Regularized MSBL algorithm with spatial correlation for sparse hyperspectral unmixing

Sparse unmixing is a promising approach that is formulated as a linear regression problem by assuming that observed signatures can be expressed as a linear combination of a few endmembers in the spectral library. Under this formulation, a novel regularized multiple sparse Bayesian learning model, which is constructed via Bayesian inference with the conditional posterior distributions of model parameters under a hierarchical Bayesian model, is proposed to solve the sparse unmixing problem. Then, the total variation regularization and the non-negativity constraint are incorporated into the model, thus exploiting the spatial information and the physical property in hyperspectral images. The optimal problem of the model is decomposed into several simpler iterative optimization problems that are solved via the alternating direction method of multipliers, and the model parameters are updated adaptively from the algorithm. Experimental results on both synthetic and real hyperspectral data demonstrate that the proposed method outperforms the other algorithms.