# Weighted Group Sparse Regularized Tensor Decomposition for Hyperspectral Image Denoising
## 4 Experimental Results

Table 2: Results of removing noise from the Washington DC Mall dataset in different cases. Figure 4: Denoising results of case 4-2 on the Pavia City Center dataset. Figure 3: Denoising results of case 3-1 on the Pavia City Center dataset. Figure 5: Denoising results of case 5-1 on the Pavia City Center dataset. Figure 6: Denoising results of case 1-2 on the Washington DC Mall dataset. In addition, Figures 3 and 6 show the denoising results of the testing HSIs for case 1 and case 3, respectively. LRTRDGS, the method that is being proposed, demonstrates exceptional outcomes in terms of visual quality in comparison to the alternative methods. LRTRDGS showcases its ability to eliminate both Gaussian noise and impulse noise while simultaneously maintaining the fundamental structure of HSI. LRMR and TLR-\(L_{1-2}\)SSTV produce results with some noise. LRTV and LRTDGS can eliminate hyperspectral image noise, but some details may be lost in the process. For cases 2, 4 and 5, the focus is  
Figure 8: Denoising results of case 5-2 on the Washington DC Mall dataset. Figure 7: Denoising results of case 4-1 on the Washington DC Mall dataset. on evaluating the performance of deadline noise removal. Figures 4 and 5 depict the denoising outcomes obtained from the Pavia City Center dataset. Similarly, the denoising results for the Washington DC Mall dataset are shown in Figures 7 and 8. The proposed LRTRDGS method demonstrates its capability to effectively remove unexpected deadline noise while preserving the underlying HSI details. The results of LRTV and LRTDGS also show a small amount of deadline noise. Additionally, we present the values of PSNR-HVS and MSSIM for each frequency band in the Washington DC Mall simulation dataset case 3-1 (Figures 9 and 10) and case 5-1 (Figures 11 and 12). The results demonstrate that our proposed LRTRDGS method outperforms the other methods in terms of both PSNR-HVS and MSSIM. Specifically, when applied to two different hyperspectral images, the LRTRDGS method achieves superior results compared to the four other comparison methods. These findings suggest that tensor ring decomposition plays a positive role in denoising hyperspectral images. Our proposed LRTRDGS does not have an advantage in CPU time. This is because the tensor ring structure is slightly more complex, resulting in longer calculation times. Because of the use of tensor rings, our proposed method achieves better results in quantification (Tables 1 and 2) and visualization (Figures 6-12). In the LRTRDGS method, the selection of parameters determines the denoising results of the hyperspectral images. The parameters include the total variation regularization parameter \(\delta\), sparse noise regularization parameter \(\lambda_{1}\), Gaussian noise regularization parameter \(\lambda_{2}\), the rank of the tensor ring \(r=[r_{1}.r_{2},r_{3}]\), adjacent operator parameter \(\sigma\) and other parameters \(v_{1},v_{2},v_{3},v_{4},v_{5}\) and \(v_{6}\). Based on the simulation data of case 3 in the Washington DC Mall dataset, the influence of the parameters is discussed. The influence of the total variation regularization parameter \(\delta\) is shown below. Figure 13 shows the PSNR value for \(\delta\) values of 0.01, 0.05, 0.1, 0.5, 1 and 1.5. The results show that \(\delta=0.05\) has the best effect. Figure 11: PSNR-HVS of the different methods for each band of case 5-1 on the Washington DC Mall dataset. Figure 10: MSSIM of the different methods for each band of case 3-1 on the Washington DC Mall dataset. Figure 12: MSSIM of the different methods for each band of case 5-1 on the Washington DC Mall dataset. Figure 4:0 Influence of parameter \(\delta\). Here, we consider the influence of the sparse noise regularization parameter \(\lambda_{2}\). This parameter plays a role in limiting the sparsity of Gaussian noise. Figure 15 shows the PSNR values when \(\lambda_{2}\) is set to 100, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290 and 300. The results show that \(\lambda_{2}=210\) yields the best PSNR value.