基于似零范数和混合优化的压缩感知信号快速重构算法
欠定系统（又称超完备系统）的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究.目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解,但这些方法存在收敛速度慢、恢复精度不高等缺陷.提出一种快速恢复稀疏信号的算法,该算法采用一种新的近似l0范数代替l1范数构造代价函数,并融合牛顿法和最陡梯度法推导出寻优迭代式,以获得似零范数代价函数的最优解.仿真实验和真实数据实验结果表明,与经典算法相比,该算法在能提供相同精度、甚至更好精度的条件下,收敛速度更快....
Saved in:
| Published in | 自动化学报 Vol. 40; no. 10; pp. 2145 - 2150 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | Chinese |
| Published |
厦门大学水声通信与海洋信息技术教育部重点实验室 厦门 361005
2014
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0254-4156 1874-1029 |
| DOI | 10.3724/SP.J.1004.2014.02145 |
Cover
| Abstract | 欠定系统（又称超完备系统）的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究.目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解,但这些方法存在收敛速度慢、恢复精度不高等缺陷.提出一种快速恢复稀疏信号的算法,该算法采用一种新的近似l0范数代替l1范数构造代价函数,并融合牛顿法和最陡梯度法推导出寻优迭代式,以获得似零范数代价函数的最优解.仿真实验和真实数据实验结果表明,与经典算法相比,该算法在能提供相同精度、甚至更好精度的条件下,收敛速度更快. |
|---|---|
| AbstractList | 欠定系统（又称超完备系统）的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究.目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解,但这些方法存在收敛速度慢、恢复精度不高等缺陷.提出一种快速恢复稀疏信号的算法,该算法采用一种新的近似l0范数代替l1范数构造代价函数,并融合牛顿法和最陡梯度法推导出寻优迭代式,以获得似零范数代价函数的最优解.仿真实验和真实数据实验结果表明,与经典算法相比,该算法在能提供相同精度、甚至更好精度的条件下,收敛速度更快. 欠定系统(又称超完备系统)的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究。目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解，但这些方法存在收敛速度慢、恢复精度不高等缺陷。提出一种快速恢复稀疏信号的算法，该算法采用一种新的近似l0范数代替l1范数构造代价函数，并融合牛顿法和最陡梯度法推导出寻优迭代式，以获得似零范数代价函数的最优解。仿真实验和真实数据实验结果表明，与经典算法相比，该算法在能提供相同精度、甚至更好精度的条件下，收敛速度更快。 |
| Abstract_FL | Obtaining sparse solutions of under-determined, or over-complete, linear systems of equations has found extensive applications in signal processing of compressive sensing, source separation and signal acquisition. However, the previous approaches to this problem, which generally minimize the l1 norm using linear programming (LP) techniques or greedy methods, are subject to drawbacks such as low accuracy and slow convergence. This paper proposes to replace the l1 norm with a newly defined approximate l0 norm (AL0), the optimization of which leads to the derivation of a hybrid approach by incorporating the steepest descent method with the Newton iteration. Numerical simulations and real data experiment show that the proposed algorithm is about two to three orders of magnitude faster than the state-of-the-art interior-point LP solvers, while providing the same (or better) accuracy. |
| Author | 伍飞云 周跃海 童峰 |
| AuthorAffiliation | 厦门大学水声通信与海洋信息技术教育部重点实验室,厦门361005 |
| AuthorAffiliation_xml | – name: 厦门大学水声通信与海洋信息技术教育部重点实验室 厦门 361005 |
| Author_FL | ZHOU Yue-Hai WU Fei-Yun TONG Feng |
| Author_FL_xml | – sequence: 1 fullname: WU Fei-Yun – sequence: 2 fullname: ZHOU Yue-Hai – sequence: 3 fullname: TONG Feng |
| Author_xml | – sequence: 1 fullname: 伍飞云 周跃海 童峰 |
| BookMark | eNotkE1LAkEcxocoyMxv0KlDt93-MzuzO3MMqSyEgrzL7MuoUWsp0cspSCjILAIrClo6dIgggiBBFvwyu2t-izbs9Fx-PG8zaNKv-x5Ccxh0wyJ0cWtTX9cxANUJYKoDwZRNoAzmFtUwEDGJMkAY1Shm5jTKNZs1G7BFLUEMyKBCHPSjficKw9HT90_7LOl-xrftpNeLby6i8CFu3w0fW3Hnchi-Ja1gGLxGg5f4uhcP3kenwej8KnluDT_uk6_uLJpScqfp5f41i0ory6V8QSturK7ll4qawzjXHNdWyhEmU-AJSCtaysFEOkwaNniUg3CJAAkulwK7ynGpxbGbzjAxUUxSI4sWxraH0lfSr5S36wcNPw0sn7jVI_vvgvQL4Ck4Pwadat2v7NdSdK9R25WN47JpEsYFYDB-AeG4dlc |
