Hyperspectral Unmixing Based on Dual-Graph Manifold Regularization: Joint Preservation of Spatial-Spectral Geometric Structure

Hyperspectral unmixing techniques face challenges of insufficient endmember separability and degradation of abundance spatial continuity in complex scenarios. Traditional methods, which often overlook the geometric structure information of the data and feature space, exhibit significant performance limitations in the presence of noise and microscopic mixing. To address these issues, this paper proposes a dual-graph manifold-regularized hyperspectral unmixing framework, which, for the first time, jointly embeds a data graph (modeling the similarity of pixel spatial distribution) and a feature graph (constraining the endmember spectral manifold structure) into the nonnegative matrix factorization (NMF) model. By jointly preserving the spatial-spectral geometric properties, the proposed approach achieves precise decoupling of endmembers and abundances. This method innovatively designs dual-graph Laplacian regularization terms, which simultaneously enhance the spatial smoothness of abundances and the spectral discriminability of endmembers within a unified optimization objective. An adaptive alternating optimization algorithm is developed to solve the resulting nonconvex problem. Experiments on both synthetic and real hyperspectral data demonstrate that the proposed method significantly outperforms state-of-the-art algorithms, providing a robust and physically interpretable unmixing paradigm for complex mixing scenarios.