# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 5 Results and Analysis
### Hyperspectral Unmixing  
We selected a popular benchmark named \"Jasper Ridge\" as an example to qualitatively demonstrate the performance of the proposed hyperspectral unmixing method. It contained \(100\times 100\) pixels with bands ranging from 380 nm to 2500 nm. The spectral resolution was up to 9.46 nm. Channels 1-3, 108-112, 154-166, and 220-224 were removed, in order to eliminate water absorption and atmospheric effects. Finally, 198 bands remained, and there were four latent endmembers in this data: \"Water\", \"Tree\", \"Soil\", and \"Road\". The SLIC superpixels of the benchmark \"Jasper Ridge\" \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Data Sets** & **CURRITE** & **CHIKUSEI** & **INDIAN PINES** & **PAVIA** & **HOUSTON** \\ \hline Bands of ground truth images & 185 & 128 & 192 & 103 & 144 \\ Bands of conventional images & 16 & 8 & 16 & 4 & 4 \\ Size of ground truth images & 420 \(\times\) 360 & 540 \(\times\) 420 & 360 \(\times\) 360 & 560 \(\times\) 320 & 320 \(\times\) 540 \\ Size of hyperspectral images & 84 \(\times\) 72 & 90 \(\times\) 70 & 90 \(\times\) 90 & 70 \(\times\) 40 & 64 \(\times\) 108 \\ /Scale factor & /5 & /6 & /4 & /8 & /5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for the remote sensing data sets. are illustrated in Figure 3. The SLIC superpixels are shown in Figure 3a, whose shape and size are adaptive and related to the spectral similarity of the neighboring pixels. Figure 3b shows the ground truth spectral reflectances, while Figure 3c gives two examples that indicate pixels within a superpixel share similar spectral properties. The abundances were well estimated by the proposed method and were close to the ground truth. Figure 4 shows the estimated abundance. To verify the efficiency of the proposed Spatial Group Sparsity Regularization based unmixing (SGSU) algorithm, simulated experiments were performed. Synthetic HSIs with \(100\times 100\) pixels contained six endmembers. The endmembers were randomly selected from the USGS library and randomly distributed. The proposed unmixing was compared to that of several typical sparse-based unmixing algorithms, such as SUnSAL [38], CLSUnSAL [39], and SUnSAL-TV [40]. The synthetic data were formed by spectra randomly selected from the digital spectral library of the United States Geological Survey (USGS), which is available at: [[https://www.usgs.gov/labs/spec-lab](https://www.usgs.gov/labs/spec-lab)]([https://www.usgs.gov/labs/spec-lab](https://www.usgs.gov/labs/spec-lab)). We adopt two metrics to quantificationally evaluate the unmixing performance: the spectral angle difference (SAD) [41] and the root-mean-square error (RMSE) [41]. SAD and RMSE are typically used to evaluate the performance of hyperspectral unmixing. SAD is similar to SAM, as in Equation (20), but changes the input variable to endmembers. The input variable for RMSE is abundances. SAD was applied  
Figure 4: Estimated abundances. Figure 3: Illustration of SLIC superpixels. to evaluate the spectral angle between the estimated endmember and the ground truth endmember. RMSE is an evaluation metric for signal reconstruction, which represents the difference between the reconstructed signal and the original signal. Generally, smaller SAD and RMSE indicate better unmixing performance. We conducted a experiment with the simulated data to analyze the sensitivity of the proposed unmixing method with regard to different endmember numbers. The number of endmembers was varied from 3 to 18 with a step length of 3. As Figure 5 shows that the values of SAD and RMSE increase as the number of endmembers increases, which means the difficulty of the unmixing increases as the number of endmembers increases. Noise and outliers also have significant impacts on hyperspectral unmixing.