Low-rank matrix completion against missing rows and columns with separable 2-D sparsity priors

Most existing matrix completion approaches assume that entries of matrices are missing at random, which could be violated in practical applications. This paper proposes a novel matrix completion method equipped with Joint Priors of LOw-rank and Separable 2-D Sparsity (JPLOSS) to complete missing rows and columns besides random missing. The underlying matrix is regularized by a low-rank prior, and its rows and columns are regularized by a row and a column dictionary, respectively. An reweighting scheme is incorporated into both the low-rank and sparsity terms to promote the low-rankness and sparseness simultaneously. The proposed model is effectively solved by an alternating direction method under the augmented Lagrangian multiplier framework. Experiments on both synthetic data and real images demonstrate the effectiveness and superiority of the proposed model in completing matrices with missing rows and columns compared with state-of-the-art matrix completion approaches.