On the interest of regularized non-negative matrix factorization algorithms versus geometrical algorithms

Many algorithms have been recently proposed in order to solve the unsupervised hyperspectral data unmixing problem, under the linear spectral mixing model assumption (LMM). The main approaches can be roughly gathered in three groups : non-negative matrix factorization (NMF), geometrical algorithms and Bayesian estimation. The choice of an adequate algorithm can be somewhat tricky for the analysis of real hyperspectral data, due to the possible distance to the mixing model, or the sensitivity to noise. The aim of this paper is to compare two of these approaches, the pure geometrical one and the NMF factorization, in order to give some guideline for the expected performances and the choice of an appropriate algorithm in specific situations. We have tested the sensitivity to many parameters as the degree of purity of the endmembers, the number of endmembers, the sensitivity to noise and, in the case of real data, the dispersion of the responses. We assess our experiments on simulated data and real scenes extracted from AVIRIS Cuprite data. We summarize our results and conclusions in a synthetic table and give some indications for real data. These results are part of a methodological study made for the Centre National d´Etudes Spatiales (CNES), in order to further implement unmixing algorithms in the Orfeo Toolbox (OTB), an open source remote sensing image processing library developed by the CNES.