A Joint Spectral Unmixing and Subpixel Mapping Framework Based on Multiobjective Optimization

Conventional subpixel mapping (SPM) is performed based on the abundance maps obtained by spectral unmixing (SU), to interpret the mixed pixels and improve the mapping resolution for hyperspectral remote-sensing imagery. However, the SU and SPM tasks are separately conducted, so that the unmixing error is propagated to SPM, and the mapping result is strongly reliant on the quality of the abundance maps. In this article, a novel joint SPM and SU framework (MO_SUSM) based on multiobjective optimization is proposed to simultaneously perform unmixing and mapping. Specifically, the multiobjective joint optimization model with a data fidelity term and a Laplacian prior term is constructed for SU and SPM. For the data fidelity term, since the unmixing result can be recovered by downsampling the mapping result, the unmixing model is joined with the mapping model by the downsampling matrix, so that the reconstruction errors of the unmixing and mapping results can be minimized together. Meanwhile, the Laplacian prior term is used to maximize the spatial dependence of the mapping result and provide the spatial constraint for SU. In addition, the multiobjective optimization algorithm with local search is designed to search for the optimal unmixing and mapping results that can balance the objective terms. Since the two objective terms are dynamically integrated during optimization, there is no need to set sensitive weights for the objectives combination. Four experiments were conducted on hyperspectral images of various data sources, including ground, airborne, and satellite images. The unmixing results show that MO_SUSM can reduce the unmixing error and can improve the quality of the abundance maps. The mapping results show that MO_SUSM can alleviate the dependence of SPM on the abundance maps and can improve the mapping accuracy.