Cuicui Peng
ABSTRACT
Low rank representation (LRR) can recover clean data from its degraded observation data, widely used in fields such as machine learning, signal processing, and data mining. This paper proposes a new enhanced tensor low rank representation method (WSETLRR) for image denoising. Firstly, unlike existing LRR related methods, each singular value is given a different weight, i.e. using weighted tensor Schatten p-norm handle the singular value, thereby mining prior information hidden between different singular values, making data recovery more effective. Secondly, a WSETLRR optimization iterative update method based on alternating direction multiplier method (ADMM) was proposed. Finally, the results in image and video denoising experiments validate the effectiveness of our method and indicate that it outperforms other comparison methods based on tensor low rank representation.
- T. Li, W. Wang, L. Xu and X. Feng, "Image Denoising Using Low-Rank Dictionary and Sparse Representation," 2014 Tenth International Conference on Computational Intelligence and Security, Kunming, China, 2014, pp. 228-232, doi: 10.1109/CIS.2014.56.Google Scholar
Digital Library
- H. Xu, "A new low-rank sparse image denoising algorithm based on non-local self-similarity," 2020 IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA), Dalian, China, 2020, pp. 929-933, doi: 10.1109/ICAICA50127.2020.9182706.Google ScholarCross Ref
- Q. Lu, Z. Lu, X. Tao and H. Li, "A new non-local video denoising scheme using low-rank representation and total variation regularization," 2014 IEEE International Symposium on Circuits and Systems (ISCAS), Melbourne, VIC, Australia, 2014, pp. 2724-2727, doi: 10.1109/ISCAS.2014.6865736.Google ScholarCross Ref
- R.A. Harshman, , Foundations of the PARAFAC procedure: Models and conditions for an‘‘ explanatory’’ multimodal factor analysis, 1970.Google Scholar
- L.R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika 31 (3) (1966) 279–311.Google ScholarCross Ref
- I.V. Oseledets, Tensor-train decomposition, SIAM Journal on Scientific Computing 33 (2011) 2295–2317.Google ScholarDigital Library
- M.E. Kilmer, C.D. Martin, Factorization strategies for third-order tensors, Linear Algebra and its Applications 435 (3) (2011) 641–658.Google ScholarCross Ref
- C. Lu, J. Feng, W. Liu, Z. Lin, S. Yan, , Tensor robust principal component analysis with a new tensor nuclear norm, IEEE Trans. Pattern Anal. Mach. Intell. 42 (4) (2020) 925–938.Google ScholarDigital Library
- W. Cao , “Total variation regularized tensor RPCA for background subtraction from compressive measurements,” IEEE Trans. Image Process., vol. 25, no. 9, pp. 4075–4090, Sep. 2016.Google ScholarDigital Library
- Y. Liu, L. Chen, and C. Zhu, “Improved robust tensor principal component analysis via low-rank core matrix,” IEEE J. Sel. Topics Signal Process.,vol. 12, no. 6, pp. 1378–1389, Dec.018.Google ScholarCross Ref
- P. Zhou, C. Lu, J. Feng, Z. Lin, S. Yan, Tensor low-rank representation for data recovery and clustering, IEEE Trans. Pattern Anal. Mach. Intell. 43 (5) (2021) 1718–1732.Google ScholarCross Ref
- S. Du, B. Liu, G. Shan, Y. Shi, W. Wang, Enhanced tensor low-rank representation for clustering and denoising, Knowl. Based Syst. 243 (2022) 108468.Google ScholarDigital Library
- M.E. Kilmer, C.D. Martin, Factorization strategies for third-order tensors, Linear Algebra Appl. 435 (3) (2011) 641–658.Google ScholarCross Ref
- W. Xia, X. Zhang, Q. Gao, X. Shu, J. Han, and X. Gao, “Multiview subspace clustering by an enhanced tensor nuclear norm,” IEEE Trans. Cybern., vol. 52, no. 9, pp. 8962–8975, Sep. 2022.Google ScholarCross Ref
- Y. Xie, S. Gu, Y. Liu, W. Zuo, W. Zhang, and L. Zhang, “Weighted Schatten p-norm minimization for image denoising and background subtraction,” IEEE Trans. Image Process., vol. 25, no. 10, pp. 4842–4857,Oct. 2016.Google ScholarDigital Library
- B. Huang, C. Mu, D. Goldfarb, J. Wright, Provable models for robust low-rank tensor completion, Pac. J. Optim. 11 (2) (2015) 339–364.Google Scholar
Index Terms
- A New Enhanced Tensor Low Rank Representation Method for Image Denoising
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