Hyperspectral data unmixing with graph-based regularization

This work proposes to solve the unmixing problem in a graph setting. The hyperspectral image is mapped to a weighted graph where every pixel spectrum is represented by a node, and similar nodes are connected by weighted edges. A graph-based Total Variation framework is incorporated within the unmixing problem. The graph topology allows to promote smoothness over similar data in arbitrary neighborhood structures, while the weights allow to preserve details in the reconstructed image. The resulting constrained optimization problem is convex and is solved using an Alternating Direction Method of Multipliers (ADMM). The particular variable splitting allows to obtain closed form solutions for each ADMM sub-problem and avoids encountering more complicated Sylvester equations. Finally, experiments are conducted using synthetic and real hyperspectral data to demonstrate the effectiveness of the proposed algorithm.