Shifting Inequality and Recovery of Sparse Signals
In this paper, we present a concise and coherent analysis of the constrained ℓ₁ minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/69941 https://orcid.org/0000-0003-3582-8898 |
| _version_ | 1811089901285801984 |
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| author | Wang, Lie Cai, T. Tony Xu, Guangwu |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Wang, Lie Cai, T. Tony Xu, Guangwu |
| author_sort | Wang, Lie |
| collection | MIT |
| description | In this paper, we present a concise and coherent analysis of the constrained ℓ₁ minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via ℓ₁ minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the ℓ₂ norm of a subsequence in terms of the ℓ₁ norm of another subsequence by shifting the elements to the upper end. |
| first_indexed | 2024-09-23T14:27:02Z |
| format | Article |
| id | mit-1721.1/69941 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:27:02Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/699412022-10-01T21:21:32Z Shifting Inequality and Recovery of Sparse Signals Wang, Lie Cai, T. Tony Xu, Guangwu Massachusetts Institute of Technology. Department of Mathematics Wang, Lie Wang, Lie In this paper, we present a concise and coherent analysis of the constrained ℓ₁ minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via ℓ₁ minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the ℓ₂ norm of a subsequence in terms of the ℓ₁ norm of another subsequence by shifting the elements to the upper end. National Basic Research Program of China (973 Program) (No. 2007CB807902) National Science Foundation (U.S.) (Grant DMS-0604954) 2012-04-04T20:56:14Z 2012-04-04T20:56:14Z 2010-02 2009-04 Article http://purl.org/eprint/type/JournalArticle 1053-587X 1941-0476 INSPEC Accession Number: 11136165 http://hdl.handle.net/1721.1/69941 Cai, T.T., Lie Wang, and Guangwu Xu. “Shifting Inequality and Recovery of Sparse Signals.” IEEE Transactions on Signal Processing 58.3 (2010): 1300–1308. Web. 4 Apr. 2012. © 2010 Institute of Electrical and Electronics Engineers https://orcid.org/0000-0003-3582-8898 en_US http://dx.doi.org/10.1109/tsp.2009.2034936 IEEE Transactions on Signal Processing 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) IEEE |
| spellingShingle | Wang, Lie Cai, T. Tony Xu, Guangwu Shifting Inequality and Recovery of Sparse Signals |
| title | Shifting Inequality and Recovery of Sparse Signals |
| title_full | Shifting Inequality and Recovery of Sparse Signals |
| title_fullStr | Shifting Inequality and Recovery of Sparse Signals |
| title_full_unstemmed | Shifting Inequality and Recovery of Sparse Signals |
| title_short | Shifting Inequality and Recovery of Sparse Signals |
| title_sort | shifting inequality and recovery of sparse signals |
| url | http://hdl.handle.net/1721.1/69941 https://orcid.org/0000-0003-3582-8898 |
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