# Panchromatic and Multispectral Image Fusion Combining GHS, NSST, and PCA
## 6 Conclusions  
For the fusion of PAN and MS images, a fusion framework combining GIHS, NSST, and PCA was proposed in this paper. The GIHS method was improved to take advantage of its concise formulas and high execution efficiency, while there was no limitation on the number of bands of input data. The constructed fusion algorithm contains more spatial structure information of MS and PAN images and retains some spectral information of MS. PCA is applied to each band of the PAN image and MS image to obtain the first principal \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Satellite** & **Index** & **EXP** & **GIHS** & **SFIM** & **Brovey** & **GS** & **PCA** & **Proposed** \\ \hline \multirow{4}{*}{GE-1} & \(D_{\lambda}\) & **0.0685** & 0.1090 & 0.1429 & 0.1055 & 0.1064 & 0.1259 & 0.0927 \\  & \(D_{s}\) & 0.1516 & 0.0298 & 0.0178 & 0.0297 & 0.0298 & 0.0196 & **0.0065** \\  & \(HQNR\) & 0.7901 & 0.8643 & 0.8417 & 0.8678 & 0.8668 & 0.8568 & **0.9012** \\ \hline \multirow{4}{*}{WV-4} & \(D_{\lambda}\) & 0.1014 & 0.2130 & 0.1123 & 0.2006 & 0.1977 & 0.2737 & **0.0806** \\  & \(D_{s}\) & 0.2714 & 0.1123 & 0.1411 & 0.1123 & 0.1123 & 0.0923 & **0.0855** \\  & \(HQNR\) & 0.6545 & 0.6985 & 0.7623 & 0.7094 & 0.7120 & 0.6592 & **0.8406** \\ \hline \multirow{4}{*}{GF-7} & \(D_{\lambda}\) & **0.0086** & 0.1114 & 0.0225 & 0.1082 & 0.1273 & 0.2889 & 0.0153 \\  & \(D_{s}\) & 0.2004 & 0.0375 & 0.0751 & 0.0375 & 0.0375 & 0.0103 & **0.0705** \\  & \(HQNR\) & 0.7926 & 0.8552 & 0.9040 & 0.8582 & 0.8398 & 0.7036 & **0.9152** \\ \hline \multirow{4}{*}{GFDM} & \(D_{\lambda}\) & 0.0426 & 0.2020 & **0.0271** & 0.1876 & 0.0312 & 0.1354 & 0.0459 \\  & \(D_{s}\) & 0.0694 & 0.0312 & 0.0253 & 0.0312 & 0.1372 & 0.0253 & **0.0197** \\ \cline{1-1}  & \(HQNR\) & 0.8908 & 0.7729 & **0.9482** & 0.7869 & 0.8357 & 0.8425 & 0.9351 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Objective assessment indexes of fusion results without references. component, and then NSST decomposition is used in the fusion with the PAN image. Finally, the fused image is used to replace the original intensity component, which can enhance the fusion effect and reduce the spectral distortion. Compared with the traditional algorithms, the algorithm in this paper obtained more spatial structure components from PAN and MS and could preserve spectral information with high fidelity while effectively retaining spatial structure information. In the process of low-frequency coefficient fusion, this paper proposed a new fusion rule based on the gradient-domain SVD, using a local structure description operator to obtain the initial fusion weights and bootstrap filtering to increase the spatial continuity of these weights. Four scenes of urban, plants and water, farmland, and desert images from GeoEye-1, WorldView-4, Gaofen-7, and GFDM were used as experimental data for a fusion method study. The method was compared with five other fusion algorithms, using the average gradient, structural similarity, correlation coefficient, common image quality index, spectral angle mapping, and relative global error, with and without evaluation indexes, including the spectral aberration index, spectral distortion index, and comprehensive evaluation index in the reference mode. The results showed that the method proposed in this paper achieved outstanding results in spectral preservation and spatial information incorporation. Conceptualization, L.X. and G.X. ; methodology, L.X. ; software, G.X. ; validation, L.X., G.X. and S.Z. ; formal analysis, S.Z. ; investigation, L.X. ; resources, L.X. ; data curation, G.X. ; writing--original draft preparation, L.X. and G.X. ; writing--review and editing, G.X. and S.Z. ; visualization, G.X. ; supervision, L.X. and G.X. ; project administration, L.X. ; funding acquisition, L.X. All authors have read and agreed to the published version of the manuscript.