## 4 Experiments and Performance Analysis
### Parameter Settings  
This article focuses on joint spatial-spectral smoothing in a minimum-volume simplex for hyperspectral image super-resolution, which is performed by incorporating four regularizers with the corresponding weights into the original CNMF method. The parameters, including \(\lambda_{a}\), \(\lambda_{e}\), \(\lambda_{h}\) and \(\lambda_{s}\) are to balance data fidelity terms and regularizers [32, 51], which are relevant to the noise powers  
Figure 5: Display of (top row) the reference images and (bottom row) observed hyperspectral images (HSIs) for the two datasets; i.e., (**a**) Pavia University and (**b**) Moffett. of HSIs and MSIs. For simplicity, all the weights in this article were set to the same value 0.001, i.e., \(\lambda_{a}=\lambda_{e}=\lambda_{h}=\lambda_{s}=\) 0.001, although the settings of these parameters deserve further study. The convergence of the proposed algorithm can be guaranteed by the threshold value and the iteration number of inner and outer loops. The stopping rule of the outer loop is that the relative difference threshold value between the successive updates of the objective function \(\mathbf{F}_{0}(\mathbf{A},\mathbf{S})\) is set to 0.001 [51]; that is,  
\[\frac{\mathbf{F}_{0}(\mathbf{A}^{k+1},\mathbf{S}^{k+1})-\mathbf{F}_{0}( \mathbf{A}^{k},\mathbf{S}^{k})}{\mathbf{F}_{0}(\mathbf{A}^{k},\mathbf{S}^{k})} \leq 0.001. \tag{25}\]  
Moreover, the experimental tests show that Algorithm 3 generally converges within 15 steps, which is faster than Algorithm 2 in iterating 50 steps. Considering the relation between inner and outer loops, the inner iterations need not run exhaustively to reach the stopping condition of (25), because varying the number of iterations will not have much effect on the convergence performance [51]. Thus, the iteration numbers of two ADMM-based inner loops are set to 30 [51], respectively. Therefore, the predefined stopping rule of two inner loops is that each algorithm run until it converges or iterates 30 times. That is, Algorithms 2 and 3 will stop if one of the convergence condition or the number of iterations is satisfied. Assume that the observed data \(\mathbf{Y}_{m}\) and \(\mathbf{Y}_{h}\) are corrupted by additive Gaussian white noise with three different sets of SNRs, in which the first set is 40 and 35 dB, the second set is 30 and 30 dB, and the third set is 25 and 20 dB. The parameter \(N\) denotes the number of endmembers, which can be estimated by virtual dimensionality algorithm [54; 55] as four and 10 for datasets, respectively. The spectral-unmixing-based CNMF has a property that the performance can remain stable as long as the number of endmembers is set larger than the ground truth [25]. To verify the robustness of \(N\), the performance of two CNMF-based algorithms is estimated with the change of \(N\), as shown in Figure 6. One can observe that the proposed JSMV-CNMF performs better than the original CNMF methods. When the value of \(N\) is very small, the performances of both algorithms decrease to different degrees. However, with the increase in \(N\), the performances of two algorithms tend to be stable, although there are slight fluctuations. But setting \(N>10\) does not significantly improve the performance of the algorithm, which indicates that the parameter is robust. Without loss of generality, the number of endmembers \(N\) is set to 10 in the experiments. With the above parameter settings, the reconstructed images by the proposed JSMV-CNMF and the baseline methods for two real datasets are displayed in Figure 7. From the figure, one can see that the reconstructed images are very similar to the reference image in Figure 5 for each dataset, but the spatial resolution is much higher than that of the observed image. Although the performance differences of these fusion algorithms are difficult to distinguish visually in the reconstructed images, they can be identified from the tables and curves.