Superpixel-Based Reweighted Low-Rank and Total Variation Sparse Unmixing for Hyperspectral Remote Sensing Imagery

Sparse unmixing, as a semisupervised unmixing method, has attracted extensive attention. The process of sparse unmixing involves treating the mixed pixels of hyperspectral imagery as a linear combination of a small number of spectral signatures (endmembers) in a standard spectral library, associated with fractional abundances. Over the past ten years, to achieve a better performance, sparse unmixing algorithms have begun to focus on the spatial information of hyperspectral images. However, less accurate spatial information greatly limits the performance of the spatial-regularization-based sparse unmixing algorithms. In this article, to overcome this limitation and obtain more reliable spatial information, a novel sparse unmixing algorithm named superpixel-based reweighted low-rank and total variation (SUSRLR-TV) is proposed to enhance the performance of the traditional spatial-regularization-based sparse unmixing approaches. In the proposed approach, superpixel segmentation is adopted to consider both the spatial proximity and the spectral similarity. In addition, a low-rank constraint is enforced on the objective function as pixels within each superpixel have the same endmembers and similar abundance values, and they naturally satisfy the low-rank constraint. Differing from the traditional nuclear norm, a reweighted nuclear norm is used to achieve a more efficient and accurate low-rank constraint. Meanwhile, low-rank consideration is also used to enhance the spatial continuity and suppress the effects of random noise. Furthermore, TV regularization is introduced to promote the smoothness of the abundance maps. Experiments on three simulated data sets, as well as a well-known real hyperspectral imagery data set, confirm the superior performance of the proposed method in both the qualitative assessment and the quantitative evaluation, compared with the state-of-the-art sparse unmixing methods.