# An Unsupervised Image Denoising Method Using a Nonconvex Low-Rank Model with TV Regularization
## 2 Related Work  
### Image Denoising Literature Review  
We divided the literature on image denoising into three types: traditional denoising, deep learning denoising, and RPCA denoising. Traditional denoising methods include spatial domain denoising methods [1] and transform domain denoising methods [7], which mostly appear in the early stages. For example, [PERSON] and [PERSON] [30] proposed a wavelet threshold denoising method; [PERSON] et al. proposed that the median filtering method was the most widely used method [31]; [PERSON] et al. [32] designed and used the LMMSE filter to improve the denoising effect by restoring image texture; and the antileakage least-squares spectral analysis proposed by [PERSON] [33] used the Fourier transform and least squares spectral analysis to process noise in seismic data. However, traditional denoising methods often face issues such as a high complexity and poor robustness. Deep learning denoising methods have been proposed in recent years. For instance, [PERSON] et al. [34] used a GAN to model the noise information extracted from real noisy images and completed denoising under the constraint of a correlation loss; [PERSON] et al. [35] designed a denoising method based on graphical convolution by introducing an edge attention mechanism and using a convolution operator. Deep learning denoising models typically face high computational costs and a large quantity of labeled data, whose unexplained nature makes denoising models less adaptable. RPCA achieves denoising with a new idea. In recent years, there have been a relatively large number of denoising works on RPCA. For example, [PERSON] et al. [36] proposed an improved RPCA method usinga penalty function. This method replaced the nuclear norm and L1-norm in the original RPCA with regularized and weighted versions of the penalty function, respectively, and built an improved model for medical image denoising. However, its convergence rate was slow and time-consuming, and the maximum effect of the low-rank recovery could not be brought into play. [PERSON] et al. (2019) proposed a nonconvex, local, low-rank, and sparse separation denoising method for hyperspectral images. This method focused on simultaneously developing a more accurate approximations to both rank- and columnwise sparsity for the low-rank and sparse components, respectively, and proved its effectiveness in denoising HSIs. Nonetheless, since hyperspectral images consist of many channels, this method is not suitable for grayscale images. [PERSON] et al. (2019) proposed a new denoising method based on nonlocal weighted robust principal component analysis (RPCA). They used the local similarity to build the objective function of RPCA and solved the problem by using an iterative log-thresholding algorithm to achieve the denoising function. This approach used the kernel norm and thus overpenalized large singular values, resulting in an increased error, which in turn led to poor image denoising. Moreover, the compressed sensing method is the inspiration for the RPCA method, which has also been studied in the domain of image denoising. For example, [PERSON] et al. (2019) proposed a compressed sensing method combining total variation regularization and the nonlocal self-similarity constraint for image denoising. This approach addressed the problem that reconstruction techniques often fail to preserve the texture of the image and significantly improved the denoising performance. In addition, several scholars have proposed methods that combine multimodal image fusion with sparse representation denoising. For instance, [PERSON] et al. (2019) proposed a novel multimodality image simultaneous denoising and fusion method. This method decomposed the noisy source image into cartoon and texture components and used the cartoon texture decomposition to separate the noise from the original image information. A sparse representation (SR) model based on a Gaussian scale mixture was proposed for the denoising and fusion of texture components.