LRDUN: A Low-Rank Deep Unfolding Network for Efficient Spectral Compressive Imaging

Deep unfolding networks (DUNs) have achieved remarkable success and become the mainstream paradigm for spectral compressive imaging (SCI) reconstruction. Existing DUNs are derived from full-HSI imaging models, where each stage operates directly on the high-dimensional HSI, refining the entire data cube based on the single 2D coded measurement. However, this paradigm leads to computational redundancy and suffers from the ill-posed nature of mapping 2D residuals back to 3D space of HSI. In this paper, we propose two novel imaging models corresponding to the spectral basis and subspace image by explicitly integrating low-rank (LR) decomposition with the sensing model. Compared to recovering the full HSI, estimating these compact low-dimensional components significantly mitigates the ill-posedness. Building upon these novel models, we develop the Low-Rank Deep Unfolding Network (LRDUN), which jointly solves the two subproblems within an unfolded proximal gradient descent (PGD) framework. Furthermore, we introduce a Generalized Feature Unfolding Mechanism (GFUM) that decouples the physical rank in the data-fidelity term from the feature dimensionality in the prior module, enhancing the representational capacity and flexibility of the network. Extensive experiments on simulated and real datasets demonstrate that the proposed LRDUN achieves state-of-the-art (SOTA) reconstruction quality with significantly reduced computational cost.