# Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data

arXiv: https://arxiv.org/abs/2106.10422 · HTML: https://mlsanity.com/paper/2106.10422/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 77 references that are in the map.
- First posted on arXiv 19 Jun 2021.

## Builds on (most cited first, 20 of 20)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Multi-modal Factorized Bilinear Pooling with Co-Attention Learning for Visual Question Answering](https://mlsanity.com/paper/1708.01471/) (2017)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion](https://mlsanity.com/paper/1809.02288/) (2018)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Low-tubal-rank Tensor Completion using Alternating Minimization](https://mlsanity.com/paper/1610.01690/) (2016)
- [Tensor-Ring Nuclear Norm Minimization and Application for Visual Data Completion](https://mlsanity.com/paper/1903.08888/) (2019)
- [On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems](https://mlsanity.com/paper/1409.8033/) (2014)
- [Provable Tensor Ring Completion](https://mlsanity.com/paper/1903.03315/) (2019)
- [Top-N Recommender System via Matrix Completion](https://mlsanity.com/paper/1601.04800/) (2016)
- [Exactly Robust Kernel Principal Component Analysis](https://mlsanity.com/paper/1802.10558/) (2018)
- [Tensor train rank minimization with nonlocal self-similarity for tensor completion](https://mlsanity.com/paper/2004.14273/) (2020)
- [Robust Non-Linear Matrix Factorization for Dictionary Learning, Denoising, and Clustering](https://mlsanity.com/paper/2005.01317/) (2020)
- [High-order Tensor Completion for Data Recovery via Sparse Tensor-train Optimization](https://mlsanity.com/paper/1711.02271/) (2017)
- [An Iterative Reweighted Method for Tucker Decomposition of Incomplete Multiway Tensors](https://mlsanity.com/paper/1511.04695/) (2015)
- [Restricted Low-Rank Approximation via ADMM](https://mlsanity.com/paper/1512.01748/) (2015)

## Built on by (most cited first, 3 of 3)

- [Nonconvex Robust High-Order Tensor Completion Using Randomized Low-Rank Approximation](https://mlsanity.com/paper/2305.11495/) (2023)
- [Robust Low-Rank Matrix Completion via a New Sparsity-Inducing Regularizer](https://mlsanity.com/paper/2310.04762/) (2023)
- [Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers](https://mlsanity.com/paper/2510.12425/) (2025)

## Abstract (arXiv)

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which catalyzed the development of robust algorithms that alleviate the effect of outliers. However, existing robust methods largely presume that the corruption is sparse, which may not hold in practice. In this paper, we develop a two-stage robust tensor completion approach to deal with tensor completion of visual data with a large amount of gross corruption. A novel coarse-to-fine framework is proposed which uses a global coarse completion result to guide a local patch refinement process. To efficiently mitigate the effect of a large number of outliers on tensor recovery, we develop a new M-estimator-based robust tensor ring recovery method which can adaptively identify the outliers and alleviate their negative effect in the optimization. The experimental results demonstrate the superior performance of the proposed approach over state-of-the-art robust algorithms for tensor completion.