# Hyperspectral Super-Resolution Technique Using Histogram Matching and Endmember Optimization
## 4 Experiment
### Proposed Method Evaluation  
To test the performance of the proposed algorithm under a condition in which a mismatch between a low-resolution image and a high-resolution image is significant, the original HSIs were edited in two ways. To construct the first dataset, the upper left corner of the original HSIs was cut off for the specific number of pixels, increasing in 20-unit increments from 20 to 100 pixels, as represented in Figure 5a. For the second dataset, an affine transformation was applied, as displayed in Figure 5b, to make horizontally sheared images from the pixels not cut off from the original images. The affine matrix for the shear transformation used in this research was:  
\[\left[ \begin{array}{ccc}1&C_{x}&0\\ 0&1&0\\ 0&0&0\end{array} \right] \tag{11}\]  
The numbers used for the constants \(C_{x}\) in the shear transformation matrix are listed in Table 3.  
We ran our method with the maximum number of endmembers set to p = 10, which is sufficient for both datasets. The inner loops of optimization steps (8a) and (8b) were run for 5000 iterations. Operation times depended on the image size and the number of iterations. For a \(1392\times 1040\) pixel  
Figure 4: Example of a per-pixel RMSE (root–mean–square error) image from the Harvard dataset [34]: (**a**) Image where translation is applied by cutting off and (**b**) an image in which the histogram is not matched with that of an RGB image. Figure 5: Example of pixel mismatch representation using (**a**) cutting off (\(P_{n}\) indicates the number of pixels cut off from the left and upper sides) and (**b**) shear transformation. image with 31 channels, it took \(\sim\)660 s on a single Intel i7-7700, operating at 3.60 GHz with GPU computation on a GTX 1080 Ti (11 GB). The ratio between low-resolution image and high-resolution image is set to 1:8. Table 3 compares the average and median RMSE and SAM values by the method of [PERSON] et al. (2018), with those by the proposed method for the eight cases, using images with and without geometric transformation. For all of the experimental cases, the color difference is applied. For the ideal images without any transformation, the method of [PERSON] et al. (2018) shows slightly lower RMSE and SAM values than the proposed method. If any transformation is applied to the images, however, the method of [PERSON] et al. (2018) results in significantly increased errors. With the small shear deformation (\(C_{x}=0.1\)), the average RMSE and SAM values increase from 2.68 to 9.79, and 5.58 to 7.16, respectively. With the small cut-off of images (\(P_{n}=20\)), the average RMSE and SAM values increase from 2.68 to 9.12, and 5.58 to 6.71, respectively. On the other hand, the proposed method results in slightly increased errors with the transformation. With the small shear deformation (\(C_{x}=0.1\)), the average RMSE and SAM values increase from 2.68 to 3.64, and 6.69 to 6.73, respectively. With the small cut-off of images (\(P_{n}=20\)), the average RMSE values increase from 2.68 to 3.56, and the average SAM values change negligibly, from 6.69 to 6.65. Even with larger transformations, the proposed method results in significantly smaller RMSE and SAM values than the method by [PERSON] et al. (2018). The results quantitatively confirm that the proposed algorithm can solve the super-resolution problem of an HSI, where an HSI and a target RGB image have different fields of view. To qualitatively evaluate the performance of the proposed method, we verified the performance of the per-pixel error rate image and the RGB image reconstructed from the high-resolution HSI, as shown in Figure 6. Figure 6a,c show the per-pixel RMSE and reconstructed RGB images of the high-resolution HSI of super-resolution in an environment where the shear transformation for \(C_{x}\) was 0.3. Figure 6b,d show the per-pixel RMSE and reconstructed RGB images of high-resolution HSI of super-resolution, in an environment where \(P_{n}\) was 80.