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Article

Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data

by 1,2,3, 1,3 and 1,2,*
1
School of Automation, Guangdong University of Technology, Guangzhou 510006, China
2
Tensor Learning Team, RIKEN AIP, Tokyo 103-0027, Japan
3
Key Laboratory of Intelligent Detection and The Internet of Things in Manufacturing, Ministry of Education, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Academic Editors: Karen Egiazarian, Aleksandra Pizurica and Vladimir Lukin
Remote Sens. 2021, 13(18), 3671; https://doi.org/10.3390/rs13183671
Received: 30 July 2021 / Revised: 3 September 2021 / Accepted: 9 September 2021 / Published: 14 September 2021
(This article belongs to the Special Issue Remote Sensing Image Denoising, Restoration and Reconstruction)
This paper conducts a rigorous analysis for the problem of robust tensor completion, which aims at recovering an unknown three-way tensor from incomplete observations corrupted by gross sparse outliers and small dense noises simultaneously due to various reasons such as sensor dead pixels, communication loss, electromagnetic interferences, cloud shadows, etc. To estimate the underlying tensor, a new penalized least squares estimator is first formulated by exploiting the low rankness of the signal tensor within the framework of tensor L-Singular Value Decomposition (L-SVD) and leveraging the sparse structure of the outlier tensor. Then, an algorithm based on the Alternating Direction Method of Multipliers (ADMM) is designed to compute the estimator in an efficient way. Statistically, the non-asymptotic upper bound on the estimation error is established and further proved to be optimal (up to a log factor) in a minimax sense. Simulation studies on synthetic data demonstrate that the proposed error bound can predict the scaling behavior of the estimation error with problem parameters (i.e., tubal rank of the underlying tensor, sparsity of the outliers, and the number of uncorrupted observations). Both the effectiveness and efficiency of the proposed algorithm are evaluated through experiments for robust completion on seven different types of remote sensing data. View Full-Text
Keywords: remote sensing data restoration; robust tensor completion; tensor SVD; statistical performance; ADMM remote sensing data restoration; robust tensor completion; tensor SVD; statistical performance; ADMM
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MDPI and ACS Style

Wang, A.; Zhou, G.; Zhao, Q. Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data. Remote Sens. 2021, 13, 3671. https://doi.org/10.3390/rs13183671

AMA Style

Wang A, Zhou G, Zhao Q. Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data. Remote Sensing. 2021; 13(18):3671. https://doi.org/10.3390/rs13183671

Chicago/Turabian Style

Wang, Andong, Guoxu Zhou, and Qibin Zhao. 2021. "Guaranteed Robust Tensor Completion via ∗L-SVD with Applications to Remote Sensing Data" Remote Sensing 13, no. 18: 3671. https://doi.org/10.3390/rs13183671

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