# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
## 3 Results
### Evaluation of Sharpening Quality
#### 3.1.2 Qualitative Results Using Real Data  
Figure 5 presents qualitative comparisons using Sentinel-2 imagery of Reykjavik, Iceland, processed using our proposed method and five leading S2 sharpening approaches. The comparison spans multiple spectral band combinations arranged in rows for direct visual assessment.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ERGAS \(\downarrow\)**} & \multicolumn{2}{c}{**RMSE \(\downarrow\)**} & \multicolumn{2}{c}{**SAM \(\downarrow\)**} & \multicolumn{2}{c}{**SRE \(\uparrow\)**} & \multicolumn{2}{c}{**SSIM \(\uparrow\)**} & \multicolumn{2}{c}{**UQI \(\uparrow\)**} \\ \cline{2-13}  & **20 m** & **60 m** & **All** & **20 m** & **60 m** & **20 m** & **All** & **All** & **20 m** & **60 m** & **All** & **20 m** & **60 m** & **All** & **20 m** & **60 m** \\ \hline ATPRK & _1.80_ & 1.96 & 52.90 & _28.10_ & 93.25 & 1.19 & 1.75 & 30.36 & 33.24 & 21.71 & _0.99_ & _0.99_ & 0.97 & 0.81 & 0.86 & _0.67_ \\ S2 Sharp & 1.91 & _0.63_ & 33.43 & 32.44 & 35.92 & 1.06 & _1.18_ & 31.32 & 31.79 & _29.92_ & **1.00** & _0.99_ & _0.99_ & _0.87_ & _0.87_ & 0.86 \\ SSSS & 4.57 & 2.89 & 109.43 & 80.43 & 167.81 & 1.85 & 2.59 & 21.82 & 23.34 & 17.28 & 0.97 & 0.97 & 0.91 & 0.72 & 0.78 & 0.53 \\ SupReME & 2.00 & 1.10 & 40.10 & 31.50 & 57.71 & 1.12 & 1.33 & 30.51 & 31.79 & 26.66 & _0.99_ & _0.99_ & _0.99_ & 0.86 & _0.87_ & 0.82 \\ SUSS & 2.11 & 0.85 & 43.19 & 39.01 & 51.44 & 1.47 & 1.29 & 29.60 & 30.34 & 27.36 & _0.99_ & _0.99_ & 0.99 & 0.86 & 0.86 & _0.88_ \\ Proposed & **1.64** & **0.48** & **26.57** & **27.37** & **23.57** & **1.03** & **0.92** & **33.42** & **33.19** & **34.10** & **1.00** & **1.00** & **0.88** & **0.88** & **0.89** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance metrics for the synthetic S2 images from Figure 4. Arrows denote when lower or higher values are better. For ERGAS and RMSE, lower values are better; for SRE, SSIM, and UQI, higher values are better. The **best results** are bold, and the _second-best results_ are italicized.  
Figure 5: False color composites generated using different bands from a sharpened S2 image taken over Reykjavik, Iceland, instead of the red, green, and blue bands. The top row uses the 60 m atmospheric bands (B1, B9, B1), the middle row the vegetation red edge bands (B5, B6, B7), originally at 20 m resolution, and the bottom row the NIR and SWIR bands (B8A, B11, B12), also originally at 20 m resolution. Results from different methods are arranged in columns for direct comparison: proposed method (leftmost), followed by ATPRK, S2 Sharp, SSSS, SupReME, and SUSS. Note the consistent performance of the proposed method across all resolution levels.  
The 60 m bands (top row) demonstrate our method's superior performance in preserving architectural details, exhibiting enhanced building edge definition and improved color contrast compared with existing approaches. In the vegetation red edge bands (center row), while our method and ATPRK achieve comparable spatial resolution, our approach yields superior results and enhanced contrast relative to other methods. Analysis of the NIR and SWIR bands (bottom row) further validates our method's effectiveness in preserving image fidelity. The enhanced definition of building structures and distinct shadow boundaries demonstrates superior spatial resolution retention compared with existing sharpening techniques.