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Breaking the ℓ_1 recovery thresholds with reweighted ℓ_1 optimization

Xu, Weiyu and Khajehnejad, M. Amin and Avestimehr, A. Salman and Hassibi, Babak (2009) Breaking the ℓ_1 recovery thresholds with reweighted ℓ_1 optimization. In: 47th Annual Allerton Conference on Communication, Control, and Computing, 2009. Allerton 2009. IEEE , Piscataway, NJ, pp. 1026-1030. ISBN 978-1-4244-5870-7 . https://resolver.caltech.edu/CaltechAUTHORS:20150224-074243785

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Abstract

It is now well understood that ℓ_1 minimization algorithm is able to recover sparse signals from incomplete measurements and sharp recoverable sparsity thresholds have also been obtained for the l1 minimization algorithm. In this paper, we investigate a new iterative reweighted ℓ_1 minimization algorithm and showed that the new algorithm can increase the sparsity recovery threshold of ℓ_1 minimization when decoding signals from relevant distributions. Interestingly, we observed that the recovery threshold performance of the new algorithm depends on the behavior, more specifically the derivatives, of the signal amplitude probability distribution at the origin.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ALLERTON.2009.5394882DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5394882PublisherArticle
Subject Keywords:compressed sensing, basis pursuit, Grassmann angle, reweighted ℓ_1 minimization, random linear subspaces
Record Number:CaltechAUTHORS:20150224-074243785
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150224-074243785
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55135
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:25 Feb 2015 00:43
Last Modified:03 Oct 2019 08:03

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