# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
###### Abstract  
This paper implements an unsupervised single-image sharpening method for multispectral images, focusing on Sentinel-2 and Landsat 8 imagery. Our method combines traditional model-based methods with neural network optimization techniques. Our method solves the same optimization problem as traditional model-based methods while leveraging neural network optimization techniques through a customized U-Net architecture and specialized loss function. The key innovation lies in simultaneously optimizing a low-rank approximation of the target image and a linear transformation from the subspace to the sharpened image within an unsupervised training framework. Our method offers several distinct advantages: it requires no external training data beyond the image being processed, it provides fast training speeds through a compact, interpretable network model, and most importantly, it adapts to different input images without requiring extensive parameter tuning--a common limitation of traditional methods. The method was developed with a focus on sharpening Sentinel-2 imagery. The Copernicus Sentinel-2 satellite constellation captures images at three different spatial resolutions, 10, 20, and 60 m, and many applications benefit from a unified 10 m resolution. Still, the method's effectiveness extends to other remote sensing tasks, achieving competitive results in both sharpening and multisensor fusion scenarios. It is evaluated using both real and simulated data, and its versatility is shown through successful applications to Sentinel-2 sharpening and Sentinel-2/Landsat 8 fusion. In comparison with leading methods, it is shown to give excellent results. s 2025 17 4320  
final image. Quantitative and qualitative comparisons demonstrate excellent results across all spectral bands, with notably consistent performance across both 20 and 60 m bands. While the focus of this paper is Sentinel-2 sharpening, our method could be extended to many other satellite resolution enhancement applications, including pansharpening and image fusion, by using the correct observational models to match each satellite's unique image acquisition characteristics. To demonstrate its versatility beyond Sentinel-2 sharpening, we also show how the method can be extended to fusing Sentinel-2 and Landsat 8 images. The European Space Agency's (ESA) Sentinel-2 satellite constellation is a key component of the Copernicus Earth observation program, providing crucial multispectral imagery for a wide range of environmental monitoring applications. While Sentinel-2 captures data at 10 m resolution in four bands (visible and near-infrared), six bands are acquired at 20 m resolution and three atmospheric bands at 60 m resolution. This variation in spatial resolution across spectral bands is a common characteristic of satellite imaging systems, driven by the physical constraints of capturing light at different wavelengths and the need to balance spatial detail with signal-to-noise ratio. The availability of all S2 bands at 10 m resolution can significantly enhance numerous remote sensing applications [3; 4; 5; 6]. In agricultural monitoring, higher resolution versions of the red-edge bands B5, B6, and B7 (currently at 20 m) can improve crop health assessment and yield prediction and increase the utility of various vegetation indices [7; 8]. For urban planning, increased detail in short-wave infrared bands B11 and B12 enhances water body maps by sharpening them to 10 m, as has been carried out using several pan-sharpening approaches in [9]. It has also been used to improve land-cover maps through the fusion of all S2 bands at 10 m resolution [10], as well as in several applications that fuse S2 images with other data such as synthetic aperture radar or Landsat thermal bands [5]. In forest monitoring, the finer resolution of S2 bands fused to 10 m resolution enables the production of high-quality forest stand species maps [11] and improves forest height estimations [12].