A linear-quadratic unsupervised hyperspectral 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 unique spectral signature, called an endmember, can be associated with each pure material present in the scene. This assumption is no more valid for materials that exhibit spectral variability due to illumination conditions, weathering, slight variations of the composition, etc. Methods currently appear dealing with this spectral variability and based on linear mixing assumption. However, intra-class variability issues frequently appear in nonflat scenes, and particularly in urban scenes. For urban scenes, the linear-quadratic mixing models better depict the radiative transfer. In this paper, we propose a new unsupervised unmixing method based on the assumption of a linear-quadratic mixing model, that deals with intra-class spectral variability. A new formulation of linear-quadratic mixing is proposed. An unmixing method is presented to process this new model. The method is tested on a semi-synthetic data set built with spectra extracted from a real hyperspectral image and mixtures of these spectra. Based on the results of nonlinear and linear unmixing, we discuss the interest of considering the nonlinearity regarding the impact of intra-class variability.