mlsanityData to 14 Oct 2026

Multi-dimensional imaging data recovery via minimizing the partial sum of tubal nuclear norm

arXiv 1712.05870 ↗First posted 15 Dec 2017math.NA cs.CV cs.NAcited by 19

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Abstract (arXiv)

In this paper, we investigate tensor recovery problems within the tensor singular value decomposition (t-SVD) framework. We propose the partial sum of the tubal nuclear norm (PSTNN) of a tensor. The PSTNN is a surrogate of the tensor tubal multi-rank. We build two PSTNN-based minimization models for two typical tensor recovery problems, i.e., the tensor completion and the tensor principal component analysis. We give two algorithms based on the alternating direction method of multipliers (ADMM) to solve proposed PSTNN-based tensor recovery models. Experimental results on the synthetic data and real-world data reveal the superior of the proposed PSTNN.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Dec 2017.

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Citing papers per year: 2021: 3; 2022: 4; 2023: 4; 2024: 3; 2025: 4; 2026: 1.

19 papers.

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  1. 2022Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Functioncited by 7
  2. 2024Low-Tubal-Rank Tensor Recovery via Factorized Gradient Descentcited by 7
  3. 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
  4. 2022Bayesian Robust Tensor Ring Model for Incomplete Multiway Datacited by 2
  5. 2025Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCAcited by 2
  6. 2023Non-convex approaches for low-rank tensor completion under tubal samplingcited by 1
  7. 2023A Novel Tensor Factorization-Based Method with Robustness to Inaccurate Rank Estimationcited by 1
  8. 2023Low-rank tensor completion via tensor joint rank with logarithmic composite normcited by 1
  9. 2024DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recoverycited by 1
  10. 2025Efficient Low-Tubal-Rank Tensor Estimation via Alternating Preconditioned Gradient Descentcited by 1
  11. 2021Hyperspectral Image Denoising via Multi-modal and Double-weighted Tensor Nuclear Normcited by 0
  12. 2021Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoisingcited by 0
7 more
  1. 2021Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recoverycited by 0
  2. 2022Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penaltycited by 0
  3. 2022Global Weighted Tensor Nuclear Norm for Tensor Robust Principal Component Analysiscited by 0
  4. 2024Variational Bayesian Inference for Tensor Robust Principal Component Analysiscited by 0
  5. 2025A novel non-convex minimax p-th order concave penalty function approach to low-rank tensor completioncited by 0
  6. 2025Outlier-aware Tensor Robust Principal Component Analysis with Self-guided Data Augmentationcited by 0
  7. 2026Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Normcited by 0