Abstract
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 \ell -{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.
Original language | English (US) |
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Article number | 8025394 |
Pages (from-to) | 2066-2080 |
Number of pages | 15 |
Journal | IEEE Transactions on Pattern Analysis and Machine Intelligence |
Volume | 40 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2018 |
Bibliographical note
Publisher Copyright:© 1979-2012 IEEE.
Keywords
- Frobenius/nuclear norm penalty
- Robust principal component analysis
- Schatten-p quasi-norm
- alternating direction method of multipliers (ADMM)
- double nuclear norm penalty
- p-norm
- rank minimization