A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing

Ricardo Augusto Borsoi, Tales Imbiriba, José Carlos Moreira Bermudez, Cédric Richard

Abstract: 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.