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 l₀ norm 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 l₀ problem 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 l₀ norm constraint guarantees sparser and more accurate results. Moreover, the antinoise ability of CSUnL0 also gets improved. Second, CSUnL0 uses l2 norm 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 l₀ norm contributes to acquiring a more sparser solution and helps CSUnL0 to enhance calculation accuracy.