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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Chenlu Qiu Vaswani, N. |
| Copyright Year | 2013 |
| Description | Author affiliation: ECE Dept., Iowa State Univ., Ames, IA, USA (Chenlu Qiu; Vaswani, N.) |
| Abstract | We study the problem of recursively recovering a time sequence of sparse vectors, $S_{t},$ from measurements $M_{t}$ := $S_{t}$ + $L_{t}$ that are corrupted by structured noise $L_{t}$ which is dense and can have large magnitude. The structure that we require is that $L_{t}$ 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 any model on the sequence of sparse vectors. Their support sets and their nonzero element values may be either independent or correlated over time (usually in many applications they are correlated). The only thing required is that there be some support change every so often. We introduce a novel solution approach called Recursive Projected Compressive Sensing with cluster-PCA (ReProCS-cPCA) that addresses some of the limitations of earlier work. Under mild assumptions, we show that, with high probability, ReProCS-cPCA can exactly recover the support set of $S_{t}$ at all times; and the reconstruction errors of both $S_{t}$ and $L_{t}$ are upper bounded by a time-invariant and small value. |
| Starting Page | 864 |
| Ending Page | 868 |
| File Size | 145639 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781479904464 |
| ISSN | 21578117 |
| DOI | 10.1109/ISIT.2013.6620349 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2013-07-07 |
| Publisher Place | Turkey |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Principal component analysis Vectors Robustness Noise Sparse matrices Matrix decomposition Eigenvalues and eigenfunctions |
| Content Type | Text |
| Resource Type | Article |
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