# Hyperspectral Image Super-Resolution Based on Spatial Group Sparsity Regularization Unmixing
## 5 Results and Analysis
### Hyperspectral Unmixing
To study how the level of noise affects the unmixing performance and prove the superiority of the proposed unmixing method, we added Gaussian white noise with a signal-to-noise ratio (SNR) varying from 5 db to 50 db, and compared the proposed SGSU with some classical unmixing methods. Figure 6 shows the SAD and RMSE values as a function of the SNR of Gaussian white noise. We can see, from Figure 6a, that the SAD of all methods decreased with the increase of SNR, which indicates that noise had a bad effect on the hyperspectral unmixing. However, the proposed unmixing method obtained the best RMSE in most conditions; Figure 6b indicates that the proposed unmixing  
A region of interest is magnified in each reconstructed image for better visual comparison. As can be seen from the magnified regions, Figure 6(c) shows that the reconstructed image had a good visual result and the same high spatial resolution as the RGB image. We also randomly selected three pixel points in the reconstructed image and the corresponding ground truth. The spectral responses of all the pixel points are shown in Figure 6(d), where the solid lines are related to the ground truth and the dashed lines are related to the reconstructed image. The mean square error (MSE) values of the reconstructed spectral reflectance and the ground truth reflectance are presented in colors corresponding to the curves. The MSE values are very small, indicating that the reconstructed data were close to the ground truth data. In fact, in addition to the three example pixel-points, the spectral reflectances of other pixels were also reconstructed with high accuracy. Overall, these results show that our method has an efficient reconstruction performance in both spatial and spectral domains. Figure 8 shows the estimated spectral reflectance of three randomly selected pixel points and their corresponding ground truths. The left image is the pseudo-color image of the super-resolution HSI of image1 in the \"Harvard\" data set. It has the same high spatial resolution as the input conventional image, which was presented in Figure 0(a). The estimated reflectance curves visually match the ground truth well. The MSE of the estimated reflectances and the ground truth were very small, which indicates that the spectrum was efficiently reconstructed. To compare our method with the other state-of-the-art methods, Figure 9 shows a visual comparison of all of the methods for image1 in the \"Harvard\" data set. For each sub-figure, the image on the top shows the super-resolution results of the corresponding methods in band 21 (620 nm) and image at the bottom is the error map, constructed by comparison with the ground truth. For ease of comparison, a region of interest is magnified in each reconstructed image. The smokestacks on the roof are highlighted by red squares. As we can see from Figure 8(b),c, the results of FUSE were more blurry than the ground truth, and the results of BSR had the worst error map. Figure 8(d)-h show that CSU, CMS, and LTTR get close visual results to our method. However, if we check the  
Figure 7: Super-resolution results of the proposed method with imgd2 of the Harvard database. region in the red square, the smokestack in the error map of sub-figure (g) is closer to zero than in (d), (e), and (f). This indicates that our method performed better in the reconstruction of detailed textures. Visual comparison by human eye is inevitably subjective and, therefore, quantitative objective evaluation is necessary. For objective comparison, we carried out all methods to construct high resolution hyperspectral images from the input low spatial resolution hyperspectral images and conventional images. All quality metrics mentioned in Section 4.1 were applied to the resulting images and corresponding ground truth images. In particular, the images in the \"Harvard\" data set are all ground-based hyperspectral images, which have similar spatial and spectral properties.