Tech Report: A Fast Multiscale Spatial Regularization for Sparse Hyperspectral Unmixing
This work addresses a computational bottleneck for researchers and practitioners in remote sensing and hyperspectral imaging, offering an incremental improvement over existing spatial regularization methods.
The paper tackles the challenge of efficiently introducing spatial context in sparse hyperspectral unmixing, which often leads to large nonsmooth optimization problems, by proposing a novel multiscale spatial regularization approach that outperforms state-of-the-art Total Variation-based algorithms with comparable computation time to unregularized methods.
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.