Estimation of the hyperspectral tucker ranks

In hyperspectral image analysis, one often assumes that observed pixel spectra are linear combinations of pure substance spectra. Unmixing a hyperspectral image consists in finding the number of pure substances in the scene, finding their spectral signatures and estimating the abundance fraction of each pure substance spectrum in each spectral pixel. In this paper, we show that the tensor Tucker decomposition could be considered to solve this problem, and a preliminary problem to overcome consists in estimating the 3 required data Tucker ranks, corresponding to the 3 dimensions of the data cube. Then, we propose an optimal method to estimate them.