## 4 Results and Analysis
### Timeliness of The FSF  
Figure 4 shows the fusion results of the compared methods on the Pavia University dataset. When there are more black pixels in the error image, the fusion result is better. It is evident from the figure that NLSTF has the worst fusion result, and the error image contains a large number of white spots. The STEREO fusion result is also unsatisfactory, and the \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{3}{c}{**Pavia University**} \\ \hline Method & Parameters \\ \hline CSTF & \(W=400\); \(H=400\); S = 8; \(\lambda=1\times 10^{-6}\); \\ \hline Hysure & \(\lambda_{\_}m=1\times 10^{5}\); \(\lambda_{\_}{\_}{\text{{}^{\prime}}}\)\(\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{  \text{ \text{   \text{  }}}}}}}}}}}}}}}}} 1\) \\ \hline LTTR & K = 3900; \(\eta=0.002\); \\ \hline NLSTF & \(W=10\); \(H=10\); S = 14; \(\lambda=1\times 10^{-6}\); K = 151; \(\lambda_{\_}1=1\times 10^{-5}\); \(\lambda_{\_}2=1\times 10^{-5}\); \(\lambda_{\_}3=1\times 10^{-5}\); \\ \hline STEREO & s\_iter = 1; kernel\_length = 31; t\_rank = 40; maxit = 100; \(\lambda=1\times 10^{-4}\); \\ \hline NSSR & par.ro = 1.3; par.Iter = 30; par.K = 40; par.lambda = 1 \(\times 10^{-5}\); \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings on the Pavia University dataset. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{3}{c}{**CAVE**} \\ \hline Method & Parameters \\ \hline CSTF & \(W=400\); \(H=400\); S = 10; \(\lambda=1\times 10^{-5}\); \\ \hline Hysure & \(\lambda_{\_}m=1\times 10^{3}\); \(\lambda_{\_}{\text{{}^{\prime}}}\)\(\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{\text{ \text{ \text{ \texttext{ \texttext{  
error image contains many white pixel points. The main reason for the unsatisfactory fusion results of NLSTF and STEREO is that the downsampling factor influences the fusion effect of NLSTF and STEREO, and the larger the downsampling factor is, the worse the fusion effect is. The fusion quality of NSSR is usually closely related to the selection of endmembers, and the fusion quality of pixel points at the edges of endmembers is generally poor. Therefore, we can see that the error images of the fusion results obtained by the NSSR method also contain many noticeable white pixels. Among all the methods, only our proposed method, FSF, gives the best fusion results with the least number of white pixel points in the error image. Table 3 corresponds to the quantitative metrics of the fusion results of the competing approaches on the Pavia University dataset. Our proposed method achieves the best results in all metrics, and only the CSTF and Hysure methods achieve fusion results similar to ours when the time required for fusion is not taken into account. When considering the running time, CSTF and Hysure consume 289.643 s and 60.61 s, respectively, while our proposed method FSF takes only 0.26 s, consuming less than 0.1% of the time for CSTF and less than 1% that for Hysure. Aside from our FSF, the fastest algorithm is STEREO; this is because STEREO reduces the tensor calculation in three dimensions to a one-dimensional vector to calculate, which significantly improves the speed of fusion, but even STEREO takes 8.088 s.  
Figure 5 shows the fusion results of the compared methods on the CAVE dataset. Similarly, the NLSTF and STEREO methods obtained the worst fusion results due to the poor fusion of these two methods at 32\(\times\) super-resolution. Our FSF method still achieves better fusion results. Table 4 corresponds to the quantitative metrics of the fusion results of the competing approaches on the CAVE dataset. In terms of the quantitative evaluation metrics of fusion,