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Abstract:
The problem of recovering a low-rank matrix from partial entries, known as low-rank matrix completion, has been extensively investigated in recent years. It can be viewed as a special case of the affine constrained rank minimization problem which is NP-hard in general and is computationally hard to solve in practice. One widely studied approach is to replace the matrix rank function by its nuclear-norm, which leads to the convex nuclear-norm minimization problem solved efficiently by many popular convex optimization algorithms. In this paper, we propose a new nonconvex approach to better approximate the rank function. The new approximation function is actually the Moreau envelope of the rank function (MER) which has an explicit expression. The new approximation problem of low-rank matrix completion based on MER can be converted to an optimization problem with two variables. We then adapt the proximal alternating minimization algorithm to solve it. The convergence (rate) of the proposed algorithm is proved and its accelerated version is also developed. Numerical experiments on completion of low-rank random matrices and standard image inpainting problems have shown that our algorithms have better performance than some state-of-art methods. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
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Multidimensional Systems and Signal Processing
ISSN: 0923-6082
Year: 2019
Issue: 1
Volume: 30
Page: 145-174
1 . 8 1
JCR@2019
2 . 0 3 0
JCR@2020
ESI Discipline: COMPUTER SCIENCE;
ESI HC Threshold:93
JCR Journal Grade:2
CAS Journal Grade:3
Cited Count:
WoS CC Cited Count: 6
SCOPUS Cited Count: 10
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 9
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