A fast matrix completion method based on truncated$ {\mathit{L}}_{2, 1} $ norm minimization

Abstract

<abstract> <p>In recent years, a truncated nuclear norm regularization (TNNR) method has obtained much attention from researchers in machine learning and image processing areas, because it is much more accurate on matrices with missing data than other traditional methods based on nuclear norm. However, the TNNR method is reported to be very slow, due to its large number of singular value decomposition (SVD) iterations. In this paper, a truncated $ {\boldsymbol{L}}_\bf{2, 1} $ norm minimization method was presented for fast and accurate matrix completion, which is abbreviated as TLNM. In the proposed TLNM method, the truncated nuclear norm minimization model of TNNR was improved to a truncated $ {\boldsymbol{L}}_\bf{2, 1} $ norm minimization model that aimed to optimize the truncated $ {\boldsymbol{L}}_\bf{2, 1} $ Norm and a weighted noisy matrix simultaneously for improving the accuracy of TLNM. Using Qatar Riyal (QR) decomposition to calculate the orthogonal bases for reconstructing recovery results, the proposed TLNM method is much faster than the TNNR method. Adequate results for color images validate the effectiveness and efficiency of TLNM comparing with TNNR and other competing methods.</p> </abstract>