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Title: HOSVD-Based Algorithm for Weighted Tensor Completion
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.
Authors:
; ;
Award ID(s):
1934319
Publication Date:
NSF-PAR ID:
10294115
Journal Name:
Journal of Imaging
Volume:
7
Issue:
7
Page Range or eLocation-ID:
110
ISSN:
2313-433X
Sponsoring Org:
National Science Foundation
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