Accelerated Low-Rank Visual Recovery by Random Projection

Exact recovery from contaminated visual data plays an important role in various tasks. By assuming the observed data matrix as the addition of a low-rank matrix and a sparse matrix, theoretic guarantee exists under mild conditions for exact data recovery. Practically matrix nuclear norm is adopted as a convex surrogate of the non-convex matrix rank function to encourage low-rank property and serves as the major component of recently-proposed Robust Principal Component Analysis (R-PCA). Recent endeavors have focused on enhancing the scalability of RPCA to large-scale datasets, especially mitigating the computational burden of frequent large-scale Singular Value Decomposition (SVD) inherent with the nuclear norm optimization. In our proposed scheme, the nuclear norm of an auxiliary matrix is minimized instead, which is related to the original low-rank matrix by random projection. By design, the modified optimization entails SVD on matrices of much smaller scale, as compared to the orig...

• Type: Journal
• Year: 2011
• Where: CVPR
• Authors: Yadong Mu, Jian Dong, Xiaotong Yuan, Shuicheng Yan
• Keywords: Computer Vision, CVPR 2011, Low-rank Matrix, Matrix, Nuclear Norm