Robustly stable signal recovery in compressed sensing with structured matrix perturbation
The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in the sensing instruments. This paper considers the problem of...
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| 其他作者: | |
| 格式: | Journal Article |
| 语言: | English |
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2013
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| 主题: | |
| 在线阅读: | https://hdl.handle.net/10356/100144 http://hdl.handle.net/10220/13582 |
| _version_ | 1826126514188451840 |
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| author | Yang, Zai Zhang, Cishen Xie, Lihua |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Yang, Zai Zhang, Cishen Xie, Lihua |
| author_sort | Yang, Zai |
| collection | NTU |
| description | The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in the sensing instruments. This paper considers the problem of compressed sensing subject to a structured perturbation in the sensing matrix. Under mild conditions, it is shown that a sparse signal can be recovered by l1 minimization and the recovery error is at most proportional to the measurement noise level, which is similar to the standard CS result. In the special noise free case, the recovery is exact provided that the signal is sufficiently sparse with respect to the perturbation level. The formulated structured sensing matrix perturbation is applicable to the direction of arrival estimation problem, so has practical relevance. Algorithms are proposed to implement the l1 minimization problem and numerical simulations are carried out to verify the results obtained. |
| first_indexed | 2024-10-01T06:53:34Z |
| format | Journal Article |
| id | ntu-10356/100144 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:53:34Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1001442020-03-07T14:02:37Z Robustly stable signal recovery in compressed sensing with structured matrix perturbation Yang, Zai Zhang, Cishen Xie, Lihua School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in the sensing instruments. This paper considers the problem of compressed sensing subject to a structured perturbation in the sensing matrix. Under mild conditions, it is shown that a sparse signal can be recovered by l1 minimization and the recovery error is at most proportional to the measurement noise level, which is similar to the standard CS result. In the special noise free case, the recovery is exact provided that the signal is sufficiently sparse with respect to the perturbation level. The formulated structured sensing matrix perturbation is applicable to the direction of arrival estimation problem, so has practical relevance. Algorithms are proposed to implement the l1 minimization problem and numerical simulations are carried out to verify the results obtained. 2013-09-23T06:23:12Z 2019-12-06T20:17:23Z 2013-09-23T06:23:12Z 2019-12-06T20:17:23Z 2012 2012 Journal Article Yang, Z., Zhang, C., & Xie, L. (2012). Robustly Stable Signal Recovery in Compressed Sensing With Structured Matrix Perturbation. IEEE Transactions on Signal Processing, 60(9), 4658 - 4671. https://hdl.handle.net/10356/100144 http://hdl.handle.net/10220/13582 10.1109/TSP.2012.2201152 en IEEE transactions on signal processing |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering Yang, Zai Zhang, Cishen Xie, Lihua Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title | Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title_full | Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title_fullStr | Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title_full_unstemmed | Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title_short | Robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| title_sort | robustly stable signal recovery in compressed sensing with structured matrix perturbation |
| topic | DRNTU::Engineering::Electrical and electronic engineering |
| url | https://hdl.handle.net/10356/100144 http://hdl.handle.net/10220/13582 |
| work_keys_str_mv | AT yangzai robustlystablesignalrecoveryincompressedsensingwithstructuredmatrixperturbation AT zhangcishen robustlystablesignalrecoveryincompressedsensingwithstructuredmatrixperturbation AT xielihua robustlystablesignalrecoveryincompressedsensingwithstructuredmatrixperturbation |