Multiobjective Endmember Extraction Based on Bilinear Mixture Model

Abstract

Hyperspectral imagery is always composed of mixed pixels because of the limited spatial resolution of a sensor and the macroscopic/microscopic mixture of distinct substances. The linear mixing model (LMM) is proven to be simple and effective in extensive literature when the macroscopic mixture dominates the mixing process. But when the photons undergo multiple reflections before reaching the sensor, the LMM becomes invalid. In this circumstance, the bilinear mixture model (Bi-LMM), which considers secondary reflections with a bilinear term, is a viable alternative. However, the bilinear term in most existing Bi-LMMs is constructed based on the pre-estimated endmembers, and thus, most Bi-LMMs focus mainly on the abundance estimation. This may lead to inaccurate estimation of endmembers and abundances for a given hyperspectral image. In this article, we propose a multiobjective endmember extraction (Bi-MoEE) method within the bilinear mixture paradigm, which considers each secondary reflection as a virtual endmember. Then, Bi-MoEE selects real and virtual endmembers from an extended spectral library consisting of a standard spectral library and their virtual products. By imposing some intuitive constraints, the solution space is greatly reduced, and the multipoint crossover and restricted bit-flip mutation operators are specially designed. Finally, Bi-MoEE can efficiently obtain a set of tradeoff solutions by minimizing the unmixing residuals and the number of selected endmembers, and automatically determine the optimal solution with multiobjective decision-making techniques. Compared with some advanced endmember extraction methods, the proposed Bi-MoEE does not need to know the number of real endmembers. In addition, the time efficiency of Bi-MoEE is mainly related to the image size and the algorithmic parameters, and has little to do with the size of spectral library, thus facilitating the practical implementation of Bi-MoEE with regard to the oversized spectral library. The experiments on synthetic and real data sets demonstrated the excellent performance of Bi-MoEE.