## 1 Introduction  
During acquisition and transmission, the quality of digital images inevitably degrades owing to corruption caused by various reasons. Therefore, the ability to recover a clean image from a noisy one is of great importance, and image denoising is a fundamental step applied in all image processing pipelines. In the computer vision field, image denoising has been a research hotspot since the 1990s. After decades of research, many denoising algorithms had achieved good results through approaches such as non-local self-similarityin natural images [1; 2; 3], low rankness-based models [4; 5], sparse representation-based models [3; 6; 7], and fuzzy (or neuro-fuzzy)-based models [8; 9]. Nevertheless, researchers are still aiming to further improve the performance of image denoising algorithms. Existing denoising algorithms can be roughly divided into internal algorithms and external algorithms [10]. Internal algorithms utilize the noisy image itself, while the external algorithms exploit clean, natural images related to the noisy image. Internal image denoising algorithms include filter algorithms, low rankness-based models, and sparse representation-based algorithms. Representative examples of filter algorithms are the non-local means (NLM) algorithm and the block-matching and 3D filtering (BM3D) algorithm. The NLM algorithm [1], proposed by [PERSON] et al. in 2005, exploited non-local self-similarity in natural images. It first finds similar patches and obtains their weighted average to achieve the denoised patches. Although it exhibits excellent performance, the NLM algorithm is limited by its inability to identify truly similar patches in a noisy environment. BM3D [2], a benchmark denoising algorithm, starts with the block-matching of each reference block, and obtains 3D arrays by grouping similar blocks together. The authors used a two-step algorithm to denoise an image. First, they denoised the input image simply and obtained a basic estimate; next, they achieved an improved denoising effect through collaborative filtering of the basic estimate. Among low rankness-based methods, nuclear norm minimization (NNM) and weighted nuclear norm minimization (WNNM) are two well-known algorithms. The NNM algorithm [4] was proposed by [PERSON] et al. for video denoising. In their work, the problem of removing noise was transformed into a low-rank matrix completion problem, which can be well solved by singular value decomposition. However, the authors equalized each singular value to ensure the convexity of the objective function, which severely restricts its capability and flexibility when dealing with denoising problems. Based on the NMM algorithm and proposed in [5], the WNNM algorithm takes advantage of the non-local self-similarity of the image for denoising. Among sparse representation-based algorithms, the K-singular value decomposition (K-SVD) algorithm, the learned simultaneous sparse coding (LSSC) algorithm, and the non-locally centralized sparse representation (NCSR) algorithm are three noteworthy algorithms. K-SVD [6] is a classic dictionary learning algorithm, which utilizes the sparsity and redundancy of over-complete learning dictionaries to produce high-quality denoising images. LSSC [3] exploits the combination of the self-similarity of image patches and sparse coding to further boost denoising performance. The NCSR [7] algorithm was proposed by [PERSON] et al. and utilizes non-local self-similarity and sparse representation of images. It introduces the concept of sparse coding noise with the goal of suppressing the sparse coding noise to denoise an image. In general, most of these traditional denoising methods use custom-made image priority and multiple, manually selected parameters, providing ample room for improvement. In recent years, deep learning-based methods have become a popular research direction in the field of image denoising. These methods can be categorized as external methods whose denoising performance is superior to internal methods.