Graph Construction for Hyperspectral Data Unmixing

This chapter presents graph construction for hyperspectral data and associated unmixing methods based on graph regularization. Graph is a ubiquitous mathematical tool for modeling relations between objects under study. In the context of hyperspectral image analysis, constructing graphs can be useful to relate pixels in order to perform corporative analysis instead of analyzing each pixel individually. In this chapter, we review fundamental elements of graphs and present different ways to construct graphs in both spatial and spectral senses for hyperspectral images. By incorporating a graph regularization, we then formulate a general hyperspectral unmixing problem that can be important for applications such as remote sensing and environment monitoring. Alternating direction method of multipliers (ADMM) is also presented as a generic tool for solving the formulated unmixing problems. Experiments validate the proposed scheme with both synthetic data and real remote sensing data.

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