Row-Sparsity Spectral Unmixing via Total Variation

Row sparsity of hyperspectral unmixing has attracted considerable attention in recent years. It exploits the fact that a hyperspectral image contains only a few number of endmembers. This property has been well investigated by the ℓ2,0norm-based algorithms. The ℓ2,0norm, however, is sensitive to noise in some cases. Therefore, we propose an unmixing model, which contains a total variation (TV) regularization and the ℓ2,0norm, to address the drawback of the ℓ2,0norm in the noise scenario, and promote piecewise smoothness in abundance maps. To solve the proposed model, we design an algorithm, termed as row-sparsity spectral unmixing via total variation (RSSUn-TV), under the nonconvex alternating direction method of multipliers (ADMM) framework. Particularly, we establish the convergence analysis of the RSSUn-TV algorithm. Experimental results on both synthetic and real hyperspectral data demonstrate that our proposed algorithm is effective for hyperspectral unmixing.