Tensor completion and Tensor recovery from Gaussian measurements

Introduction

In our work [1], we give the exact recovery guarantees of tensor completion and tensor recovery from Gaussian measurements by tensor nuclear norm minimization. The tensor nuclear norm was proposed in our works [3][4]. A more general tensor nuclear norm undear general invertible linear transform was proposed in [5] and applied to tensor completion [5] and tensor robust PCA [6].

We provide the codes of the following two models in [1].

1. Tensor completion by tensor nuclear norm minimization
   

   

2. Tensor recovery from Gaussian measurements by tensor nuclear norm minimization
   

   

Related Toolboxes

• Tensor-Tensor Product Toolbox 2.0
• Tensor robust PCA and tensor completion based on tensor nuclear norm under linear transform
• Tensor robust principal component analysis
• A Library of ADMM for Sparse and Low-rank Optimization

References

1. Canyi Lu, Jiashi Feng, Zhouchen Lin, Shuicheng Yan. Exact Low Tubal Rank Tensor Recovery from Gaussian Measurements. International Joint Conference on Artificial Intelligence (IJCAI). 2018
2. Canyi Lu. Tensor-Tensor Product Toolbox. Carnegie Mellon University, June 2018. https://github.com/canyilu/tproduct.
3. Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, Shuicheng Yan. Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm. TPAMI. 2019
4. Canyi Lu, Jiashi Feng, Yudong Chen, Wei Liu, Zhouchen Lin, Shuicheng Yan. Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization. CVPR, 2016
5. Canyi Lu, Xi Peng, Yunchao Wei. Low-Rank Tensor Completion With a New Tensor Nuclear Norm Induced by Invertible Linear Transforms. IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 2019
6. Canyi Lu, Pan Zhou. Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms. arXiv preprint arXiv:1907.08288. 2019