# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
## 4 Discussion  
The experimental results demonstrate that combining traditional model-based methods with deep learning techniques yields superior performance for Sentinel-2 image sharpening. The method's strong performance can be attributed to several key innovations in its design and implementation.  
Figure 10: Comparative analysis of spatial resolution enhancement results of sharpening Sentinel-2 bands B1, B5, and B7 and Landsat 8 bands L1, L5, and L8 from the Glen Canyon study area. Original bands in the first row are compared with results from the ATPRK, Baseline, and SLSharp methods in the second, third, and fourth rows, respectively, and the proposed method in the bottom row.  
The joint optimization of low-rank approximation and linear transformation within an end-to-end trainable architecture proves particularly effective. The ablation study results show that this approach significantly outperforms variants that use either feature alone. The maintenance of model interpretability, a key advantage of traditional approaches, while leveraging the power of deep learning optimization, allows the method to achieve better results than either approach alone.  
The customized U-Net architecture's effectiveness is evident in the consistent performance across different spatial resolutions. The resolution-matched pooling layers, corresponding directly to Sentinel-2's native resolutions, enable the network to learn meaningful features at each scale. This is particularly apparent in the superior performance on 60 m bands, where traditional methods often struggle. The ablation study demonstrates that both the PReLU activation and scaled skip connections contribute meaningfully to this performance, with their removal leading to significant degradation in results.  
The simplified regularization approach operating directly in the low-rank subspace proves both effective and computationally efficient. The removal of complex weighting matrices while maintaining strong performance suggests that simpler regularization schemes can be sufficient when properly integrated with deep learning architectures. The adaptive parameter determination through singular value decomposition eliminates the need for extensive manual tuning, making the method more practical for varied applications.  
The method does have some limitations. In the Landsat fusion results, performance on 30 m bands, while competitive, does not achieve the same level of superiority as seen in the Sentinel-2 results. This suggests that while the method is adaptable to other satellite imagery, architecture modifications may be needed for optimal performance with different resolution patterns. Additionally, as shown in Table 3, the per-image processing time is longer than traditional approaches due to the neural network training phase. However, this represents a run-time cost that eliminates the extensive parameter tuning typically required by methods like S2 Sharp and SupReME.  
The method's ability to achieve high-quality results without external training data is particularly significant for practical applications. This unsupervised approach, combined with minimal parameter tuning requirements, makes the method more accessible and easier to deploy across different geographical regions and imaging conditions. The consistent performance across both 20 and 60 m bands represents a significant advance over existing methods, which often show marked degradation at lower resolutions.  
These results suggest several promising directions for future research, including incorporating additional regularization techniques, adapting the architecture for other satellite platforms, and exploring more sophisticated training strategies.