mlsanityData to 7 Oct 2026

Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion

arXiv 1909.06982 ↗First posted 16 Sep 2019eess.IV cs.CVcited by 36

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Abstract (arXiv)

The main aim of this paper is to develop a framelet representation of the tensor nuclear norm for third-order tensor completion. In the literature, the tensor nuclear norm can be computed by using tensor singular value decomposition based on the discrete Fourier transform matrix, and tensor completion can be performed by the minimization of the tensor nuclear norm which is the relaxation of the sum of matrix ranks from all Fourier transformed matrix frontal slices. These Fourier transformed matrix frontal slices are obtained by applying the discrete Fourier transform on the tubes of the original tensor. In this paper, we propose to employ the framelet representation of each tube so that a framelet transformed tensor can be constructed. Because of framelet basis redundancy, the representation of each tube is sparsely represented. When the matrix slices of the original tensor are highly correlated, we expect the corresponding sum of matrix ranks from all framelet transformed matrix frontal slices would be small, and the resulting tensor completion can be performed much better. The proposed minimization model is convex and global minimizers can be obtained. Numerical results on several types of multi-dimensional data (videos, multispectral images, and magnetic resonance imaging data) have tested and shown that the proposed method outperformed the other testing methods.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 16 Sep 2019.

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Citing papers per year: 2021: 7; 2022: 5; 2023: 5; 2024: 7; 2025: 11; 2026: 1.

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  1. 2022Low-Rank Tensor Function Representation for Multi-Dimensional Data Recoverycited by 45
  2. 2023DDS2M: Self-Supervised Denoising Diffusion Spatio-Spectral Model for Hyperspectral Image Restorationcited by 32
  3. 2021Fusformer: A Transformer-based Fusion Approach for Hyperspectral Image Super-resolutioncited by 31
  4. 2021Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recoverycited by 16
  5. 2024Revisiting Nonlocal Self-Similarity from Continuous Representationcited by 14
  6. 2021Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completioncited by 13
  7. 2022Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Functioncited by 7
  8. 2022T2LR-Net: An unrolling network learning transformed tensor low-rank prior for dynamic MR image reconstructioncited by 4
  9. 2023H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorizationcited by 3
  10. 2023To Fold or Not to Fold: Graph Regularized Tensor Train for Visual Data Completioncited by 3
  11. 2025Cross-Frequency Implicit Neural Representation with Self-Evolving Parameterscited by 2
  12. 2025Iterative Low-rank Network for Hyperspectral Image Denoisingcited by 2
24 more
  1. 2021Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Normcited by 1
  2. 2023Low-rank tensor completion via tensor joint rank with logarithmic composite normcited by 1
  3. 2024Adaptive Block Sparse Regularization under Arbitrary Linear Transformcited by 1
  4. 2024DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recoverycited by 1
  5. 2024Haar Nuclear Norms with Applications to Remote Sensing Imagery Restorationcited by 1
  6. 2024Low-Rank Tensor Learning by Generalized Nonconvex Regularizationcited by 1
  7. 2025Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detectioncited by 1
  8. 2025When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learningcited by 1
  9. 2021Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoisingcited by 0
  10. 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recoverycited by 0
  11. 2021"Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videoscited by 0
  12. 2022Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penaltycited by 0
  13. 2022Tensor Robust PCA with Nonconvex and Nonlocal Regularizationcited by 0
  14. 2023Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representationcited by 0
  15. 2024Exact Tensor Completion Powered by Slim Transformscited by 0
  16. 2024Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representationscited by 0
  17. 2025A novel non-convex minimax p-th order concave penalty function approach to low-rank tensor completioncited by 0
  18. 2025MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Normcited by 0
  19. 20253DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpaintingcited by 0
  20. 2025Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Normcited by 0
  21. 2025Superpixel-informed Continuous Low-Rank Tensor Representation for Multi-Dimensional Data Recoverycited by 0
  22. 2025Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoiserscited by 0
  23. 2025An Interdisciplinary and Cross-Task Review on Missing Data Imputationcited by 0
  24. 2026Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recoverycited by 0