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Matric completion based on TV norm regularization and its application in image restoration

Matrix completion is addressed to recover an unknown large low-rank matrix from a small subset of its entries. Several methods have been proposed for solving matrix completion problem. However, when the desired matrix becomes complicated and the rank is unknown, these traditional methods may not achieve promising performance. In this paper, a novel low-rank matrix completion algorithm based on nuclear norm is presented, which is a rank adaptive method. The proposed method integrates the nuclear norm and TV norm together. The nuclear norm is used to exploit the low-rank property, and the TV norm is adopted to explore the smooth structure. Experimental results show that our proposed method has a better performance than the state-of-the-art low-rank matrix completion methods.