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SCIENCE CHINA Information Sciences, Volume 64 , Issue 1 : 119101(2021) https://doi.org/10.1007/s11432-019-2717-4

Tensor restricted isometry property analysis for a large class of random measurement ensembles

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  • ReceivedJun 4, 2019
  • AcceptedNov 6, 2019
  • PublishedJul 24, 2020

Abstract

There is no abstract available for this article.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 61673015, 61273020, 11901476), Fundamental Research Funds for the Central Universities (Grant Nos. XDJK2018C076, SWU1809002), China Postdoctoral Science Foundation (Grant No. 2018M643390), and Graduate Student Scientific Research Innovation Projects in Chongqing (Grant No. CYB19083).


Supplement

Notations, definitions, and probabilistic tools are introduced in Appendixes A and B. Appendixes C and D present the proof of Theorem 1 and some numerical experiments.


References

[1] Lu C, Feng J, Lin Z, et al. Exact low tubal rank tensor recovery from Gaussian measurements. In: Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI), Stockholm, 2018. 2504--2510. Google Scholar

[2] Wang J, Zhang F, Huang J. A nonconvex penalty function with integral convolution approximation for compressed sensing. Signal Processing, 2019, 158: 116-128 CrossRef Google Scholar

[3] Candès E J, Plan Y. Tight Oracle Inequalities for Low-Rank Matrix Recovery From a Minimal Number of Noisy Random Measurements. IEEE Trans Inform Theor, 2011, 57: 2342-2359 CrossRef Google Scholar

[4] Recht B, Fazel M, Parrilo P A. Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization. SIAM Rev, 2010, 52: 471-501 CrossRef Google Scholar

[5] Lu C, Feng J, chen . Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm.. IEEE Trans Pattern Anal Mach Intell, 2019, : 1-1 CrossRef PubMed Google Scholar

[6] Zhang F, Wang W, Huang J, et al. RIP-based performance guarantee for low-tubal-rank tensor recovery. 2019,. arXiv Google Scholar

[7] Wang A, Song X, Wu X, et al. Generalized dantzig selector for low-tubal-rank tensor recovery. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, 2019. 3427--3431. Google Scholar

[8] Shi Z, Han J, Zheng T, et al. Guarantees of augmented trace norm models in tensor recovery. In: Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI), Beijing, 2013. 1670--1676. Google Scholar