期刊
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
卷 40, 期 9, 页码 2066-2080出版社
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2017.2748590
关键词
Robust principal component analysis; rank minimization; Schatten-p quasi-norm; l(p)-norm; double nuclear norm penalty; Frobenius/nuclear norm penalty; alternating direction method of multipliers (ADMM)
资金
- Hong Kong RGC [CUHK 14206715, 14222816]
- ITF - Research Committee of CUHK [6904079, 3132821]
- National Science Foundation (NSF) [CCF-1526434]
- National Natural Science Foundation of China [61571384, 61731018]
- Leading Talents of Guang Dong Province program [00201510]
- National Basic Research Program of China (973 Program) [2015CB352502]
- National Natural Science Foundation (NSF) of China [61731018, 61625301, 61231002]
- Qualcomm
The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they can be well modeled by a hyper-Laplacian. However, the use of such distributions generally leads to challenging non-convex, non-smooth and non-Lipschitz problems, and makes existing algorithms very slow for large-scale applications. Together with the analytic solutions to 'p-norm minimization with two specific values of p, i.e., p = 1/2 and p = 2/3, we propose two novel bilinear factor matrix norm minimization models for robust principal component analysis. We first define the double nuclear norm and Frobenius/nuclear hybrid norm penalties, and then prove that they are in essence the Schatten-1/2 and 2/3 quasi-norms, respectively, which lead to much more tractable and scalable Lipschitz optimization problems. Our experimental analysis shows that both our methods yield more accurate solutions than original Schatten quasi-norm minimization, even when the number of observations is very limited. Finally, we apply our penalties to various low-level vision problems, e.g., text removal, moving object detection, image alignment and inpainting, and show that our methods usually outperform the state-of-the-art methods.
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