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A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing

Abstract:

We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement matrices, we derive a sufficient condition for the convergence of IHT to a fixed point and a necessary condition for the existence of fixed points. These conditions allow us to perform a sparse signal recovery analysis in the deterministic noiseless case by imp...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1109/TIT.2015.2399919

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
More by this author
Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publisher:
IEEE Publisher's website
Journal:
IEEE Transactions on Information Theory Journal website
Volume:
61
Issue:
4
Pages:
2019-2042
Publication date:
2015-04-05
DOI:
EISSN:
1557-9654
ISSN:
0018-9448
URN:
uuid:19b06a3e-a98e-495b-a4a3-f8a045eb68b3
Source identifiers:
521210
Local pid:
pubs:521210

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