# Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Norm

arXiv: https://arxiv.org/abs/2108.03002 · HTML: https://mlsanity.com/paper/2108.03002/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 50 references that are in the map.
- First posted on arXiv 6 Aug 2021.

## Builds on (most cited first, 7 of 7)

- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Deep Plug-and-play Prior for Low-rank Tensor Completion](https://mlsanity.com/paper/1905.04449/) (2019)
- [Total Variation Regularized Tensor RPCA for Background Subtraction from Compressive Measurements](https://mlsanity.com/paper/1503.01868/) (2015)
- [Semiblind Hyperspectral Unmixing in the Presence of Spectral Library Mismatches](https://mlsanity.com/paper/1507.01661/) (2015)

## Built on by (most cited first, 1 of 1)

- [Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function](https://mlsanity.com/paper/2206.13506/) (2022)

## Abstract (arXiv)

The low rank tensor completion (LRTC) problem has attracted great attention in computer vision and signal processing. How to acquire high quality image recovery effect is still an urgent task to be solved at present. This paper proposes a new tensor L2,1 norm minimization model (TLNM) that integrates sum nuclear norm (SNN) method, differing from the classical tensor nuclear norm (TNN)-based tensor completion method, with L2,1 norm and Qatar Riyal decomposition for solving the LRTC problem. To improve the utilization rate of the local prior information of the image, a total variation (TV) regularization term is introduced, resulting in a new class of tensor L2,1 norm minimization with total variation model (TLNMTV). Both proposed models are convex and therefore have global optimal solutions. Moreover, we adopt the Alternating Direction Multiplier Method (ADMM) to obtain the closed-form solution of each variable, thus ensuring the feasibility of the algorithm. Numerical experiments show that the two proposed algorithms are convergent and outperform compared methods. In particular, our method significantly outperforms the contrastive methods when the sampling rate of hyperspectral images is 2.5%.