Impact of the initialisation of a blind unmixing method dealing with intra-class variability

In hyperspectral imagery, unmixing methods are often used to analyse the composition of the pixels. Such methods usually suppose 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 investigate 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 provided. In our model a pure material cannot be described by a single spectrum in the image but it can in a pixel. An approach method is presented to handle this new model. It is based on pixel-by-pixel Nonnegative Matrix Factorization (NMF) methods. The methods are tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and mixtures of these spectra. We particularly focused our tests to study the impact of the initialisation of our methods.