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Open AccessArticle

Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms

by Wei Fang 1,*, Dongxu Wei 2 and Ran Zhang 3
1
Department of Computer Science and Technology, Huaibei Vocational and Technical College, Huaibei 235000, China
2
School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian 223300, China
3
Mathematics Teaching and Research Group, Nanjing No.9 High School, Nanjing 210018, China
*
Author to whom correspondence should be addressed.
Sensors 2019, 19(23), 5335; https://doi.org/10.3390/s19235335
Received: 13 November 2019 / Revised: 28 November 2019 / Accepted: 29 November 2019 / Published: 3 December 2019
(This article belongs to the Special Issue Sensor Signal and Information Processing III)
The rapid development of sensor technology gives rise to the emergence of huge amounts of tensor (i.e., multi-dimensional array) data. For various reasons such as sensor failures and communication loss, the tensor data may be corrupted by not only small noises but also gross corruptions. This paper studies the Stable Tensor Principal Component Pursuit (STPCP) which aims to recover a tensor from its corrupted observations. Specifically, we propose a STPCP model based on the recently proposed tubal nuclear norm (TNN) which has shown superior performance in comparison with other tensor nuclear norms. Theoretically, we rigorously prove that under tensor incoherence conditions, the underlying tensor and the sparse corruption tensor can be stably recovered. Algorithmically, we first develop an ADMM algorithm and then accelerate it by designing a new algorithm based on orthogonal tensor factorization. The superiority and efficiency of the proposed algorithms is demonstrated through experiments on both synthetic and real data sets. View Full-Text
Keywords: tensor principal component pursuit; stable recovery; tensor SVD; ADMM tensor principal component pursuit; stable recovery; tensor SVD; ADMM
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Fang, W.; Wei, D.; Zhang, R. Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms. Sensors 2019, 19, 5335.

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