Endmember Extraction From Highly Mixed Data Using Linear Mixture Model Constrained Particle Swarm Optimization

Spectral unmixing is one of the most important techniques for analyzing hyperspectral images. Many of the hyperspectral unmixing algorithms developed in recent years have been developed under an assumption that pure pixels exist, and some algorithms, such as N-finder algorithm (N-FINDR) and vertex component analysis (VCA), can only search data points in this case. However, the pure-pixel assumption may be seriously violated for highly mixed data. Whether a pure pixel exists or not, the endmember extraction can be regarded as an optimization problem. In this paper, we incorporate the linear mixture model (LMM) and particle swarm optimization (PSO) to develop LMM constrained PSO (LMMC-PSO) for endmember extraction from highly mixed data. The main contribution of the proposed method is that we redefine the particle motion rules. Each particle in LMMC-PSO moves in the search space according to the LMM, rather than with a velocity. The LMM is one kind of relationship between endmembers and mixed pixels, which can help guide efforts to build a path from mixed pixels to endmembers in PSO. The proposed algorithm was tested and evaluated with both synthetic and real hyperspectral data sets. The experimental results indicated that the proposed method obtains better results with highly mixed data than the algorithms of VCA, minimum volume constrained nonnegative matrix factorization, minimum volume simplex analysis (MVSA), robust MVSA, the convex analysis-based minimum volume enclosing simplex, and simplex identification via variable splitting and augmented Lagrangian.