Collaborative sparse unmixing of hyperspectral data

Sparse unmixing aims at estimating the constituent materials (endmembers) and their respective fractional abundances in each pixel of a hyperspectral image by assuming that the endmembers are present in a large collection of pure spectral signatures (spectral library), known a priori. In this paper, we propose a refinement of the sparse unmixing approach by taking into account the fact that all the pixels of the image share the same set of endmembers, thus lying in a lower dimensional subspace. Our idea is based on the collaborative lasso, which enforces sparsity across the pixels. The goal of this line of attack is to obtain higher accuracy of the estimated fractional abundances, at the same time with a decrease in the number of endmembers used to explain the observed data. The experimental results, obtained with both simulated and real data, confirm the potential of the proposed approach in the unmixing problem.