Compressive Online Robust Principal Component Analysis via n - ℓ1 Minimization

Journal article


Publication Details

Author(s): van Luong H, Deligiannis N, Seiler J, Forchhammer S, Kaup A
Journal: IEEE Transactions on Image Processing
Publication year: 2018
Volume: 27
Journal issue: 9
Pages range: 4314-4329
ISSN: 1057-7149
Language: English


Abstract

This paper considers online robust principal component analysis (RPCA) in time-varying decomposition problems such as video foreground-background separation. We propose a compressive online RPCA algorithm that decomposes recursively a sequence of data vectors (e.g., frames) into sparse and low-rank components. Different from conventional batch RPCA, which processes all the data directly, our approach considers a small set of measurements taken per data vector (frame). Moreover, our algorithm can incorporate multiple prior information from previous decomposed vectors via proposing an n - ℓ1 minimization method. At each time instance, the algorithm recovers the sparse vector by solving the n- ℓ1 minimization problem—which promotes not only the sparsity of the vector but also its correlation with multiple previously recovered sparse vectors—and, subsequently, updates the low-rank component using incremental singular value decomposition. We also establish theoretical bounds on the number of measurements required to guarantee successful compressive separation under the assumptions of static or slowly changing low-rank components. We evaluate the proposed algorithm using numerical experiments and online video foreground-background separation experiments. The experimental results show that the proposed method outperforms the existing methods.


FAU Authors / FAU Editors

Kaup, Andre Prof. Dr.-Ing.
Lehrstuhl für Multimediakommunikation und Signalverarbeitung
Seiler, Jürgen PD Dr.-Ing.
Lehrstuhl für Multimediakommunikation und Signalverarbeitung
van Luong, Huynh
Lehrstuhl für Multimediakommunikation und Signalverarbeitung


How to cite

APA:
van Luong, H., Deligiannis, N., Seiler, J., Forchhammer, S., & Kaup, A. (2018). Compressive Online Robust Principal Component Analysis via n - ℓ1 Minimization. IEEE Transactions on Image Processing, 27(9), 4314-4329. https://dx.doi.org/10.1109/TIP.2018.2831915

MLA:
van Luong, Huynh, et al. "Compressive Online Robust Principal Component Analysis via n - ℓ1 Minimization." IEEE Transactions on Image Processing 27.9 (2018): 4314-4329.

BibTeX: 

Last updated on 2018-11-08 at 02:28