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**1 - 3**of**3**### A GRAPH LAPLACIAN REGULARIZATION FOR HYPERSPECTRAL DATA UNMIXING

"... This paper introduces a graph Laplacian regularization in the hyper-spectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel’s spectrum, and edges connect spectrally and spa ..."

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This paper introduces a graph Laplacian regularization in the hyper-spectral unmixing formulation. The proposed regularization relies upon the construction of a graph representation of the hyperspectral image. Each node in the graph represents a pixel’s spectrum, and edges connect spectrally and spatially similar pixels. The proposed graph framework promotes smoothness in the estimated abundance maps and collaborative estimation between homogeneous areas of the image. The resulting convex optimization problem is solved us-ing the Alternating Direction Method of Multipliers (ADMM). A special attention is given to the computational complexity of the al-gorithm, and Graph-cut methods are proposed in order to reduce the computational burden. Finally, simulations conducted on synthetic data illustrate the effectiveness of the graph Laplacian regularization with respect to other classical regularizations for hyperspectral un-mixing. Index Terms — Hyperspectral imaging, unmixing, graph Lapla-cian regularization, ADMM, sparse regularization.

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, 2015

"... A manifold learning approach to target detection in high-resolution hyperspectral imagery ..."

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A manifold learning approach to target detection in high-resolution hyperspectral imagery