Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model
Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/111666 https://orcid.org/0000-0003-1132-8477 |
| _version_ | 1811094441376612352 |
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| author | Misra, Sidhant Parrilo, Pablo A |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Misra, Sidhant Parrilo, Pablo A |
| author_sort | Misra, Sidhant |
| collection | MIT |
| description | Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted ℓ₁-minimization with suitable choice of weights has been shown to improve performance in the so-called non-uniform sparse model of signals. In this paper, we consider a full generalization of the non-uniform sparse model with very mild assumptions. We prove that when the measurements are obtained using a matrix with independent identically distributed Gaussian entries, weighted ℓ₁-minimization successfully recovers the sparse signal from its measurements with overwhelming probability. We also provide a method to choose these weights for any general signal model from the non-uniform sparse class of signal models. |
| first_indexed | 2024-09-23T16:00:07Z |
| format | Article |
| id | mit-1721.1/111666 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:00:07Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1116662022-10-02T05:40:20Z Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model Misra, Sidhant Parrilo, Pablo A Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Misra, Sidhant Parrilo, Pablo A Model-based compressed sensing refers to compressed sensing with extra structure about the underlying sparse signal known a priori. Recent work has demonstrated that both for deterministic and probabilistic models imposed on the signal, this extra information can be successfully exploited to enhance recovery performance. In particular, weighted ℓ₁-minimization with suitable choice of weights has been shown to improve performance in the so-called non-uniform sparse model of signals. In this paper, we consider a full generalization of the non-uniform sparse model with very mild assumptions. We prove that when the measurements are obtained using a matrix with independent identically distributed Gaussian entries, weighted ℓ₁-minimization successfully recovers the sparse signal from its measurements with overwhelming probability. We also provide a method to choose these weights for any general signal model from the non-uniform sparse class of signal models. 2017-10-02T14:30:44Z 2017-10-02T14:30:44Z 2015-06 Article http://purl.org/eprint/type/JournalArticle 0018-9448 1557-9654 http://hdl.handle.net/1721.1/111666 Misra, Sidhant, and Parrilo, Pablo A. “Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Modell.” IEEE Transactions on Information Theory 61, 8 (August 2015): 4424–4439 © 2015 Institute of Electrical and Electronics Engineers (IEEE) https://orcid.org/0000-0003-1132-8477 en_US http://dx.doi.org/10.1109/TIT.2015.2442922 IEEE Transactions on Information Theory Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Misra, Sidhant Parrilo, Pablo A Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title | Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title_full | Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title_fullStr | Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title_full_unstemmed | Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title_short | Weighted ℓ₁ -Minimization for Generalized Non-Uniform Sparse Model |
| title_sort | weighted l₁ minimization for generalized non uniform sparse model |
| url | http://hdl.handle.net/1721.1/111666 https://orcid.org/0000-0003-1132-8477 |
| work_keys_str_mv | AT misrasidhant weightedl1minimizationforgeneralizednonuniformsparsemodel AT parrilopabloa weightedl1minimizationforgeneralizednonuniformsparsemodel |