期刊
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
卷 58, 期 1, 页码 734-749出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TGRS.2019.2940534
关键词
Alternating direction method of multipliers (ADMMs); hyperspectral image (HSI); log-based function; tensor fibered rank; tensor nuclear norm
类别
资金
- National Natural Science Foundation of China [61772003, 61876203, 11901450]
- Fundamental Research Funds for the Central Universities [31020180QD126]
- National Postdoctoral Program for Innovative Talents [BX20180252]
- China Postdoctoral Science Foundation [2018M643611]
The tensor tubal rank, defined based on the tensor singular value decomposition (t-SVD), has obtained promising results in hyperspectral image (HSI) denoising. However, the framework of the t-SVD lacks flexibility for handling different correlations along different modes of HSIs, leading to suboptimal denoising performance. This article mainly makes three contributions. First, we introduce a new tensor rank named tensor fibered rank by generalizing the t-SVD to the mode- t-SVD, to achieve a more flexible and accurate HSI characterization. Since directly minimizing the fibered rank is NP-hard, we suggest a three-directional tensor nuclear norm (3DTNN) and a three-directional log-based tensor nuclear norm (3DLogTNN) as its convex and nonconvex relaxation to provide an efficient numerical solution, respectively. Second, we propose a fibered rank minimization model for HSI mixed noise removal, in which the underlying HSI is modeled as a low-fibered-rank component. Third, we develop an efficient alternating direction method of multipliers (ADMMs)-based algorithm to solve the proposed model, especially, each subproblem within ADMM is proven to have a closed-form solution, although 3DLogTNN is nonconvex. Extensive experimental results demonstrate that the proposed method has superior denoising performance, as compared with the state-of-the-art competing methods on low-rank matrix/tensor approximation and noise modeling.
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