Joint low-rank representation and matrix completion under a singular value thresholding framework

Matrix completion is the process of estimating missing entries from a matrix using some prior knowledge. Typically, the prior knowledge is that the matrix is low-rank. In this paper, we present an extension of standard matrix completion that leverages prior knowledge that the matrix is low-rank and that the data samples can be efficiently represented by a fixed known dictionary. Specifically, we compute a low-rank representation of a data matrix with respect to a given dictionary using only a few observed entries. A novel modified version of the singular value thresholding (SVT) algorithm named joint low-rank representation and matrix completion SVT (J-SVT) is proposed. Experiments on simulated data show that the proposed J-SVT algorithm provides better reconstruction results compared to standard matrix completion.