An Improved Low-Rank Matrix Fitting Method Based on Weighted L1,p Norm Minimization for Matrix Completion

Abstract

Low-rank matrix completion, which aims to recover a matrix with many missing values, has attracted much attention in many fields of computer science. A low-rank matrix fitting (LMaFit) method has been proposed for fast matrix completion recently. However, this method cannot converge accurately on matrices of real-world images. For improving the accuracy of LMaFit method, an improved low-rank matrix fitting (ILMF) method based on the weighted [Formula: see text] norm minimization is proposed in this paper, where the [Formula: see text] norm is the summation of the [Formula: see text]-power [Formula: see text] of [Formula: see text] norms of rows in a matrix. In the proposed method, i.e. the ILMF method, the incomplete matrix that may be corrupted by noises is decomposed into the summation of a low-rank matrix and a noise matrix at first. Then, a weighted [Formula: see text] norm minimization problem is solved by using an alternating direction method for improving the accuracy of matrix completion. Experimental results on real-world images show that the ILMF method has much better performances in terms of both the convergence accuracy and convergence speed than the compared methods.