A Low-complexity Tensor Completion Scheme Combining Matrix Factorization and Smoothness

In this paper, the low-complexity tensor completion (LTC) scheme is proposed to improve the efficiency of tensor completion. On one hand, the matrix factorization model is established for complexity reduction, which adopts the matrix factorization into the model of low-rank tensor completion. On the other hand, we introduce the smoothness by total variation regularization and framelet regularization to guarantee the completion performance. Accordingly, given the proposed smooth matrix factorization (SMF) model, an alternating direction method of multiple- (ADMM-) based solution is further proposed to realize the efficient and effective tensor completion. Additionally, we employ a novel tensor initialization approach to accelerate convergence speed. Finally, simulation results are presented to confirm the system gain of the proposed LTC scheme in both efficiency and effectiveness.

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A Mixture of Nuclear Norm and Matrix Factorization for Tensor Completion

Journal of Scientific Computing ◽

10.1007/s10915-017-0521-9 ◽

2017 ◽

Vol 75 (1) ◽

pp. 43-64 ◽

Cited By ~ 4

Author(s):

Shangqi Gao ◽

Qibin Fan

Keyword(s):

Matrix Factorization ◽

Nuclear Norm ◽

Tensor Completion

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Matrix factorization for low-rank tensor completion using framelet prior

Information Sciences ◽

10.1016/j.ins.2018.01.035 ◽

2018 ◽

Vol 436-437 ◽

pp. 403-417 ◽

Cited By ~ 30

Author(s):

Tai-Xiang Jiang ◽

Ting-Zhu Huang ◽

Xi-Le Zhao ◽

Teng-Yu Ji ◽

Liang-Jian Deng

Keyword(s):

Matrix Factorization ◽

Low Rank ◽

Tensor Completion ◽

Rank Tensor

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Low-complexity privacy preserving scheme based on compressed sensing and non-negative matrix factorization for image data

Optics and Lasers in Engineering ◽

10.1016/j.optlaseng.2020.106056 ◽

2020 ◽

Vol 129 ◽

pp. 106056

Author(s):

Jia Liang ◽

Di Xiao ◽

Mengdi Wang ◽

Min Li ◽

Ran Liu

Keyword(s):

Compressed Sensing ◽

Matrix Factorization ◽

Image Data ◽

Low Complexity ◽

Privacy Preserving ◽

Non Negative Matrix Factorization

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Robust tensor-completion algorithm for 5D seismic-data reconstruction

Geophysics ◽

10.1190/geo2018-0109.1 ◽

2019 ◽

Vol 84 (2) ◽

pp. V97-V109 ◽

Cited By ~ 4

Author(s):

Fernanda Carozzi ◽

Mauricio D. Sacchi

Keyword(s):

Matrix Factorization ◽

Seismic Data ◽

Data Reconstruction ◽

Reconstruction Technique ◽

Seismic Data Processing ◽

Tensor Completion ◽

The Difference ◽

New Formulation ◽

Seismic Data Reconstruction ◽

Reconstructed Data

Multidimensional seismic data reconstruction has emerged as a primary topic of research in the field of seismic data processing. Although there exists a large number of algorithms for multidimensional seismic data reconstruction, they often adopt the [Formula: see text] norm to measure the discrepancy between observed and reconstructed data. Strictly speaking, these algorithms assume well-behaved noise that ideally follows a Gaussian distribution. When erratic noise contaminates the seismic traces, a 5D reconstruction must adopt a robust criterion to measure the difference between observed and reconstructed data. We develop a new formulation to the parallel matrix factorization tensor completion method and adapt it for coping with erratic noise. We use synthetic and field-data examples to examine our robust reconstruction technique.

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