Robust hyperspectral data unmixing with spatial and spectral regularized NMF

This paper considers the problem of unsupervised hyperspectral data unmixing under the linear spectral mixing model assumption (LSMM). The aim is to recover both end member spectra and abundances fractions. The problem is ill-posed and needs some additional information to be solved. We consider here the Non-negative Matrix Factorization (NMF), which is degenerated on its own, but has the advantage of low complexity and the ability to easily include physical constraints. In addition with abundances sum-to-one constraint, we propose to introduce relevant information within spatial and spectral regularization for the NMF, derived from the analysis of the hyperspectral data. We use an alternate projected gradient to minimize the regularized error reconstruction function. This algorithm, called MDMD-NMF for Minimum Spectral Dispersion Maximum Spatial Dispersion NMF, allows to simultaneously estimate the number of end members, the abundances fractions, and accurately recover more than 10 end members without any pure pixel in the scene.