## 4 Experiments and Performance Analysis
### Performance Evaluation  
The regularizers based on total variation are used to achieve joint spatial-spectral smoothing of reconstructed images and improve the anti-noise performance of the fusion method. To evaluate the anti-noise performance, the test results of three sets of SNRs are summarized in Tables 2 and 3 for two datasets, in which the boldface numbers denote the best performance (i.e., the highest RSNR/SSIM, or the lowest DD/SAM/RMSE/ERGAS). From the tables, we can observe that the proposed JSMV-CNMF outperforms the baseline methods for two datasets in three noise environments. The performance of the original CNMF algorithm decreases rapidly with the increase in noise, while the proposed JSMV-CNMF can significantly improve its performance. Especially, the results of the proposed JSMV-CNMF at low SNRs provide improvements of 43% on RMSE and 46% on spectral quality over the original CNMF for two datasets, which must be caused by the regularization used in this paper. For the Pavia University dataset in Table 2, the performance of the CSTF is second only to that of the proposed JSMV-CNMF and almost better than that of other baseline methods. For the Moffett dataset in Table 3, the BSR method achieves the second best performance in the low-SNR environment with the SNR set of 25 and 20 dB. This fully shows the validity of the regularization in the proposed method. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Methods** & & **CNMF** & **BSR** & **HySure** & **CSTF** & **Proposed** & **Ideal** \\ \hline \multirow{6}{*}{SNR(Ym) = 35 dB} & DD & 62.15 & 94.72 & 96.51 & 61.15 & **45.76** & 0 \\  & RSNR(dB) & 25.78 & 22.04 & 21.97 & 26.23 & **27.61** & \(+\infty\) \\  & RMSE & 96.38 & 148.24 & 149.49 & 91.52 & **78.11** & 0 \\  & SAM & 2.55 & 3.16 & 4.04 & 2.90 & **2.52** & 0 \\  & ERGAS & 1.38 & 2.07 & 2.10 & 1.30 & **1.13** & 0 \\  & SSIM & 0.97 & 0.96 & 0.96 & 0.97 & **0.98** & 1 \\ \hline \multirow{6}{*}{SNR(Ym) = 30 dB} & DD & 80.80 & 102.41 & 110.38 & 72.13 & **63.59** & 0 \\  & RSNR(dB) & 24.20 & 21.74 & 21.10 & 25.31 & **25.90** & \(+\infty\) \\  & RMSE & 115.63 & 153.56 & 165.24 & 101.74 & **95.05** & 0 \\  & SAM & 3.23 & 3.43 & 4.42 & 3.24 & **3.03** & 0 \\  & ERGAS & 1.59 & 2.13 & 2.24 & 1.44 & **1.35** & 0 \\  & SSIM & 0.96 & 0.95 & 0.95 & 0.96 & **0.97** & 1 \\ \hline \multirow{6}{*}{SNR(Ym) = 25 dB} & DD & 152.02 & 119.75 & 138.96 & 114.90 & **92.19** & 0 \\  & RSNR(dB) & 18.64 & 20.73 & 19.36 & 21.78 & **23.46** & \(+\infty\) \\ \cline{1-1}  & RMSE & 219.22 & 172.35 & 201.77 & 152.74 & **125.83** & 0 \\ \cline{1-1}  & SAM & 7.23 & 3.95 & 5.49 & 5.13 & **3.93** & 0 \\ \cline{1-1}  & ERGAS & 2.59 & 2.37 & 2.63 & 2.15 & **1.69** & 0 \\ \cline{1-1}  & SSIM & 0.87 & 0.93 & 0.91 & 0.91 & **0.94** & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of fusion algorithms for Pavia University dataset (the boldface numbers denote the best performance). Figure 7: The reconstructed images by such fusion methods as (**a**) CNMF, (**b**) BSR, (**c**) HySure, (**d**) CSTF and (**e**) JSMV-CNMF for (top row) Pavia University and (bottom row) Moffett datasets, respectively. To further study the performance of the methods in terms of spectral bands (wavelength), we drew the RSNR and RMSE curves w.r.t. wavelength in the environment, wherein the set of SNRs is 25 and 20 dB for two datasets in Figure 8. One can see that the proposed JSMV-CNMF yields better performance than all the baseline methods for the Pavia University and Moffett datasets, except for a small range of wavelengths, i.e., 750 to 850 nm, in the Pavia University dataset. In addition, from the perspective of smoothness, the curves of the JSMV-CNMF and BSR algorithms are relatively smooth, owing to good anti-noise performance, while the other three methods fluctuate violently because of their sensitivity to noise. In summary, the JSMV-CNMF algorithm can significantly improve the performance of CNMF, which fully verifies the effectiveness of the joint spatial-spectral smoothing regularization.