Regularized Simultaneous Forward–Backward Greedy Algorithm for Sparse Unmixing of Hyperspectral Data

Sparse unmixing assumes that each observed signature of a hyperspectral image is a linear combination of only a few spectra (endmembers) in an available spectral library. It then estimates the fractional abundances of these endmembers in the scene. The sparse unmixing problem still remains a great difficulty due to the usually high correlation of the spectral library. Under such circumstances, this paper presents a novel algorithm termed as the regularized simultaneous forward-backward greedy algorithm (RSFoBa) for sparse unmixing of hyperspectral data. The RSFoBa has low computational complexity of getting an approximate solution for the l₀ problem directly and can exploit the joint sparsity among all the pixels in the hyperspectral data. In addition, the combination of the forward greedy step and the backward greedy step makes the RSFoBa more stable and less likely to be trapped into the local optimum than the conventional greedy algorithms. Furthermore, when updating the solution in each iteration, a regularizer that enforces the spatial-contextual coherence within the hyperspectral image is considered to make the algorithm more effective. We also show that the sublibrary obtained by the RSFoBa can serve as input for any other sparse unmixing algorithms to make them more accurate and time efficient. Experimental results on both synthetic and real data demonstrate the effectiveness of the proposed algorithm.