# A Learned Reduced-Rank Sharpening Method for Multiresolution Satellite Imagery
###### Abstract
For water resource management, higher-resolution short-wave infrared bands B11 and B12 again improve water body delineation at 10 m in [13], using a multidimensional clustering approach. Automated monthly surface water maps of France at 10 m resolution were developed in [14], with low-resolution inputs only upsampled using the nearest neighbor approach. While many studies employ basic upsampling methods like bicubic interpolation or nearest neighbor resampling for the 20 m bands, more sophisticated fusion techniques should improve results across these applications. Similar resolution challenges exist in other satellite systems, such as NASA's MODIS, ASTER, and Landsat series, as well as commercial platforms like WorldView-3. Some systems include a high-resolution panchromatic band for sharpening lower-resolution spectral bands. For example, the Landsat 8 Operational Land Imager provides seven spectral bands at a 30 m spatial resolution and one panchromatic band at a 15 m resolution [15]. Sentinel-2 has no panchromatic band, necessitating alternative approaches to resolution enhancement. The relationship between spatial resolution and signal quality is governed by multiple factors, including sensor characteristics, atmospheric conditions, and the physics of light transmission [16; 17; 18; 19]. While increasing spatial resolution typically involves trade-offs with spectral bandwidth and signal-to-noise ratio, super-resolution techniques offer a promising approach to overcome these limitations. Previously noted application studies [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14] have demonstrated the benefits of enhanced spatial resolution in various remote sensing applications, from improved image classification to more accurate change detection. However, the specific characteristics of Sentinel-2's band configuration and the wide range of applications it serves create unique opportunities and challenges for resolution enhancement. Although pansharpening and Sentinel-2 sharpening share the goal of enhancing spatial resolution, fundamental differences make direct adaptation of methods between these tasks challenging. In pansharpening, a single high-resolution panchromatic band guides the enhancement of multiple lower-resolution spectral bands, with the panchromatic bandwidth typically overlapping most spectral bands [18]. Instead of one guiding panchromatic band, Sentinel-2 has four 10 m bands (RGB and near-infrared), six 20 m bands, and three 60 m bands, each capturing narrow, specific wavelength ranges. Without broad spectral overlap between resolutions, enhancing lower-resolution bands requires learning more complex relationships between spatial and spectral information across different wavelengths. Additionally, while pansharpening typically involves a fixed upsampling factor, Sentinel-2 sharpening must handle multiple scaling ratios simultaneously (2\(\times\) and 6\(\times\)). These differences affect the model architecture and loss function design; Sentinel-2 sharpening requires more sophisticated approaches to extract and transfer spatial details across different spectral ranges and resolution scales, while pansharpening methods can directly leverage the panchromatic band's spatial information. Previous sharpening methods broadly fall into three categories: Classical component substitution and multiresolution analysis methods, traditional model-based methods, and deep learning methods. The classical methods are often used for pansharpening and image fusion [20; 21; 22; 23; 24] and have also been applied to Sentinel-2 data [25]. For Sentinel-2, traditional model-based sharpening algorithms such as Area-To-Point Regressive Kriging (ATPRK) [26], Multiresolution Sharpening Approach (MuSA) [27], S2 Sharp [28], Super-Resolution for multispectral Multiresolution Estimation (SupReME) [29], and Sentinel-2 Super-resolution via Scene-adapted Self-similarity (SSSS) [30] give good results. Finally, deep learning methods have proven useful in remote sensing, just as in other fields.