Blind Hyperspectral Unmixing Using an Extended Linear Mixing Model to Address Spectral Variability
Spectral unmixing is one of the main research topics in hyperspectral imaging. It can be formulated as a source separation problem, whose goal is to recover the spectral signatures of the materials present in the observed scene (called endmembers) as well as their relative proportions (called fractional abundances), and this for every pixel in the image. A linear mixture model (LMM) is often used for its simplicity and ease of use, but it implicitly assumes that a single spectrum can be completely representative of a material. However, in many scenarios, this assumption does not hold, since many factors, such as illumination conditions and intrinsic variability of the endmembers, induce modifications on the spectral signatures of the materials. In this paper, we propose an algorithm to unmix hyperspectral data using a recently proposed extended LMM. The proposed approach allows a pixelwise spatially coherent local variation of the endmembers, leading to scaled versions of reference endmembers. We also show that the classic nonnegative least squares, as well as other approaches to tackle spectral variability can be interpreted in the framework of this model. The results of the proposed algorithm on two different synthetic datasets, including one simulating the effect of topography on the measured reflectance through physical modelling, and on two real data sets, show that the proposed technique outperforms other methods aimed at addressing spectral variability, and can provide an accurate estimation of endmember variability along the scene because of the scaling factors estimation.