Fast and Robust Recursive Algorithms for Separable Nonnegative Matrix Factorization

A hyperspectral image consists of a set of images taken at different wavelengths. It is acquired by measuring the spectral signature of each pixel present in the scene, that is, by measuring the reflectance (the fraction of the incident electromagnetic power that is reflected by a surface at a given wavelength) of each pixel at different wavelengths. One of the most important tasks in hyperspectral imaging is called unmixing. It requires the identification of the constitutive materials present in the image and estimation of their abundances in each pixel. The most widely used model is the linear mixing model: the spectral signature of each pixel results from the additive linear combination of the spectral signatures of the constitutive materials, called endmembers, where the weights of the linear combination correspond to the abundances of the different endmembers in that pixel.