An overview on hyperspectral unmixing: Geometrical, statistical, and sparse regression based approaches

Hyperspectral instruments acquire electromagnetic energy scattered within their ground instantaneous field view in hundreds of spectral channels with high spectral resolution. Very often, however, owing to low spatial resolution of the scanner or to the presence of intimate mixtures (mixing of the materials at a very small scale) in the scene, the spectral vectors (collection of signals acquired at different spectral bands from a given pixel) acquired by the hyperspectral scanners are actually mixtures of the spectral signatures of the materials present in the scene. Given a set of mixed spectral vectors, spectral mixture analysis (or spectral unmixing) aims at estimating the number of reference materials, also called endmembers, their spectral signatures, and their fractional abundances. Spectral unmixing is, thus, a source separation problem. This paper presents an overview of the principal research directions in hyperspectral unmixing. The paper is organized into six main topics: i) mixing models, ii) signal subspace identification, iii) geometrical-based spectral unmixing, iv) statistical-based spectral unmixing, v) sparse regression based unmixing, and vi) spatial-contextual information. For each topic, we summarize what is the mathematical problem involved and give relevant pointers to state-of-the-art algorithms to address these problems.