Nonlinear Unmixing for Hyperspectral Images via Kernel-Transformed Bilinear Mixing Models

Due to the presence of multiple scatterings, linear unmixing methods may not perform well in practical applications, and thus nonlinear unmixing has become an urgent problem to be solved. Usually, the mixing process in the observed scenarios is physically based, and many well-designed models have been proposed to interpret it. Recently, kernel-based nonlinear unmixing methods have been popularly studied to achieve a model-free and flexible representation of the nonlinearity. However, the existing kernel-based methods are mainly data-driven, which could make them fail to match the real physical mixing mechanism and result in the occurrence of overfitting. In this article, a kernel-based bilinear unmixing (KBU) method was proposed to transform the classic bilinear mixing models into their equivalent kernel forms that are more general and effective in expressing second-order scatterings. Two specific types of kernel transformations were designed, and the alternating direction method of multipliers (ADMM) was used to solve the kernel-transformed model-based optimization problem for unmixing. Moreover, the spatial prior was exploited to further improve the unmixing accuracy, and here we employ the total variation (TV) regularization as a paradigm. Experiments on synthetic data sets, physics-based simulated data sets, and real data were conducted to evaluate the algorithms. It is validated that our methods have better performance in abundance estimation and nonlinear reconstruction compared with other nonlinear unmixing methods.