Low rank matrix completion using truncated nuclear norm and sparse regularizer

• Published in: Signal processing. Image communication 2018-10, Vol.68, p.76-87
• Main Authors: Dong, Jing, Xue, Zhichao, Guan, Jian, Han, Zi-Fa, Wang, Wenwu
• Format: Article
• Language: English
• Subjects: Algorithms; Image processing systems; Low rank; Matrix completion; Signal processing; Sparse representation; Sparsity; State of the art; Truncated nuclear norm
• ISSN: 0923-5965; 1879-2677
• DOI: 10.1016/j.image.2018.06.007

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 ℓ1-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. •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.