A method based on nonnegative matrix factorization dealing with intra-class variability for unsupervised hyperspectral unmixing

In hyperspectral imagery, unmixing methods are often used to analyse the composition of the pixels. Such methods usually supposed that a single spectral signature, called an endmember, can be associated with each pure material present in the scene. Such an assumption is no more valid for materials that exhibit spectral variability due to illumination conditions, weathering, slight variations of the composition, etc. In this paper, we proposed a new method based on the assumption of a linear mixing model, that deals with intra-class spectral variability. A new formulation of the linear mixing is proposed. It introduces not only a scaling factor but a complete representation of the spectral variability in the pure spectrum representation. In our model a pure material cannot be described by a single spectrum in the image but it can in a pixel. A method is presented to process this new model. It is based on a pixel-by-pixel Nonnegative Matrix Factorization (NMF) method. The method is tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and mixtures of these spectra. Thus we demonstrate the interest of our method on realistic intra-class variabilities.