| ContentType | Journal Article |
| Copyright | Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| Copyright_xml | – notice: Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
| DBID | 2RA 92L CQIGP W92 ~WA 2B. 4A8 92I 93N PSX TCJ |
| DOI | 10.3724/SP.J.1004.2014.02145 |
| DatabaseName | 维普期刊资源整合服务平台 中文科技期刊数据库-CALIS站点 维普中文期刊数据库 中文科技期刊数据库-工程技术 中文科技期刊数据库- 镜像站点 Wanfang Data Journals - Hong Kong WANFANG Data Centre Wanfang Data Journals 万方数据期刊 - 香港版 China Online Journals (COJ) China Online Journals (COJ) |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| DocumentTitleAlternate | A Fast Sparse Signal Recovery Algorithm Based on Approximate l0 Norm and Hybrid Optimization |
| DocumentTitle_FL | A Fast Sparse Signal Recovery Algorithm Based on Approximate l 0 Norm and Hybrid Optimization |
| EISSN | 1874-1029 |
| EndPage | 2150 |
| ExternalDocumentID | zdhxb201410008 662589010 |
| GrantInformation_xml | – fundername: 国家自然科学基金; 教育部高等学校博士点专项基金(20120121110030)资助Supported by National Natural Science Foundation of China; the Specialized Research Fund for the Doctoral Program of Higher Education of China funderid: (11274259); (11274259); (20120121110030) |
| GroupedDBID | --K -0Y .~1 0R~ 1B1 1~. 1~5 2B. 2C0 2RA 4.4 457 4G. 5GY 5VS 5XA 5XJ 7-5 71M 8P~ 92H 92I 92L AAIKJ AALRI AAQFI AAXUO ACGFS ADEZE ADTZH AECPX AEKER AFTJW AGHFR AGYEJ AITUG AJOXV ALMA_UNASSIGNED_HOLDINGS BLXMC CCEZO CQIGP CS3 CUBFJ CW9 EBS EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FNPLU GBLVA HVGLF HZ~ IHE J1W JJJVA M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 ROL RPZ SDF SDG SES TCJ TGT U1G U5S W92 ~WA 4A8 93N ABJNI ABWVN ACRPL ADNMO PSX |
| ID | FETCH-LOGICAL-c588-cdbffc965f0e908747fc12ac5a3b0e4809d290a0d8a91dfcd4781d102612f5a43 |
| ISSN | 0254-4156 |
| IngestDate | Thu May 29 04:10:30 EDT 2025 Wed Feb 14 10:36:26 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Keywords | compressed sensing 稀疏水声信通 sparse signal reconstruction 压缩感知 sparse underwater acoustic channel approximate l0 norm 范数约束 似零范数 稀疏信号恢复 Norm constraint |
| Language | Chinese |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c588-cdbffc965f0e908747fc12ac5a3b0e4809d290a0d8a91dfcd4781d102612f5a43 |
| Notes | Norm constraint, sparse signal reconstruction, approximate 10 norm, sparse underwater acoustic channel,compressed sensing WU Fei-Yun ZHOU Yue-Hai TONG Feng 1. Key Laboratory of Underwater Acoustic Communication and Marine Information Technique of the Ministry of Education, Xiamen University, Xiamen 361005 Obtaining sparse solutions of under-determined, or over-complete, linear systems of equations has found extensive applications in signal processing of compressive sensing, source separation and signal acquisition. However, the previous approaches to this problem, which generally minimize the 11 norm using linear programming （LP） techniques or greedy methods, are subject to drawbacks such as low accuracy and slow convergence. This paper proposes to replace the 11 norm with a newly defined approximate 10 norm （AL0）, the optimization of which leads to the derivation of a hybrid approach by incorporating the steepest descent method with the Newton iteration. Numerical simulations and real data experiment show that |
