Publication Type

Journal Article

Version

acceptedVersion

Publication Date

10-2017

Abstract

Recently, a tensor nuclear norm (TNN) based method [1] was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the lowrank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker (KKT) point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN [1] and matricization methods [2]–[5].

Keywords

Tensor Factorization, Tensor Completion, Lowrank Factorization

Discipline

Databases and Information Systems

Research Areas

Intelligent Systems and Optimization

Areas of Excellence

Digital transformation

Publication

IEEE Transactions on Image Processing

Volume

27

Issue

3

First Page

1152

Last Page

1163

ISSN

1057-7149

Identifier

10.1109/TIP.2017.2762595

Publisher

Institute of Electrical and Electronics Engineers

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1109/TIP.2017.2762595

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