# Sharpening of Worldview-3 Satellite Images by Generating Optimal High-Spatial-Resolution Images
## 2 Materials and Methods
### Proposed Pansharpening Technique
#### 2.3.1 Sharpening of SWIR Bands with 7.2 m Spatial Resolution  
The first phase of the pansharpening technique for Worldview-3 satellite images aims to improve the spatial resolution of SWIR bands with a 7.2 m spatial resolution using VNIR bands with a 1.2 m spatial resolution. Because panchromatic images could not be utilized in this phase, optimal panchromatic images were produced using the selected and synthesized band schemes. To do this, the MTF filter was applied to the VNIR bands first to produce \(\mathbf{VNIR}^{L}\), which was then transformed into the number of pixels of the SWIR band.  
A correlation analysis was conducted to generate an optimal panchromatic image through the selected band scheme using the SWIR band, which will be sharpened, and \(\mathbf{VNIR}^{L}\). The \(\mathbf{VNIR}^{L}\) band that showed the highest correlation with the SWIR band was set as the optimal panchromatic image, and the pansharpening technique was applied. The process to generate an optimal panchromatic image through the selected band scheme is presented in Equations (6) and (7):  
\[\overline{n}=\text{arg}max_{n}\text{corr}\big{(}\mathbf{VNIR}_{n}^{L},\mathbf{ SWIR}_{n}\big{)},\ t=1,\ldots,8 \tag{6}\]  
\[\mathbf{P}_{n}^{sel}=\sum_{n=1}^{8}\alpha_{n}\mathbf{VNIR}_{n},\ \text{where}\ \alpha_{n}=\left\{\begin{array}{ll}1,\ if\ n= \overline{n}\\ 0,\ otherwise\end{array}\right. \tag{7}\]  
where \(n\) refers to the number of bands in VNIR and SWIR; \(\mathbf{SWIR}_{n}\) refers to the \(n\)th SWIR band, which will be sharpened; \(\mathbf{VNIR}_{n}^{L}\) refers to the \(n\)th VNIR band, which is transformed into the number  
Figure 2: Workflow of the proposed Worldview-3 satellite image pansharpening technique.  
of pixels of the SWIR band; and \(\mathbf{P}_{n}^{sel}\) refers to the optimal panchromatic image generated through the selected band scheme.  
To produce an optimal panchromatic image that has a spectral characteristic similar to that of a SWIR band to be sharpened, in the synthesized band scheme, multiple regression analysis was conducted with \(\mathbf{VNIR}^{L}\) to obtain the regression coefficient. This coefficient was then applied to the VNIR band again to produce the optimal panchromatic image \(\mathbf{P}^{syn}\). The process to generate an optimal panchromatic image through the synthesized band scheme is presented in Equations (8) and (9).  
\[\mathbf{SWIR}_{n}=\omega_{0}+\sum_{n=1}^{8}\omega_{n}\mathbf{VNIR}_{n}^{L} \tag{8}\]  
\[\mathbf{P}_{n}^{syn}=\omega_{0}+\sum_{n=1}^{8}\omega_{n}\mathbf{VNIR}_{n} \tag{9}\]  
SWIR band sharpening was performed using the optimal panchromatic image generated through the selected and synthesized band schemes. Because the pansharpening technique of Worldview-3 satellite images proposed in this study was performed in two phases, spectral information distortion could be accumulated. Thus, GS2, which is a pansharpening technique that generates relatively little spectral distortion, was chosen in this study. The image whose spatial resolution was reduced by applying the MTF filter to the optimal panchromatic image and generated in the selected and synthesized band schemes was utilized as the optimal low-spatial-resolution image \(\mathbf{I}_{L_{n}}\) to which the GS2 technique was applied. The injection gain \(g_{n}\) was calculated using the covariance of the optimal low-spatial-resolution image \(\mathbf{I}_{L_{n}}\) and SWIR bands and the variances of \(\mathbf{I}_{L_{n}}\), as presented in Equation (10):  
\[g_{n}=\frac{cov(\mathbf{I}_{L_{n}},\mathbf{MS}_{n})}{var(\mathbf{I}_{L_{n}})} \tag{10}\]  
The GS2 technique process of the SWIR bands using the generated \(\mathbf{I}_{L_{n}}\) and \(g_{n}\) is presented in Equation (11):  
\[\widehat{\mathbf{SWIR}}_{n}=\widehat{\mathbf{SWIR}}_{n}+g_{n}(\mathbf{P}- \mathbf{I}_{L_{n}}),\ n=1,\ldots,8 \tag{11}\]