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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Vydáno v:	IEEE transactions on pattern analysis and machine intelligence Ročník 38; číslo 4; s. 744 - 758
Hlavní autoři:	Tae-Hyun Oh, Yu-Wing Tai, Bazin, Jean-Charles, Hyeongwoo Kim, In So Kweon
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	United States IEEE 01.04.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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 Robust principal component analysis truncated nuclear norm rank minimization alternating direction method of multipliers sparse and low-rank decomposition
ISSN:	0162-8828, 1939-3539, 2160-9292, 1939-3539
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Popis
Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	0162-8828 1939-3539 2160-9292 1939-3539
DOI:	10.1109/TPAMI.2015.2465956