Sp3ctralMamba: Physics-Driven Joint State Space Model for Hyperspectral Image Reconstruction

Hyperspectral image (HSI) reconstruction aims to restore the original 3D HSIs from the 2D hyperspectral snapshot compressive images (SCIs). The key to high-fidelity HSI reconstruction lies in designing refined spatial and spectral attention mechanisms, which are crucial for generating fine-grained representations of HSI based on the limited spatial and spectral information available in SCI. Recently, Mamba has demonstrated remarkable performance and efficiency in modeling spatial correlations. Its implicit attention mechanism generates three orders of magnitude more attention matrices than transformers, significantly raising the performance ceiling for HSI reconstruction. In this paper, we propose a novel joint SSM network named Sp3ctralMamba for HSI reconstruction. Sp3ctralMamba integrates frequency domain knowledge and physical priors to enhance reconstruction quality. Specifically, we first perform hierarchical decomposition of the 3D HSI embedding to mitigate the negative impact of distant bands on reconstruction. Next, we design a joint SSM block S3Mamba (S3MAB) to perform parallel scans of the embeddings from different bands. In addition to the conventional vanilla scan, S3MAB introduces a local scanning scheme to address the reconstruction challenges posed by the spatial sparsity of spectral information. Furthermore, a spiral scanning scheme in the frequency domain is incorporated to enhance the order correlation between different frequency signals. Finally, we introduce energy priors and structural priors to constrain the generation of spectral and spatial representations during the training process. Extensive experiments on both simulated and real datasets demonstrate that Sp3ctralMamba significantly elevates HSI reconstruction performance to a new level, surpassing SOTA methods in both quantitative and qualitative metrics.