# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
## 3 Results
### Fusion Evaluation  
Our proposed method demonstrates strong fusion performance across all evaluated metrics, as shown in Table 3. For this experiment, we maintained the same parameters as in the previous section, only slightly adjusting \(\lambda=0.001\). We compared our method against three alternatives, each optimized for maximum SRE using Bayesian optimization. The quantitative comparison follows [PERSON]'s protocol, which assumes scale invariance and enables evaluation through downsampled images. Specifically, we generate a downsampled version of the S2 image for each resolution and process it using the same procedure as full-resolution data. This downsampling approach allows meaningful quantitative comparisons by providing reduced-scale reference data. The proposed method performs well, achieving the best results for all metrics apart from the SAM value for the Landsat 8 bands. While the method was developed specifically for S2 data, some minimal adaptations to L8, such as adjusting the downsampling ratio of the U-Net and extending the inputs to accept the additional bands from L8, their sampling ratios, and PSF information, were enough to achieve highly competitive results. In all other aspects, the proposed method is the same as in the preceding experiments. The baseline method achieves good spectral fidelity scores but relatively poor spatial quality metrics due to its conservative approach to sharpening. This is also evident in Figure 10, where the baseline outputs maintain spectral characteristics at the expense of spatial detail, producing noticeably pixelated results compared with other methods. This conservative sharpening explains the method's strong performance in spectral metrics \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{ERGAS \(\downarrow\)} & \multicolumn{3}{c}{RMSE \(\downarrow\)} & \multicolumn{3}{c}{SAM \(\downarrow\)} & \multicolumn{3}{c}{SRE \(\uparrow\)} & \multicolumn{3}{c}{SSIM \(\uparrow\)} & \multicolumn{3}{c}{UIGI \(\uparrow\)} \\ \cline{2-13}  & **20 m** & **30 m** & **60 m** & **20 m** & **30 m** & **60 m** & **20 m** & **30 m** & **60 m** & **20 m** & **30 m** & **60 m** & **20 m** & **30 m** & **60 m** \\ \hline ATPRK & 7.64 & 7.47 & 4.03 & 0.03 & 0.06 & 0.05 & 4.93 & 11.35 & 17.46 & 14.00 & 13.54 & 0.88 & 0.77 & 0.83 & 0.81 & 0.76 & 0.82 \\ Baseline & 6.17 & 4.93 & 3.30 & 0.03 & 0.04 & 0.05 & 4.73 & **3.47** & 19.28 & 17.90 & 15.18 & 0.90 & 0.83 & 0.83 & 0.83 & 0.79 & 0.81 \\ SLSharp & 5.99 & 4.78 & 2.73 & _0.02_ & _0.04_ & _0.04_ & 4.81 & 4.38 & 19.49 & 18.30 & _16.85_ & _0.92_ & _0.89_ & _0.90_ & _0.85_ & _0.85_ & _0.90_ \\ Proposed & **2.63** & **3.70** & **1.66** & **0.01** & **0.03** & **0.02** & **3.12** & 3.70 & **27.28** & **20.55** & **21.62** & **0.98** & **0.91** & **0.96** & **0.94** & **0.89** & **0.95** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics for the reduced scale images of Glen Canyon. Arrows denote when lower or higher values are better. For ERGAS and RMSE, lower values are better; for SRE, SSIM, and UIQI, higher values are better. The **best results** are bold, and the _second-best results_ are italicized. Figure 9: RGB images of Glen Canyon, Arizona, from [42], with areas of interest used in the qualitative detail study in Section 3.3 highlighted in the inset images. The RGB images were generated using bands 2-4 of S2 (**left**) and L8 (**right**) images. like SAM while underperforming in spatial quality measures. The visual comparison in Figure 10 clearly demonstrates this trade-off, particularly regarding the preservation of fine structural details and edge definition. The qualitative comparison of image details in Figure 10 shows individual bands from the S2 and L8 images of Glen Canyon, Arizona. The four methods, including our proposed method, were used to sharpen all the bands of both images to 10 m resolution.