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 $\ell _{2,0}$ norm-based algorithms. The $\ell _{2,0}$ norm, however, is sensitive to noise in some cases. Therefore, we propose an unmixing model, which contains a total variation (TV) regularization and the $\ell _{2,0}$ norm, to address the drawback of the $\ell _{2,0}$ norm 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.