A Sharp RIP Condition for Orthogonal Matching Pursuit
A restricted isometry property (RIP) condition δK+KθK,1<1 is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements y=Φx. This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix with δK+Kθ...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/482357 |
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| _version_ | 1832555877136072704 |
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| author | Wei Dan |
| author_facet | Wei Dan |
| author_sort | Wei Dan |
| collection | DOAJ |
| description | A restricted isometry property (RIP) condition δK+KθK,1<1 is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements y=Φx. This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix with δK+KθK,1=1 such that OMP cannot exactly recover some K-sparse signals. |
| format | Article |
| id | doaj-art-b3e04853bae041219fc630c3b9c113c7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b3e04853bae041219fc630c3b9c113c72025-02-03T05:47:04ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/482357482357A Sharp RIP Condition for Orthogonal Matching PursuitWei Dan0School of Mathematics and Statistics, Guangdong University of Finance & Economics, Guangzhou 510320, ChinaA restricted isometry property (RIP) condition δK+KθK,1<1 is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover every K-sparse signal x from measurements y=Φx. This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix with δK+KθK,1=1 such that OMP cannot exactly recover some K-sparse signals.http://dx.doi.org/10.1155/2013/482357 |
| spellingShingle | Wei Dan A Sharp RIP Condition for Orthogonal Matching Pursuit Abstract and Applied Analysis |
| title | A Sharp RIP Condition for Orthogonal Matching Pursuit |
| title_full | A Sharp RIP Condition for Orthogonal Matching Pursuit |
| title_fullStr | A Sharp RIP Condition for Orthogonal Matching Pursuit |
| title_full_unstemmed | A Sharp RIP Condition for Orthogonal Matching Pursuit |
| title_short | A Sharp RIP Condition for Orthogonal Matching Pursuit |
| title_sort | sharp rip condition for orthogonal matching pursuit |
| url | http://dx.doi.org/10.1155/2013/482357 |
| work_keys_str_mv | AT weidan asharpripconditionfororthogonalmatchingpursuit AT weidan sharpripconditionfororthogonalmatchingpursuit |