# Weighted Group Sparse Regularized Tensor Decomposition for Hyperspectral Image Denoising
## 1 Introduction
This means that data stored in a tensor ring are more secure than data stored in stationary locations. The total variational (TV) regularization method was first proposed by [PERSON] et al. [24]. This technology effectively preserves the spatial sparsity and smoothness of images, making it applicable in various image processing tasks, like denoising, magnetic resonance and superresolution. [PERSON] et al. proposed total variational regularized low-rank matrix decomposition (LRTV) [25]. [PERSON] et al. proposed a spectral-spatial total variational regularization (SSTV) method to construct a smooth structure in the spectral and spatial domains [17]. [PERSON] et al. also presented the method of local low-rank matrix recovery, known as spatial-spectral total variance regularization (LLRSSTV), which aims to effectively exploit the total variance nature of the variance in each direction of hyperspectral images for reorganizing the local low-rank patches [26]. However, most of the methods utilize one-norm constraints on the spatial difference images to promote structural segmentation smoothing. To address the issue of the ineffective depiction of the group sparse structure within the spectral dimensional spatial difference image, [PERSON] et al. introduced a novel approach for hyperspectral image recovery. This technique employs weighted group sparsity-regularized low-rank tensor decomposition to overcome the limitation of the one-norm [16]. In light of the preceding discussion, we present a novel approach for enhancing hyperspectral image quality through the utilization of weighted group sparsity-regularized low-rank tensor ring decomposition (LRTRDGS). The method combines the advantages of tensor ring decomposition and weighted group sparse regularization. A symmetric alternating direction of multipliers method with a proximity point operator is used to solve our proposed model. This paper focuses on the following main topics:  
1. Utilizing the global spatial and spectral correlation among hyperspectral images, the tensor ring decomposition technique is employed to segregate unpolluted hyperspectral images from raw observations that have been tainted with intricate noise. 2. Due to the fact that the gradient components in smooth areas of hyperspectral images typically exhibit a complete absence (a value of zero) in the spectral dimension, the gradient components in edge regions demonstrate non-zero values. Hence, to address this discrepancy, we incorporate a regularization term, with the group sparsity weighted, into the framework of tensor ring decomposition. It can explore the group structure of spatially differential images along the spectral dimension. 3. A symmetric alternating direction method multiplier is employed to solve the model of the low-rank tensor ring decomposition with regularization on weighted group sparsity. To enhance the efficiency of this method, a proximity point operator is incorporated. Through numerical experiments, it has been determined that this approach outperforms other commonly utilized methods in terms of both quantitative evaluation and visual comparison. The structure of this paper is as follows. Several notations are presented, and the tensor ring is defined in Section 2. Section 3 proposes a hyperspectral image denoising model based on weighted group sparse regularized tensor ring decomposition and presents the model solving method. In Section 4, we present the experimental results for the simulated data and discuss the parametric analysis and convergence analysis. We summarize the proposed method in Section 5.