Compressive Online Robust Principal Component Analysis Via n-‘1 Minimization

Research output: Research - peer-reviewJournal article – Annual report year: 2018

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This work 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 lowrank 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.

Original languageEnglish
JournalIEEE Transactions on Image Processing
Volume27
Issue number9
Pages (from-to)4314-4329
ISSN1057-7149
DOIs
StatePublished - 2018
CitationsWeb of Science® Times Cited: 1

    Research areas

  • Low-rank model, Compressed sensing, Low-rank models, Prior information, Robust PCA, Sparse signal
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