A Two-Stage Decoupling Framework for Blind Hyperspectral Unmixing: Separately Refining Endmembers and Abundances

Hyperspectral unmixing (HU) aims to estimate endmembers and their corresponding abundances, a task commonly referred to as blind hyperspectral unmixing (BLU). Nonnegative matrix factorization (NMF) provides a unified framework for their joint estimation. It is widely assumed that more accurate endmember estimation leads to improved abundance estimation, enabling simultaneous optimization of both variables. However, this paper shows that, in practical noisy scenarios, the relationship between endmembers and abundances in NMF-based multi-variable joint optimization problems (NMF-based JOPs) is inherently coupled and significantly more complex, making it difficult to improve both estimation accuracies simultaneously. Furthermore, we demonstrate that the hard abundance sum-to-one constraint (ASC), commonly imposed in NMF-based JOPs, is inconsistent with realistic noisy conditions. To address these limitations, we propose a novel two-stage framework for BLU that decouples the refinement of endmembers and abundances. In the first stage, a strongly convex minimum-volume simplex model is employed to ensure robust and stable endmember extraction. In the second stage, we introduce a novel formulation, L1SoftASC, which promotes abundance sparsity and physical interpretability while improving convexity and robustness in abundance estimation. Experimental results on both synthetic and real benchmark datasets demonstrate that the proposed two-stage approach consistently outperforms existing single-stage NMF-based JOP methods in terms of both endmember and abundance estimation accuracy, while providing BLU with greater flexibility in handling ASC.