New Bounds for Restricted Isometry Constants
Name
Cai-2010-New Bounds for Restr.pdf
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200.59 KB
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Adobe PDF
Checksum (MD5)
06a265fe23508d6b1e7f3c738bf398ab
Author(s)
Cai, T. Tony
Wang, Lie
Xu, Guangwu
Date Issued
August 2010
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Cai, T. Tony, Lie Wang, and Guangwu Xu. “New Bounds for Restricted Isometry Constants.” IEEE Transactions on Information Theory 56 (2010): 4388-4394. Web. 19 Oct. 2011. © 2011 IEEE
Version
Final published version
Abstract
This paper discusses new bounds for restricted isometry constants in compressed sensing. Let Φ be an n × p real matrix and A; be a positive integer with k ≤ n. One of the main results of this paper shows that if the restricted isometry constant δk of Φ satisfies δk <; 0.307 then k-sparse signals are guaranteed to be recovered exactly via ℓ1 minimization when no noise is present and k-sparse signals can be estimated stably in the noisy case. It is also shown that the bound cannot be substantially improved. An explicit example is constructed in which δk = k-1/2k-1 <; 0.5, but it is impossible to recover certain k-sparse signals.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1109/tit.2010.2054730
