Joint-Sparse-Blocks Regression for Total Variation Regularized Hyperspectral Unmixing

Sparse unmixing has attracted much attention in recent years. It aims at estimating the fractional abundances of pure spectral signatures in mixed pixels in hyperspectral images. To exploit spatial-contextual information present in the scene, the total variation (TV) regularization is incorporated into the sparse unmixing formulation, promoting adjacent pixels having similar not only endmembers but also fractional abundances, and thus having similar structural sparsity. It is therefore hoped to impose joint sparsity, instead of classic single sparsity, on these adjacent pixels to further improve the unmixing performance. To this end, we include the joint-sparse-blocks regression into the TV spatial regularization framework and present a new unmixing algorithm, termed joint-sparse-blocks unmixing via variable splitting augmented Lagrangian and total variation (JSBUnSAL-TV). In particular, a reweighting strategy is utilized to enhance sparsity along lines within each block. Simulated and real-data experiments show the advantages of the proposed algorithm.