Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications
Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but th...
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| Vydané v: | IEEE transactions on pattern analysis and machine intelligence Ročník 38; číslo 4; s. 744 - 758 |
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| Hlavní autori: | , , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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United States
IEEE
01.04.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0162-8828, 1939-3539, 2160-9292, 1939-3539 |
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| Abstract | Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g., high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method. |
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| AbstractList | Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g., high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method. Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g., high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method.Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known that the underlying structure of clean data is low-rank, but the exact rank of clean data is also known. Yet, when applying conventional rank minimization for those problems, the objective function is formulated in a way that does not fully utilize a priori target rank information about the problems. This observation motivates us to investigate whether there is a better alternative solution when using rank minimization. In this paper, instead of minimizing the nuclear norm, we propose to minimize the partial sum of singular values, which implicitly encourages the target rank constraint. Our experimental analyses show that, when the number of samples is deficient, our approach leads to a higher success rate than conventional rank minimization, while the solutions obtained by the two approaches are almost identical when the number of samples is more than sufficient. We apply our approach to various low-level vision problems, e.g., high dynamic range imaging, motion edge detection, photometric stereo, image alignment and recovery, and show that our results outperform those obtained by the conventional nuclear norm rank minimization method. |
| Author | In So Kweon Tae-Hyun Oh Hyeongwoo Kim Bazin, Jean-Charles Yu-Wing Tai |
| Author_xml | – sequence: 1 surname: Tae-Hyun Oh fullname: Tae-Hyun Oh email: thoh.kaist.ac.kr@gmail.com organization: Dept. of Electr. Eng., KAIST, Daejeon, South Korea – sequence: 2 surname: Yu-Wing Tai fullname: Yu-Wing Tai email: yuwing@gmail.com organization: Dept. of Electr. Eng., KAIST, Daejeon, South Korea – sequence: 3 givenname: Jean-Charles surname: Bazin fullname: Bazin, Jean-Charles email: jebazin@inf.ethz.ch organization: Dept. of Comput. Sci., ETH Zurich, Zurich, Switzerland – sequence: 4 surname: Hyeongwoo Kim fullname: Hyeongwoo Kim email: hyeongwoo.kim@kaist.ac.kr organization: Dept. of Electr. Eng., KAIST, Daejeon, South Korea – sequence: 5 surname: In So Kweon fullname: In So Kweon email: iskweon77@kaist.ac.kr organization: Dept. of Electr. Eng., KAIST, Daejeon, South Korea |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/26353362$$D View this record in MEDLINE/PubMed |
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| Keywords | Robust principal component analysis truncated nuclear norm rank minimization alternating direction method of multipliers sparse and low-rank decomposition |
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| SubjectTerms | alternating direction method of multipliers Approximation methods Computer vision Linear programming Minimization Noise Principal component analysis Principal components analysis rank minimization Robust principal component analysis Robustness sparse and low-rank decomposition Supply chains truncated nuclear norm |
| Title | Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications |
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