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].
- Tensor completion by tensor nuclear norm minimization
- Tensor recovery from Gaussian measurements by tensor nuclear norm minimization
- 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
- 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
- Canyi Lu. Tensor-Tensor Product Toolbox. Carnegie Mellon University, June 2018. https://github.com/canyilu/tproduct.
- 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
- 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
- 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
- Canyi Lu, Pan Zhou. Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms. arXiv preprint arXiv:1907.08288. 2019