Hyperspectral cameras acquire electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. This enhanced spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. However, due to low spatial resolution of hyperspectral cameras, microscopic material mixing, and multiple scattering, the spectra measured by these cameras are mixtures of spectra of materials, called endmembers. Thus, accurate estimation requires some sort of spectral separation.

Spectral separation, or unmixing, is a blind source separation that involves estimating all or some of the of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and dataset size.

In this talk I will present an overview of unmixing methods with focus on geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms. The underlying mathematical problems and potential solutions are described.