A Multiobjective Method Leveraging Spatial–Spectral Relationship for Hyperspectral Unmixing

Free of tuning regularization parameters, sparse unmixing based on multiobjective methods has become increasingly popular for the hyperspectral image in recent years. Moreover, inherent signatures of a hyperspectral image have been exploited in various single objective-based methods and proved relevant for improving unmixing performance. However, their utilizations in multiobjective optimization are still scarce. With the overarching goal of exploiting the spatial signature in an explicit way for hyperspectral unmixing, this work proposes a multiobjective method leveraging spatial spectral relationship for hyperspectral unmixing [graph-based multiobjective optimization method for sparse unmixing (GMoSU)]. First, a multiobjective sparse unmixing model based on spatial signatures encoded by the graph Laplacian is put forward. Then, to solve this model efficiently, an improved Tchebycheff decomposition approach and a novel local recombination strategy are rationally proposed, both of them and an operation of encoding the solution as a binary vector are plugged into the framework of multiobjective evolutionary algorithm based on decomposition (MOEA/D). Theoretically, the improved Tchebycheff formula formed by introducing a mixed spectral similarity metric enables the Pareto-optimal front to converge to a single solution exactly. Encoding the solution as a binary vector could help effectively address the endmember selection problem. The novel local recombination strategy that an individual is updated through recombining with another individual selected randomly in its neighborhood could balance the diversity and convergence of population further. Finally, comprehensive comparison experiments are conducted on synthetic and real datasets, which verify the theoretical advantages and effectiveness of the proposed GMoSU even under heavy noise.