Recovery of High-Dimensional Sparse Signals via -Minimization

Recovery of High-Dimensional Sparse Signals via -Minimization

We consider the recovery of high-dimensional sparse signals via -minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study both -minimization under the constraint and the Dantzig selector. Using the two -m...

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Main Authors: Shiqing Wang, Limin Su
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/636094
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spelling doaj-d7277051fe87479d979df12cbc417d3d2020-11-25T01:57:23ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/636094636094Recovery of High-Dimensional Sparse Signals via -MinimizationShiqing Wang0Limin Su1College of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaCollege of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaWe consider the recovery of high-dimensional sparse signals via -minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study both -minimization under the constraint and the Dantzig selector. Using the two -minimization methods and a technical inequality, some results are obtained. They improve the results of the error bounds in the literature and are extended to the general case of reconstructing an arbitrary signal.http://dx.doi.org/10.1155/2013/636094
collection DOAJ
language English
format Article
sources DOAJ
author Shiqing Wang
Limin Su
spellingShingle Shiqing Wang
Limin Su
Recovery of High-Dimensional Sparse Signals via -Minimization
Journal of Applied Mathematics
author_facet Shiqing Wang
Limin Su
author_sort Shiqing Wang
title Recovery of High-Dimensional Sparse Signals via -Minimization
title_short Recovery of High-Dimensional Sparse Signals via -Minimization
title_full Recovery of High-Dimensional Sparse Signals via -Minimization
title_fullStr Recovery of High-Dimensional Sparse Signals via -Minimization
title_full_unstemmed Recovery of High-Dimensional Sparse Signals via -Minimization
title_sort recovery of high-dimensional sparse signals via -minimization
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We consider the recovery of high-dimensional sparse signals via -minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study both -minimization under the constraint and the Dantzig selector. Using the two -minimization methods and a technical inequality, some results are obtained. They improve the results of the error bounds in the literature and are extended to the general case of reconstructing an arbitrary signal.
url http://dx.doi.org/10.1155/2013/636094
work_keys_str_mv AT shiqingwang recoveryofhighdimensionalsparsesignalsviaminimization
AT liminsu recoveryofhighdimensionalsparsesignalsviaminimization
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