mlsanityData to 14 Oct 2026

Smooth PARAFAC Decomposition for Tensor Completion

arXiv 1505.06611 ↗First posted 25 May 2015cs.CVcited by 34

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Abstract (arXiv)

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, where the ratio of missing data is extremely high. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as "smooth PARAFAC tensor completion (SPC)." In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). First posted on arXiv 25 May 2015.

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Citing papers per year: 2021: 6; 2022: 6; 2023: 9; 2024: 6; 2025: 5; 2026: 2.

34 papers.

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  1. 2021Implicit Regularization in Tensor Factorizationcited by 44
  2. 2023Guaranteed Tensor Recovery Fused Low-rankness and Smoothnesscited by 41
  3. 2021Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputationcited by 35
  4. 2022Permutation Search of Tensor Network Structures via Local Samplingcited by 13
  5. 2023Alternating Local Enumeration (TnALE): Solving Tensor Network Structure Search with Fewer Evaluationscited by 12
  6. 2021Effective Tensor Completion via Element-wise Weighted Low-rank Tensor Train with Overlapping Ket Augmentationcited by 8
  7. 2021Robust Factorization of Real-world Tensor Streams with Patterns, Missing Values, and Outlierscited by 6
  8. 2024tnGPS: Discovering Unknown Tensor Network Structure Search Algorithms via Large Language Models (LLMs)cited by 5
  9. 2024Tensor Decomposition Meets RKHS: Efficient Algorithms for Smooth and Misaligned Datacited by 5
  10. 2021New Riemannian preconditioned algorithms for tensor completion via polyadic decompositioncited by 4
  11. 2022A case study of spatiotemporal forecasting techniques for weather forecastingcited by 3
  12. 2023Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizerscited by 3
22 more
  1. 2022Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Datacited by 2
  2. 2022Variational Bayesian inference for CP tensor completion with side informationcited by 1
  3. 2023A generalizable framework for low-rank tensor completion with numerical priorscited by 1
  4. 2023Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completioncited by 1
  5. 2023Image Reconstruction using Superpixel Clustering and Tensor Completioncited by 1
  6. 2024Haar Nuclear Norms with Applications to Remote Sensing Imagery Restorationcited by 1
  7. 2024Generalized Least Squares Kernelized Tensor Factorizationcited by 1
  8. 2025Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networkscited by 1
  9. 2026Robust Low-Rank Tensor Completion based on M-product with Weighted Correlated Total Variation and Sparse Regularizationcited by 1
  10. 2021"Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videoscited by 0
  11. 2022Soft Smoothness for Audio Inpainting Using a Latent Matrix Model in Delay-embedded Spacecited by 0
  12. 2022Latent Matrices for Tensor Network Decomposition and to Tensor Completioncited by 0
  13. 2023Optical Coherence Tomography Image Enhancement via Block Hankelization and Low Rank Tensor Network Approximationcited by 0
  14. 2023Neural Gradient Regularizercited by 0
  15. 2023ADMM-MM Algorithm for General Tensor Decompositioncited by 0
  16. 2024Functional-Edged Network Modelingcited by 0
  17. 2024BAMITA: Bayesian Multiple Imputation for Tensor Arrayscited by 0
  18. 2025MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Normcited by 0
  19. 2025LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completioncited by 0
  20. 2025Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoiserscited by 0
  21. 2025Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transformcited by 0
  22. 2026Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularizationcited by 0