Recursive robust PCA or recursive sparse recovery in large but structured noise
dc.contributor.advisor | Namrata Vaswani | |
dc.contributor.author | Qiu, Chenlu | |
dc.contributor.department | Electrical and Computer Engineering | |
dc.date | 2018-07-23T01:55:37.000 | |
dc.date.accessioned | 2020-06-30T02:48:18Z | |
dc.date.available | 2020-06-30T02:48:18Z | |
dc.date.copyright | Tue Jan 01 00:00:00 UTC 2013 | |
dc.date.embargo | 2015-07-30 | |
dc.date.issued | 2013-01-01 | |
dc.description.abstract | <p>In this work, we study the problem of recursively recovering a time sequence of sparse vectors, S<sub>t</sub>, from measurements M<sub>t</sub> := S<sub>t</sub> + L<sub>t</sub> that are corrupted by structured noise L<sub>t</sub> which is dense and can have large magnitude. The structure that we require is that L<sub>t</sub> should lie in a low dimensional subspace that is either fixed or changes ``slowly enough"; and the eigenvalues of its covariance matrix are ``clustered". We do not assume anything about the sequence of sparse vectors, except a bound on their support size. Their support sets and their nonzero element values may be either independent or correlated over time (usually in many applications they are correlated). A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background (L<sub>t</sub>) from moving foreground objects (S<sub>t</sub>) on-the-fly. To solve the above problem, we introduce a novel solution called Recursive Projected Compressive Sensing (ReProCS). Under mild assumption, we show that ReProCS can exactly recover the support set of S<sub>t</sub> at all times; and the reconstruction errors of both S<sub>t</sub> and L<sub>t</sub> are upper bounded by a time-invariant and small value at all times. ReProCS is designed under the assumption that the subspace in which the most recent several L<sub>t</sub>'s lie can only grow over time. Therefore, it needs to assume a bound on the total number of subspace changes, $J$. To address this limitation, we introduce a novel subspace estimation scheme called cluster-PCA and we refer to the resulting algorithm as ReProCS with cluster-PCA (ReProCS-cPCA). ReProCS-cPCA does not need a bound on J as long as the delay between subspace change times increases in proportion to <em>log J</em>. An extra assumption that is needed though is that the eigenvalues of the covariance matrix of L<sub>t</sub> are sufficiently clustered. As a by-product, at certain times, the basis vectors for the subspace in which the most recent several L<sub>t</sub>'s lies is also recovered.</p> | |
dc.format.mimetype | application/pdf | |
dc.identifier | archive/lib.dr.iastate.edu/etd/13235/ | |
dc.identifier.articleid | 4242 | |
dc.identifier.contextkey | 4615727 | |
dc.identifier.s3bucket | isulib-bepress-aws-west | |
dc.identifier.submissionpath | etd/13235 | |
dc.identifier.uri | https://dr.lib.iastate.edu/handle/20.500.12876/27424 | |
dc.language.iso | en | |
dc.source.bitstream | archive/lib.dr.iastate.edu/etd/13235/Qiu_iastate_0097E_13564.pdf|||Fri Jan 14 19:47:52 UTC 2022 | |
dc.subject.disciplines | Electrical and Electronics | |
dc.title | Recursive robust PCA or recursive sparse recovery in large but structured noise | |
dc.type | article | |
dc.type.genre | dissertation | |
dspace.entity.type | Publication | |
relation.isOrgUnitOfPublication | a75a044c-d11e-44cd-af4f-dab1d83339ff | |
thesis.degree.level | dissertation | |
thesis.degree.name | Doctor of Philosophy |
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