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Alternating direction method of multipliers for linear hyperspectral unmixing

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Abstract

Linear hyperspectral unmixing (LHU) is a class of important problems in remote sensing. It can be modelled by a linearly constrained convex optimization problem with a coupled objective function. This paper proposes an alternating direction method of multipliers (ADMM) for solving this LHU model. The special structure of the LHU model allows explicit solutions to the subproblems in the ADMM and hence the ADMM is easily implementable. The global convergence of the ADMM is established despite the existence of a coupled term in the objective function. Our numerical experiments with four data sets demonstrated that the proposed ADMM is effective for solving the LHU model.

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Acknowledgements

Y. H. Dai was supported by the Natural Science Foundation of China (Nos. 11991020, 11631013, 11971372 and 11991021) and the Strategic Priority Research Program of Chinese Academy of Sciences (No. XDA27000000). F. Xu was supported in part by the Tian Yuan Mathematical Foundation (Nos. 12126348 and 12126370) and the National Natural Science Foundation of China No. 11901359. L. Zhang was supported by the Natural Science Foundation of China (Nos. 11971089 and 11731013) and partially supported by Dalian High-level Talent Innovation Project No. 2020RD09.

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Authors and Affiliations

  1. LSEC, AMSS, Chinese Academy of Sciences, Beijing, 100090, China

    Yu-Hong Dai

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China

    Fangfang Xu

  3. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Liwei Zhang

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  1. Yu-Hong Dai
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  2. Fangfang Xu
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  3. Liwei Zhang
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Correspondence to Fangfang Xu.

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Dai, YH., Xu, F. & Zhang, L. Alternating direction method of multipliers for linear hyperspectral unmixing. Math Meth Oper Res 97, 289–310 (2023). https://doi.org/10.1007/s00186-023-00815-2

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  • DOI: https://doi.org/10.1007/s00186-023-00815-2

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