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Article

HOSVD-Based Algorithm for Weighted Tensor Completion

by , *,† and
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Jérôme Gilles
J. Imaging 2021, 7(7), 110; https://doi.org/10.3390/jimaging7070110
Received: 15 May 2021 / Revised: 17 June 2021 / Accepted: 2 July 2021 / Published: 7 July 2021
Matrix completion, the problem of completing missing entries in a data matrix with low-dimensional structure (such as rank), has seen many fruitful approaches and analyses. Tensor completion is the tensor analog that attempts to impute missing tensor entries from similar low-rank type assumptions. In this paper, we study the tensor completion problem when the sampling pattern is deterministic and possibly non-uniform. We first propose an efficient weighted Higher Order Singular Value Decomposition (HOSVD) algorithm for the recovery of the underlying low-rank tensor from noisy observations and then derive the error bounds under a properly weighted metric. Additionally, the efficiency and accuracy of our algorithm are both tested using synthetic and real datasets in numerical simulations. View Full-Text
Keywords: HOSVD decomposition; tensor completion; weighted tensor HOSVD decomposition; tensor completion; weighted tensor
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MDPI and ACS Style

Chao, Z.; Huang, L.; Needell, D. HOSVD-Based Algorithm for Weighted Tensor Completion. J. Imaging 2021, 7, 110. https://doi.org/10.3390/jimaging7070110

AMA Style

Chao Z, Huang L, Needell D. HOSVD-Based Algorithm for Weighted Tensor Completion. Journal of Imaging. 2021; 7(7):110. https://doi.org/10.3390/jimaging7070110

Chicago/Turabian Style

Chao, Zehan, Longxiu Huang, and Deanna Needell. 2021. "HOSVD-Based Algorithm for Weighted Tensor Completion" Journal of Imaging 7, no. 7: 110. https://doi.org/10.3390/jimaging7070110

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