A Two-Phase Multiobjective Sparse Unmixing Approach for Hyperspectral Data

With the sparse unmixing becoming increasingly popular recently, some advanced regularization algorithms have been proposed for settling this problem. However, they are limited by their “decision ahead of solution” attribute, i.e., the regularization parameters must be preset before the solution is obtained. In this paper, the sparse unmixing problem is first formulated as a two-phase multiobjective problem. The first phase simultaneously minimizes the unmixing residuals and the number of estimated endmembers for automatically finding the real active endmembers from the spectral library. A decomposition-based endmember selection algorithm considering the gene exchange in the population is specially designed for better and quicker search of the decision space. This algorithm can obtain a set of nondominated solutions for better decision of the active endmembers, which are important for the subsequent calculation of the abundance matrix. The second phase concurrently minimizes the unmixing residuals and the total variation term for estimating a preferable abundance matrix. A local search strategy based on the multiplicative update rule is designed in the evolution process for better approximation of the Pareto front. The experimental results on the synthetic as well as the real data reveal that the proposed framework has a better performance in finding the real active endmembers and estimating their corresponding abundances than some advanced regularization algorithms.