## Appendix A
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Band** & **Ehlers** & **GC** & **GIHS** & **HCS** & **IHS** & **CIELab** & **NNDIF** \\ \hline \multirow{4}{*}{ERGAS} & Band 1 & 13.23542 & 6.28494 & 7.53986 & 11.51714 & 14.68644 & 6.19922 & 9.43229 \\  & Band 2 & 10.86379 & 5.49824 & 6.73039 & 10.62880 & 10.07883 & 4.07797 & 7.66444 \\  & Band 3 & 6.52447 & 4.08371 & 4.97720 & 5.58341 & 7.75358 & 2.07075 & 2.81246 \\  & Average & 10.98399 & 5.51194 & 6.97787 & 9.58868 & 10.6117 & 4.14506 & 6.93153 \\ \hline \multirow{4}{*}{QAVG} & Band 1 & 0.86547 & 1.02826 & 0.95928 & 1.02387 & 0.87788 & 1.0607 & 1.03723 \\  & Band 2 & 0.57607 & 0.65720 & 0.69449 & 0.52406 & 0.56826 & 0.70848 & 0.60802 \\  & Band 3 & 0.48901 & 0.30277 & 0.36560 & 0.31617 & 0.45130 & 0.54621 & 0.41064 \\  & Average & 0.63217 & 0.66128 & 0.65746 & 0.62070 & 0.63204 & 0.77127 & 0.68589 \\ \hline \multirow{4}{*}{RASE} & Band 1 & 49.91752 & 30.04186 & 39.39898 & 42.79105 & 54.69452 & 25.33830 & 34.82911 \\  & Band 2 & 46.79656 & 22.35778 & 35.26309 & 37.59033 & 52.26805 & 21.10608 & 31.65890 \\  & Band 3 & 34.19874 & 18.59234 & 25.44349 & 36.19742 & 45.77826 & 13.75556 & 25.58183 \\  & Average & 43.08140 & 23.69334 & 33.45619 & 38.29194 & 50.97203 & 20.06662 & 30.69262 \\ \hline \multirow{4}{*}{RMSE} & Band 1 & 0.00833 & 0.00450 & 0.00525 & 0.00625 & 0.01033 & 0.00413 & 0.00525 \\  & Band 2 & 0.00040 & 0.00010 & 0.00186 & 0.00156 & 0.00042 & 0.00008 & 0.00106 \\  & Band 3 & 0.00031 & 0.00002 & 0.00001 & 0.00009 & 0.00001 & 0.00001 & 0.00009 \\  & Average & 0.00301 & 0.00154 & 0.00233 & 0.00267 & 0.00356 & 0.00140 & 0.00214 \\ \hline \multirow{4}{*}{SAM} & Band 1 & 4.86237 & 3.61186 & 3.40619 & 3.10669 & 4.08712 & 2.22633 & 3.13166 \\  & Band 2 & 4.42003 & 2.42682 & 2.50814 & 2.87424 & 3.16997 & 1.82082 & 2.55769 \\  & Band 3 & 3.95193 & 2.35714 & 1.78239 & 2.20364 & 3.05983 & 1.53200 & 2.21219 \\  & Average & 4.48411 & 2.84298 & 2.4008 & 2.67967 & 3.52966 & 1.84331 & 2.67079 \\ \hline \multirow{4}{*}{PSNR} & Band 1 & 56.42695 & 60.52591 & 54.16646 & 54.15527 & 51.81649 & 69.90153 & 57.27461 \\  & Band 2 & 48.08904 & 59.45342 & 51.82179 & 51.08538 & 47.59585 & 67.71639 & 57.20947 \\ \cline{1-1}  & Band 3 & 47.47481 & 50.38406 & 50.63450 & 49.28219 & 46.97046 & 65.36066 & 45.98168 \\ \cline{1-1}  & Average & 50.43809 & 56.80727 & 52.63436 & 51.46174 & 48.97725 & 67.07440 & 53.383210 \\ \hline \multirow{4}{*}{SSIM} & Band 1 & 0.99888 & 0.99702 & 0.99417 & 0.99251 & 0.98071 & 1 & 0.99051 \\ \cline{1-1}  & Band 2 & 0.98443 & 0.99539 & 0.98407 & 0.99175 & 0.97231 & 1 & 0.99048 \\ \cline{1-1}  & Band 3 & 0.97331 & 0.99385 & 0.97415 & 0.99108 & 0.96142 & 0.9999 & 0.99042 \\ \cline{1-1}  & Average & 0.98554 & 0.99542 & 0.98413 & 0.99176 & 0.97134 & 1 & 0.99047 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Band-by-band calculation results of spectral quality metrics belonging to test site F3. a division by zero. These constants depend on the dynamic range of the pixel values. A higher value of the measured index shows the better quality of Pan-sharpened algorithm. **CC:** C\({}_{\text{rf}}\) is the cross-correlation between reference and fused images, while C\({}_{\text{r}}\) and C\({}_{\text{f}}\) are the correlation coefficients belonging to reference and fused images respectively. **SRMSE:** Edge magnitude (M) is calculated via spectral distance of horizontal and vertical (\(M_{x}\) and \(M_{y}\)) edge intensities. **Sp-ERGAS:**\(\frac{d\mu}{dl}\) represents the ratio between the pixel size of MS and Pan images, and \(n\) is the number of bands. Spatial RMSE is represented as below:  
\[\text{Spatial RMSE}=\sqrt{\frac{1}{\text{MN}}\sum_{i=1}^{M}\sum_{j=1}^{N} \left(\text{Pan}(i,j)-PS(i,j)\right)^{2}}, \tag{1}\]  
where MN is the image size, PS\((i,j)\) and Pan\((i,j)\) represents the pixel digital number (DN) at \((i,j)\) 'th position of Pan-sharpened and Pan image.