Range–Null Space Decomposition With Frequency-Oriented Mamba for Spectral Superresolution

Spectral super-resolution (SSR) is a technique aimed at reconstructing hyperspectral images (HSIs) from images with low spectral resolution. Previous methods combining mathematical models with deep learning have shown promising performance for HSI reconstruction. However, these methods still have limitations when dealing with complex scenes, especially in terms of data consistency and realness. To address these issues, we propose a model-driven SSR network that integrates Range-Null Space Decomposition with deep learning. Specifically, we solve for the range space (R-Space) part and null space (N-Space) part to reconstruct the desired HSI with consistency and realness. The R-Space is primarily iteratively derived from the input multispectral image (MSI) to ensure reliable data consistency, while the N-Space reflects the true distribution of the target HSI, and its proper representation helps improve visual quality. To enhance N-Space exploration, we construct a frequency-oriented null space learning module that leverages Mamba and self-attention to separately extract spatial and spectral information in the frequency domain. Additionally, we introduce a structure tensor term and a multi-kernel maximum mean discrepancy term in the loss function to constrain R-Space and N-space, respectively. Experimental results show that the proposed method achieves excellent performance.