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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/905027 |
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| _version_ | 1832562559624937472 |
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| author | Yao Wang Jianjun Wang Zongben Xu |
| author_facet | Yao Wang Jianjun Wang Zongben Xu |
| author_sort | Yao Wang |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-bd95b344d4b2457895e3aa551a9cee54 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bd95b344d4b2457895e3aa551a9cee542025-02-03T01:22:24ZengWileyDiscrete 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 |
| spellingShingle | Yao Wang Jianjun Wang Zongben Xu A Note on Block-Sparse Signal Recovery with Coherent Tight Frames Discrete Dynamics in Nature and Society |
| title | 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_short | A Note on Block-Sparse Signal Recovery with Coherent Tight Frames |
| title_sort | note on block sparse signal recovery with coherent tight frames |
| url | http://dx.doi.org/10.1155/2013/905027 |
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