A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

A Note on Block-Sparse Signal Recovery with Coherent Tight Frames

This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frame D. By introducing the notion of block D-restricted isometry property (D-RIP), we establish several sufficient conditions...

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Main Authors: Yao Wang, Jianjun Wang, Zongben Xu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2013/905027
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spelling doaj-bd95b344d4b2457895e3aa551a9cee542020-11-24T23:02:57ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/905027905027A Note on Block-Sparse Signal Recovery with Coherent Tight FramesYao Wang0Jianjun Wang1Zongben Xu2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing 400715, ChinaSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaThis note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frame D. By introducing the notion of block D-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixed l2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms of D. One of the main results of this note shows that if the measurement matrix satisfies the block D-RIP with constants δk<0.307, then the signals which are nearly block k-sparse in terms of D can be stably recovered via mixed l2/l1-analysis in the presence of noise.http://dx.doi.org/10.1155/2013/905027
collection DOAJ
language English
format Article
sources DOAJ
author Yao Wang
Jianjun Wang
Zongben Xu
spellingShingle Yao Wang
Jianjun Wang
Zongben Xu
A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
Discrete Dynamics in Nature and Society
author_facet Yao Wang
Jianjun Wang
Zongben Xu
author_sort Yao Wang
title A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
title_short A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
title_full A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
title_fullStr A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
title_full_unstemmed A Note on Block-Sparse Signal Recovery with Coherent Tight Frames
title_sort note on block-sparse signal recovery with coherent tight frames
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2013-01-01
description This note discusses the recovery of signals from undersampled data in the situation that such signals are nearly block sparse in terms of an overcomplete and coherent tight frame D. By introducing the notion of block D-restricted isometry property (D-RIP), we establish several sufficient conditions for the proposed mixed l2/l1-analysis method to guarantee stable recovery of nearly block-sparse signals in terms of D. One of the main results of this note shows that if the measurement matrix satisfies the block D-RIP with constants δk<0.307, then the signals which are nearly block k-sparse in terms of D can be stably recovered via mixed l2/l1-analysis in the presence of noise.
url http://dx.doi.org/10.1155/2013/905027
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AT zongbenxu anoteonblocksparsesignalrecoverywithcoherenttightframes
AT yaowang noteonblocksparsesignalrecoverywithcoherenttightframes
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