# Dictionary Learning with Low-rank Coding Coefficients for Tensor Completion

arXiv: https://arxiv.org/abs/2009.12507 · HTML: https://mlsanity.com/paper/2009.12507/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2020.

## Built on by (most cited first, 19 of 19)

- [Self-Supervised Nonlinear Transform-Based Tensor Nuclear Norm for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2105.14320/) (2021)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [OTLRM: Orthogonal Learning-based Low-Rank Metric for Multi-Dimensional Inverse Problems](https://mlsanity.com/paper/2412.11165/) (2024)
- [Learnable Scaled Gradient Descent for Guaranteed Robust Tensor PCA](https://mlsanity.com/paper/2501.04565/) (2025)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [Low-rank tensor completion via tensor joint rank with logarithmic composite norm](https://mlsanity.com/paper/2309.16208/) (2023)
- [DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery](https://mlsanity.com/paper/2407.05267/) (2024)
- [Multi-modal and frequency-weighted tensor nuclear norm for hyperspectral image denoising](https://mlsanity.com/paper/2106.12489/) (2021)
- ["Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos](https://mlsanity.com/paper/2110.09298/) (2021)
- [A New Low-Rank Learning Robust Quaternion Tensor Completion Method for Color Video Inpainting Problem and Fast Algorithms](https://mlsanity.com/paper/2306.09652/) (2023)
- [Robust Data Clustering with Outliers via Transformed Tensor Low-Rank Representation](https://mlsanity.com/paper/2307.09055/) (2023)
- [Exact Tensor Completion Powered by Slim Transforms](https://mlsanity.com/paper/2402.03468/) (2024)
- [Edge-guided Low-light Image Enhancement with Inertial Bregman Alternating Linearized Minimization](https://mlsanity.com/paper/2403.01142/) (2024)
- [Projected Tensor-Tensor Products for Efficient Computation of Optimal Multiway Data Representations](https://mlsanity.com/paper/2409.19402/) (2024)
- [3DeepRep: 3D Deep Low-rank Tensor Representation for Hyperspectral Image Inpainting](https://mlsanity.com/paper/2506.16735/) (2025)
- [Normalized Iterative Hard Thresholding for Tensor Recovery](https://mlsanity.com/paper/2507.04228/) (2025)
- [Multi-Dictionary Learning for Low Rank Sparse Coding](https://mlsanity.com/paper/2509.10033/) (2025)
- [Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform](https://mlsanity.com/paper/2512.10191/) (2025)
- [Pre-Trained Low-Rank Tensor Decomposition for Multi-Dimensional Image Recovery](https://mlsanity.com/paper/2609.12843/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor tubes. In the completion process, we minimize the low-rankness of each tensor slice containing the coding coefficients. By comparison with the traditional pre-defined transform basis, the advantages of the proposed model are that (i) the dictionary can be learned based on the given data observations so that the basis can be more adaptively and accurately constructed, and (ii) the low-rankness of the coding coefficients can allow the linear combination of dictionary features more effectively. Also we develop a multi-block proximal alternating minimization algorithm for solving such tensor learning and coding model, and show that the sequence generated by the algorithm can globally converge to a critical point. Extensive experimental results for real data sets such as videos, hyperspectral images, and traffic data are reported to demonstrate these advantages and show the performance of the proposed tensor learning and coding method is significantly better than the other tensor completion methods in terms of several evaluation metrics.