# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
## 5 Conclusions  
This paper introduces an unsupervised sharpening method that bridges traditional model-based approaches with modern neural network techniques to address the multiresolution challenges of Sentinel-2 imagery. Our method demonstrates superior performance across all tested metrics through comprehensive quantitative and qualitative evaluations, with particularly strong results in maintaining consistent quality between 20 m and 60 m bands--a significant advancement over existing approaches.  
The success of our approach stems from several key architectural innovations. The method combines a customized U-Net featuring resolution-matched pooling layers with adaptive regularization operating directly in the low-rank subspace. This architecture enables simultaneous optimization of low-rank approximation and linear transformation while eliminating manual parameter tuning through automated adaptation to image char acteristics. The result is a robust framework that maintains high performance across varied imaging conditions without requiring extensive manual intervention.  
The method's effectiveness extends beyond Sentinel-2, as demonstrated by successful application to Sentinel-2/Landsat-8 fusion. This adaptability, combined with the unsupervised learning approach, makes the method particularly valuable for operational deployment where consistent performance across varied imagery is essential.  
Our approach demonstrates consistently strong performance across all spectral bands, particularly notable in maintaining high quality for the 60 m resolution bands--a significant improvement over existing methods that often show degraded performance at lower resolutions. Quantitative evaluations show superior results across multiple image quality metrics, while qualitative assessments confirm enhanced preservation of spatial details and spectral fidelity.  
Looking ahead, this work opens several promising research directions. Future developments could include extensions to other satellite platforms and sensor configurations, integration of additional regularization strategies, and the development of more sophisticated training approaches for multisensor fusion. The architecture could be further optimized for specific operational requirements, potentially enabling even better performance for targeted applications. These results establish a new performance benchmark for Sentinel-2 image sharpening and a flexible framework for addressing multiresolution challenges in satellite imagery more broadly.  
Conceptualization, S.E.A. and M.O.U.; data curation, J.S.; formal analysis, S.E.A.; methodology, S.E.A., J.S. and M.O.U.; software, S.E.A.; validation, S.E.A.; visualization, S.E.A. and J.S.; writing--original draft, S.E.A.; writing--review and editing, S.E.A., M.O.U. and J.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by The Icelandic Research Fund under Grant 207233-051.  
Data Availability Statement: Data used in this study include Sentinel-2 data that are available at the ESA Sentinel-2 data hub [69] and Landsat 8 data that are available on the USGS Earth Explorer site [70]. Code for using the proposed method and the synthetic data used in this paper are available at [[https://github.com/[PERSON]/LRRS2](https://github.com/[PERSON]/LRRS2) SM]([https://github.com/[PERSON]/LRRS2](https://github.com/[PERSON]/LRRS2) SM), accessed on 23 January 2025 [48].  
The authors declare no conflicts of interest. The funders had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.