W-SpectralFormer: A Physics-Informed Transformer Model for Weakly Supervised Spectral Super-Resolution of High-Fidelity Remote Sensing Reflectance Over Inland Lakes

The inherent trade-off between spatial and spectral resolution in remote sensing sensors limits their ability to monitor inland lake eutrophication. Spectral super-resolution (SSR) provides a cost-effective solution for obtaining remote sensing images with high spatial and spectral resolution. However, the water-leaving remote sensing reflectance is characterized with weak signals and rich spectral features related to absorbing and scattering effects of water components.Without full consideration of data characteristics and proper physical modeling of SSR process, existing methods may introduce significant uncertainties in reconstructed remote sensing reflectance (Rrs) over inland waters. To this end, we propose a novel physics-informed SSR framework (referring to W-SpectralFormer) for Sentinel-2 MSI images that achieves high-fidelity spectrum, where the core idea is to integrate optical properties of water to guide the feature learning process. With Sentinel-3 OLCI data serving as the spectral reference, W-SpectralFormer features a frequency-assisted transformer-based SSR (FATSSR) network that is optimized through weak supervision using a pre-trained degradation estimator. The FATSSR network employs a F-token module that embeds fast Fourier transform (FFT) into the Transformer tokens, enabling localized attention to reconstruct vital spectral features. Moreover, a spectral-aware (SA) loss function is devised to incorporate both inherent and apparent optical properties of water as constraints during model training for enhanced spectral refinement. Both F-token module and SA loss coupled to boost the accuracy of reconstructed spectrum in inland waters with complex optical properties. Experiments demonstrate that the proposed method achieves state-of-the-art SSR performance. Moreover, validation of chlorophyll-a concentrations confirms the reconstructed images provide more reliable results than original MSI data with a coarser spectral resolution.