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Low rank matrix completion using truncated nuclear norm and sparse regularizer.
- Source :
-
Signal Processing: Image Communication . Oct2018, Vol. 68, p76-87. 12p. - Publication Year :
- 2018
-
Abstract
- Abstract Matrix completion is a challenging problem with a range of real applications. Many existing methods are based on low-rank prior of the underlying matrix. However, this prior may not be sufficient to recover the original matrix from its incomplete observations. In this paper, we propose a novel matrix completion algorithm by employing the low-rank prior and a sparse prior simultaneously. Specifically, the matrix completion task is formulated as a rank minimization problem with a sparse regularizer. The low-rank property is modeled by the truncated nuclear norm to approximate the rank of the matrix, and the sparse regularizer is formulated as an ℓ 1 -norm term based on a given transform operator. To address the raised optimization problem, a method alternating between two steps is developed, and the problem involved in the second step is converted to several subproblems with closed-form solutions. Experimental results show the effectiveness of the proposed algorithm and its better performance as compared with the state-of-the-art matrix completion algorithms. Highlights • This paper proposes a novel matrix completion algorithm by employing a low-rank prior based on truncated nuclear norm and a sparse prior simultaneously. • To address the resulting optimization problem, a method alternating between two steps is developed, and the problem involved in the second step is converted to several subproblems with closed-form solutions. • Experimental results demonstrate the effectiveness of the proposed algorithm and its better performance as compared with the state-of-the-art matrix completion algorithms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09235965
- Volume :
- 68
- Database :
- Academic Search Index
- Journal :
- Signal Processing: Image Communication
- Publication Type :
- Academic Journal
- Accession number :
- 131816366
- Full Text :
- https://doi.org/10.1016/j.image.2018.06.007