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

Using Low-Rank Representation of Abundance Maps and Nonnegative Tensor Factorization for Hyperspectral Nonlinear Unmixing