Centralized Sparse Representation (NCSR) [11], and Weighted Nuclear Norm Minimization (WNNM) [12], utilize a variety of approaches for noise reduction. Specifically, the key principle underlyingNon-Local Means (NLMs) is the identification of image patches similar to the area around the current pixel. NLM computes the similarities between these patches and the target area, and then leverages these similarity measures to weight the pixels in the patches, ultimately averaging them to produce the denoised pixel value. Spatial domain denoising algorithms like NLM determine new pixel values by analyzing the relationships among pixels within a certain window surrounding the central pixel. BM3D and other transformation domain denoising algorithms process the image by first applying transformations (such as Fourier or orthogonal transformations), then denoising in the transformed domain, and finally reconstructing the denoised image through an inverse transformation. These algorithms, which operate in the transformation domain, stand in contrast to spatial domain denoising approaches. Sparse representation-based denoising algorithms, exemplified by NCSR, capitalize on the observation that an undistorted image can be sparsely represented, whereas noise cannot. These methods endeavor to find an optimal dictionary to represent the denoised image, thereby effectively removing noise from the original data [13]. The image denoising algorithms based on low rank treat the image as a matrix and utilize the property that undistorted images are of low rank, unlike noise. [PERSON] et al. 's WNNM denoising algorithm is based on this principle of exploiting the low-rank characteristics of images. However, these traditional methods heavily rely on inherent image information and manually crafted priors. They typically require complex optimization algorithms to achieve satisfactory results, thereby incurring substantial computational costs. In contrast, Deep Neural Networks (DNNs) over the past decade have exhibited significant advantages in image denoising due to their learning capabilities and nonlinear mapping abilities. The Denoising Convolutional Neural Network (DrCNN) [14], which is rooted in Convolutional Neural Networks (CNNs), marks a series of advancements. Through the integration of intricate network architectures, residual learning, and batch normalization, the DrCNN model notably boosts the denoising efficacy. Nevertheless, the DrCNN model exhibits certain constraints in addressing noise images with unknown noise levels, prompting the necessity for training multiple denoising models to ensure practical noise reduction effectiveness. To address this concern, [PERSON] et al. further refined the model, introducing a Fast and Flexible Denoising Convolutional Neural Network (FFDNet) [15]. This innovation, building upon the foundation of the DrCNN model, incorporates a noise level map as an additional input, thereby augmenting the model's adaptability to diverse noise levels. Additionally, the Dilated Residual UNet (DRUNet) denoising model [16] combines residual learning with the UNet structure and incorporates a noise level map. This approach improves flexibility in handling different noise levels and outperforms most CNN models regarding denoising efficiency. However, DRUNet requires extensive training time and its performance is limited under extremely low Signal-to-Noise Ratio (SNR) conditions and complex real-world noise interference.