  Sparse hyperspectral unmixing from large spectral libraries has been
considered to circumvent limitations of endmember extraction algorithms in many
applications. This strategy often leads to ill-posed inverse problems, which
can benefit from spatial regularization strategies. While existing spatial
regularization methods improve the problem conditioning and promote piecewise
smooth solutions, they lead to large nonsmooth optimization problems. Thus,
efficiently introducing spatial context in the unmixing problem remains a
challenge, and a necessity for many real world applications. In this paper, a
novel multiscale spatial regularization approach for sparse unmixing is
proposed. The method uses a signal-adaptive spatial multiscale decomposition
based on superpixels to decompose the unmixing problem into two simpler
problems, one in the approximation domain and another in the original domain.
Simulation results using both synthetic and real data indicate that the
proposed method can outperform state-of-the-art Total Variation-based
algorithms with a computation time comparable to that of their unregularized
counterparts.
