This paper introduces a graph Laplacian regularization in the hyperspectralunmixing formulation. The proposed regularization relies upon the constructionof a graph representation of the hyperspectral image. Each node in the graphrepresents a pixel's spectrum, and edges connect spectrally and spatiallysimilar pixels. The proposed graph framework promotes smoothness in theestimated abundance maps and collaborative estimation between homogeneous areasof the image. The resulting convex optimization problem is solved using theAlternating Direction Method of Multipliers (ADMM). A special attention isgiven to the computational complexity of the algorithm, and Graph-cut methodsare proposed in order to reduce the computational burden. Finally, simulationsconducted on synthetic data illustrate the effectiveness of the graph Laplacianregularization with respect to other classical regularizations forhyperspectral unmixing.
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