Tensor-based methods have been widely studied to attack inverse problems in hyperspectral imaging since a hyperspectral image (HSI) cube can be naturally represented as a third-order tensor, which can perfectly retain the spatial information in the image. In this article, we extend the linear tensor method to the nonlinear tensor method and propose a nonlinear low-rank tensor unmixing algorithm to solve the generalized bilinear model (GBM). Specifically, the linear and nonlinear parts of the GBM can both be expressed as tensors. Furthermore, the low-rank structures of abundance maps and nonlinear interaction abundance maps are exploited by minimizing their nuclear norm, thus taking full advantage of the high spatial correlation in HSIs. Synthetic and real-data experiments show that the low rank of abundance maps and nonlinear interaction abundance maps exploited in our method can improve the performance of the nonlinear unmixing. A MATLAB demo of this work will be available at https://github.com/LinaZhuang for the sake of reproducibility.
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