## 2 HGF Model
### Evaluation Metrics  
When evaluating hyperspectral image fusion accuracy, the evaluation metrics are broadly divided into two categories: spatial information incorporation and spectral information fidelity. Spatial information incorporation includes the correlation coefficient (CC), standard deviation (STD), peak signal-to-noise ratio (PSNR), structural similarity, relative global error, etc. Spectral information fidelity includes the spectral angle (SAM), deviation index, etc. To verify the effectiveness of the image fusion algorithm, we evaluated both qualitative and quantitative aspects. Qualitative evaluation was performed using the visual effect, and quantitative evaluation was performed by employing the original hyperspectral image as the standard. Four indexes were used for this evaluation: CC, STD, PSNR, and SAM. The evaluation of the indicators showed that the fused image had richer gray levels and information content, clearer spatial texture information, and better spectral fidelity [2; 16]. The four indexes were calculated as follows:  
CC is an objective evaluation index reflecting the correlation between the fused image and the ideal reference image. \[\text{CC}(I_{H},I_{W})=\frac{\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(I_ {H}(i,j)-\overline{I_{H}}\right)(I_{W}(i,j)-\overline{I_{W}})}{\sqrt{\sum \limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(I_{H}(i,j)-\overline{I_{H}}\right) ^{2}\times\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(I_{W}(i,j)-\overline{ I_{W}}\right)^{2}}} \tag{5}\]  
where \(M\) and \(N\) represent the height and width of the fused image, respectively; \(I_{H}(i,j)\) and \(I_{W}(i,j)\) are the pixel gray values of the fused image and the ideal reference image located in row \(i\) and column \(j\), respectively; and \(\overline{I_{H}}\) and \(\overline{I_{w}}\) are the average pixel values of the fused image and the ideal reference image, respectively. STD is used to represent the gray level distribution and contrast of the fused image, that is, the richness of the information contained. The larger the value, the richer the information contained. \[\text{STD}=\sqrt{\sum\limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(F(i,j)-\mu \right)^{2}} \tag{6}\]  
where \(F\left(i,j\right)\) is the value of pixel points in row \(i\) and column \(j\) of the fused image, and \(\mu\) is the mean value of the fused image. PSNR is mainly used to measure the ratio between the effective information and noise of an image, which can show whether the image is distorted. The PSNR reflects the fidelity of the fused image. \[ \begin{split}\text{MSE}(I_{H},I_{W})=\frac{1}{\text{NR}}\sum \limits_{i=1}^{M}\sum\limits_{j=1}^{N}\left(I_{H}(i,j)-I_{W}(i,j)\right)^{2}\\ \text{PSNR}=10\text{lg}\frac{Z^{2}}{\text{MSE}}\end{split}  \tag{7}\]  
where the smaller the mean square error (MSE) is, the smaller the difference between the source image and the fused image is, the higher the similarity is, and the better the quality of the fused image is. \(Z\) is the difference between the maximum and minimum gray levels of the ideal reference image. SAM is the included angle between spectra, representing the similarity between two spectral curves. The smaller the value, the closer the shape of the two spectral curves is. \[\text{SAM}=\cos^{-1}\frac{\sum XY}{\sqrt{\sum\left(X\right)^{2}\cdot\sum\left( Y\right)^{2}}} \tag{8}\]  
where \(X\) is the spectral vector of the ground object on the original hyperspectral image, and \(Y\) is the spectral vector of the same ground object on the fused image. It should be noted that we analyzed the spectral characteristic band distribution of surface element studies, such as water body studies mainly in the visible band, vegetation studies mainly in the visible and near-infrared bands, and soil studies in the visible, near-infrared, and mid-infrared bands.