A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing

Sparse hyperspectral unmixing from large spectral libraries has been considered to circumvent the limitations of endmember extraction algorithms in many applications. This strategy often leads to ill-posed inverse problems, which can greatly benefit from spatial regularization strategies. However, existing spatial regularization strategies lead to large-scale 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 letter, a novel multiscale spatial regularization approach for sparse unmixing is proposed. The method uses a signal-adaptive spatial multiscale decomposition based on segmentation and oversegmentation algorithms to decompose the unmixing problem into two simpler problems: one in an approximation image domain and another in the original domain. Simulation results using both synthetic and real data indicate that the proposed method outperforms the state-of-the-art total variation-based algorithms with a computation time comparable to that of their unregularized counterparts.