# A Nested UNet Based on Multi-Scale Feature Extraction for Mixed Gaussian-Impulse Removal
## 1 Introduction  
Digital images have found extensive applications in various fields, including medical imaging, remote sensing, and semantic segmentation [1]. However, images captured by cameras often suffer from mixed noise, which degrades image quality and affects subsequent computer vision tasks [2]. For example, hyperspectral images commonly exhibit a combination of additive white Gaussian noise (AWGN) and Poisson noise, while computed tomography images and complementary DNA microarray images experience a mixture of AWGN and impulse noise (IN) [3]. As a result, the removal of mixed noise has become a critical and challenging problem that requires further investigation. In recent years, researchers have proposed many effective methods for removing combined AWGN and IN. Since IN only affects some of an image's pixel values [4], early methods for mixed noise removal typically adopted a two-stage approach, where IN is first suppressed and then AWGN is removed. [PERSON] et al. [5] introduced the rank-ordered absolute differences method for IN detection and integrated it into the bilateral filter framework [6], which performs adaptive image denoising for both AWGN and IN. [PERSON] et al. [7] employed a variational framework with a \(l_{1}\) data fidelity term and the Mumford-Shah regularization term to remove mixed noise from images. However, this method, while preserving some edge properties, may lead to image oversmoothing as it only considers local image information. To address this, [PERSON] et al. [8] proposed a \(l_{1}-l_{0}\)double-sparsity regularization-based method. They used the \(l_{1}\) term to remove IN and introduced the \(l_{0}\) term in an improved K-SVD algorithm to suppress residual noise after IN detection. [PERSON] et al. [9] developed a generalized weighted \(l_{2}-l_{0}\) method for AWGN-IN removal based on maximum likelihood estimation and sparse representation. [PERSON] et al. [10] integrated the image sparse prior and non-local similar prior into a non-local sparse regularization term and proposed the weighted encoding with sparse nonlocal regularization (WESNR) method. Furthermore, [PERSON] et al. [11] considered both the non-local self-similarity and low-rank properties of natural images and proposed a Laplace scale mixture combined with a non-local low-rank regularization (LSLR) model. In the domain of hyperspectral images, [PERSON] et al. [12] proposed a method called FastHyMix, which estimates mixed noise by exploiting its high spectral correlation. This method enhances the accuracy of mixed noise estimation by utilizing a neural denoising network to learn image priors. [PERSON] et al. [13] proposed a mixed noise removal method that combines a deterministic low-rank prior with an implicit regularization scheme. This method approximates the low-rank prior of the image using the matrix logarithm norm and utilizes an implicit regularizer to preserve image details. Deep learning has emerged as a promising approach for removing mixed noise due to its ability to adapt to complex data and establish relationships between noisy and clean images. Compared to traditional denoising methods, deep learning relies on large amounts of training data to learn stable nonlinear mappings, making it a data-driven approach. Several deep learning-based methods have been proposed for mixed noise removal. [PERSON] et al. [14] proposed a transfer learning approach called TL-CNN, which uses a convolutional neural network (CNN) to learn an end-to-end mapping from noisy to clean images. [PERSON] et al. [15] introduced a blind denoising method called BDCNN, which is entirely based on a CNN. The network structure of BDCNN consists of 50 convolution (Conv) blocks, with the first 25 blocks used for IN removal and the last 25 blocks used for AWGN removal. [PERSON] et al. [16] incorporated a CNN regularizer into a traditional model-based variational approach, resulting in VA-CNN. VA-CNN utilizes the CNN-learned natural image prior to improve the variational method's accuracy in estimating noise parameters. [PERSON] et al.