Collaborative Sparse Hyperspectral Unmixing Using l₀ Norm

Sparse unmixing has been applied on hyperspectral imagery popularly in recent years. It assumes that every observed signature is a linear combination of just a few spectra (end-members) from a known spectral library. However, solving the sparse unmixing problem directly (using l0norm to control the sparsity of solution at a low level) is NP-hard. Most related works focus on convex relaxation methods, but the sparsity and accuracy of results cannot be well guaranteed. Under these circumstances, this paper proposes a novel algorithm termed collaborative sparse hyperspectral unmixing using l0 norm (CSUnL0), which aims at solving l0problem directly. First, it introduces a row-hard-threshold function. The row-hardthreshold function makes it possible to combine l0 norm, instead of its approximate norms, with alternating direction method of multipliers. Compared with the convex relaxation methods, the l0norm constraint guarantees sparser and more accurate results. Moreover, the antinoise ability of CSUnL0 also gets improved. Second, CSUnL0 uses l2norm of each end-members' abundance across the whole map as a collaborative constraint, which can take advantage of the hyperspectral data's subspace property. The experimental results indicate that l0norm contributes to acquiring a more sparser solution and helps CSUnL0 to enhance calculation accuracy.