Abstract
The image processing usually depends on exploring the structure and the geometric information of the tensor objects generated by image data. In the process, the decomposition of the tensor objects is very significant for the dimension reduction and the low-rank representation of image data. In this paper, based on the triple decomposition of third-order tensors and the correlation between different nonnegative tensor objects, a nonnegative triple decomposition model with manifold regularization terms is constructed. Then, an algorithm for the manifold regularization nonnegative triple decomposition is proposed, and the convergence of the algorithm is discussed. Furthermore, experiments on some real-world image data sets are given to illustrate the feasibility and effectiveness of the proposed algorithms.
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The authors sincerely thank the editor and anonymous referees for their constructive comments that substantially improved the quality of this paper. This paper is supported in part by National Natural Science Foundations of China (11861077, 12061087); the Graduate Research and Innovation Project of Yunnan University (2020Z67); Program for Excellent Young Talents, Yunnan University, and Yunnan Provincial Ten Thousands Plan Young Top Talents.
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Communicated by Liqun Qi.
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Wu, F., Li, C. & Li, Y. Manifold Regularization Nonnegative Triple Decomposition of Tensor Sets for Image Compression and Representation. J Optim Theory Appl 192, 979–1000 (2022). https://doi.org/10.1007/s10957-022-02001-6
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DOI: https://doi.org/10.1007/s10957-022-02001-6