SCSU–GDO: Superpixel Collaborative Sparse Unmixing with Graph Differential Operator for Hyperspectral Imagery

Abstract

In recent years, remarkable advancements have been achieved in hyperspectral unmixing (HU). Sparse unmixing, in which models mix pixels as linear combinations of endmembers and their corresponding fractional abundances, has become a dominant paradigm in hyperspectral image analysis. To address the inherent limitations of spectral-only approaches, spatial contextual information has been integrated into unmixing. In this article, a superpixel collaborative sparse unmixing algorithm with graph differential operator (SCSU–GDO), is proposed, which effectively integrates superpixel-based local collaboration with graph differential spatial regularization. The proposed algorithm contains three key steps. First, superpixel segmentation partitions the hyperspectral image into homogeneous regions, leveraging boundary information to preserve structural coherence. Subsequently, a local collaborative weighted sparse regression model is formulated to jointly enforce data fidelity and sparsity constraints on abundance estimation. Finally, to enhance spatial consistency, the Laplacian matrix derived from graph learning is decomposed into a graph differential operator, adaptively capturing local smoothness and structural discontinuities within the image. Comprehensive experiments on three datasets prove the accuracy, robustness, and practical efficacy of the proposed method.