A Fast Spatial–Spectral NMF for Hyperspectral Unmixing

This letter proposes a fast yet efficient method to solve the hyperspectral (HS) unmixing problem in the challenging unsupervised context, i.e., when the endmember spectral signatures are unknown. First, a coarse approximation of the HS image is computed by spatially averaging neighboring pixels, which significantly reduces the amount of pixels to be handled. This reduced set of HS pixels is unmixed to derive coarse solutions of the unmixing problem, i.e., coarse estimates of the endmember signatures and the corresponding low-resolution abundance maps. Then, the plain resolution abundance maps are estimated from the corresponding HS image based on the coarse endmember signatures. A sparsity promoting prior exploiting the low-resolution map complements the conventional data fitting term to promote spatial smoothness while mitigating the loss of details in the edge areas. Finally, a least square optimization problem is solved to obtain the actual endmember signatures from the HS image and the abundance maps of plain resolution estimated in the previous step. Numerical experiments show that the proposed method is fast and performs well compared to the state-of-the-art approaches from the literature.