Geometrical projection improved multi-objective particle swarm optimization for unsupervised nonlinear hyperspectral unmixing

In recent years, a series of bilinear mixture models (BMMs) have been well studied, based on which nonlinear unmixing algorithms for hyperspectral images have been proposed. However, the performance of unsupervised nonlinear spectral unmixing can be largely affected by the collinearity and the nonconvex unmixing problem's inherent complexity. To solve the problems, this paper proposes a geometrical projection improved multi-objective particle swarm optimization (GPMOPSO) method for nonlinear unmixing, which consists of two dynamically updating procedures. First, under the assumption of the BMMs, observed pixels are geometrically projected to their approximate linear mixture components to alleviate the collinearity. Second, the linear mixture components are efficiently decomposed to refined endmembers and abundances in an improved linear unmixing framework using multi-objective particle swarm optimization. Two advanced multi-objective optimization strategies are adopted to balance the influence of an endmember distance constraint and an abundance sparsity constraint on the achieved unsupervised linear unmixing process, respectively. Then, accurate unmixing variables can be fed back to the geometrical projection procedure to produce more reliable linear mixture components which facilitate the execution of the former in turn. Experimental results of both simulated data and real hyperspectral remote sensing data verify the superior nonlinear unmixing performance of the proposed method.