Stable Recovery of Sparse Signals and an Oracle Inequality
This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific coun...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers / IEEE Information Theory Society
2011
|
| Online Access: | http://hdl.handle.net/1721.1/64813 https://orcid.org/0000-0003-3582-8898 |
| _version_ | 1811097863194673152 |
|---|---|
| author | Cai, T. Tony Wang, Lie Xu, Guangwu |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Cai, T. Tony Wang, Lie Xu, Guangwu |
| author_sort | Cai, T. Tony |
| collection | MIT |
| description | This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise. |
| first_indexed | 2024-09-23T17:06:09Z |
| format | Article |
| id | mit-1721.1/64813 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T17:06:09Z |
| publishDate | 2011 |
| publisher | Institute of Electrical and Electronics Engineers / IEEE Information Theory Society |
| record_format | dspace |
| spelling | mit-1721.1/648132022-09-29T23:40:08Z Stable Recovery of Sparse Signals and an Oracle Inequality Cai, T. Tony Wang, Lie Xu, Guangwu Massachusetts Institute of Technology. Department of Mathematics Wang, Lie Wang, Lie This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise. National Science Foundation (U.S.) (Grant DMS-0604954) National 973 Project of China (no. 2007CB807902) 2011-07-14T18:07:08Z 2011-07-14T18:07:08Z 2010-07 2009-10 Article http://purl.org/eprint/type/JournalArticle 0018-9448 INSPEC Accession Number: 11392283 http://hdl.handle.net/1721.1/64813 Cai, T.T., Lie Wang, and Guangwu Xu. “Stable Recovery of Sparse Signals and an Oracle Inequality.” Information Theory, IEEE Transactions On 56.7 (2010) : 3516-3522. Copyright © 2010, IEEE https://orcid.org/0000-0003-3582-8898 en_US http://dx.doi.org/10.1109/tit.2010.2048506 IEEE transactions on information theory Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Institute of Electrical and Electronics Engineers / IEEE Information Theory Society IEEE |
| spellingShingle | Cai, T. Tony Wang, Lie Xu, Guangwu Stable Recovery of Sparse Signals and an Oracle Inequality |
| title | Stable Recovery of Sparse Signals and an Oracle Inequality |
| title_full | Stable Recovery of Sparse Signals and an Oracle Inequality |
| title_fullStr | Stable Recovery of Sparse Signals and an Oracle Inequality |
| title_full_unstemmed | Stable Recovery of Sparse Signals and an Oracle Inequality |
| title_short | Stable Recovery of Sparse Signals and an Oracle Inequality |
| title_sort | stable recovery of sparse signals and an oracle inequality |
| url | http://hdl.handle.net/1721.1/64813 https://orcid.org/0000-0003-3582-8898 |
| work_keys_str_mv | AT caittony stablerecoveryofsparsesignalsandanoracleinequality AT wanglie stablerecoveryofsparsesignalsandanoracleinequality AT xuguangwu stablerecoveryofsparsesignalsandanoracleinequality |