期刊
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
卷 60, 期 -, 页码 -出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TGRS.2021.3065990
关键词
Tensors; Mathematical model; Hyperspectral imaging; Frequency modulation; Correlation; Optimization; Task analysis; Hyperspectral image (HSI); low rank; nonlinear unmixing; tensor decomposition
类别
资金
- National Natural Science Foundation of China [42030111, 41722108, 42001287]
- AXA Research Fund
This article extends linear tensor method to nonlinear tensor method and proposes a nonlinear low-rank tensor unmixing algorithm for solving generalized bilinear model. By exploiting the low-rank structures of abundance maps and nonlinear interaction abundance maps, the performance of nonlinear unmixing can be improved.
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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