| PageCount | 6 |
| ParticipantIDs | wanfang_journals_zdhxb201410008 chongqing_primary_662589010 |
| PublicationCentury | 2000 |
| PublicationDate | 2014 |
| PublicationDateYYYYMMDD | 2014-01-01 |
| PublicationDate_xml | – year: 2014 text: 2014 |
| PublicationDecade | 2010 |
| PublicationTitle | 自动化学报 |
| PublicationTitleAlternate | Acta Automatica Sinica |
| PublicationTitle_FL | Acta Automatica Sinica |
| PublicationYear | 2014 |
| Publisher | 厦门大学水声通信与海洋信息技术教育部重点实验室 厦门 361005 |
| Publisher_xml | – name: 厦门大学水声通信与海洋信息技术教育部重点实验室 厦门 361005 |
| SSID | ssib017479230 ssib001102911 ssib006576350 ssib051375349 ssib007293330 ssj0059721 ssib007290157 ssib023646446 ssib005904210 |
| Score | 2.0678358 |
| Snippet | 欠定系统（又称超完备系统）的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究.目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解,但这... 欠定系统(又称超完备系统)的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究。目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解，但这... |
| SourceID | wanfang chongqing |
| SourceType | Aggregation Database Publisher |
| StartPage | 2145 |
| SubjectTerms | 似零范数 压缩感知 稀疏信号恢复 稀疏水声信通 范数约束 |
| Title | 基于似零范数和混合优化的压缩感知信号快速重构算法 |
| URI | http://lib.cqvip.com/qk/90250X/201410/662589010.html https://d.wanfangdata.com.cn/periodical/zdhxb201410008 |
| Volume | 40 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Baden-Württemberg Complete Freedom Collection (Elsevier) customDbUrl: eissn: 1874-1029 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0059721 issn: 0254-4156 databaseCode: GBLVA dateStart: 20110101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Science Direct customDbUrl: eissn: 1874-1029 dateEnd: 20151031 omitProxy: true ssIdentifier: ssj0059721 issn: 0254-4156 databaseCode: .~1 dateStart: 20070101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LaxRBEB5ictGD-MQYHznYp7BxXj3TfezZzBqCiocouS3zTE4bHwlIToIBBWMUISoKLh48iCCCYCAs5B_4K3Z2zb-wqmayM4sBozAMvTXVPV9VzWxX13RXa9oVK8GcJo5Zw3RcNRuc3loYwihFGmYSB9Df53sD3rjpzN625xb4wsiRn5VZS6sr4XS0duC6kv-xKtDArrhK9h8sO2gUCFAG-8IZLAznQ9mY-ZzJBvMU8208C58KdTx8yaTHPIf5gok6ExbzHSY583SqZSIRKJ6LB1J0JkRRXQqkAIOE6i6T0LJNFJ8JDynAoyRWBzoAQJ4GU5yqQ8Eg5kbRMlI8xIOTKhpUcJmYITw-tewy5TPpEh6L5dth7nvMhB8YFLWpmKpi40zNMOUQErjE9x-fQg68iWTKwvvkGpJGyQIyG9ScQKC5gjyA65YsLiJHuTgC8_RqjMQoo6OFbhCIRDlyjMpmyh3CCLr3SJHKIjvkKlEVtUFBkBkLKFSwSesDHpAVcDcKoaEFVGS9oICFpSSdmcwz6RYW4Rlo3aVLkmD4pBmJ2sXHgSjKnvpTnikLHGCdV7oNGPLXcFhefXv1oT4qT-BZ-Dvg8-kH9aWWa9r4Nf_W9BxOpcH4o2FP62XtoSzla_HSw9CkWcO09n7MxPjYqDZ2zbt-R5UOOvizstKjcAmdRsUBdTgmSCx_u_iZv_JdHn5bVjngxd0PnEpAgxsWDL8xoJD7YhxzU1GUtdBJvngWRbt6kGCYYGVpubV4D9xGWsXXSoPWYsXhnD-hHS9GipMqf-1PaiNrS6e0Y5X8oae12ay9093Z7HY6e-9__Np43Nv6lr3a6G1vZy-fdjtvs43X_Xfr2eazfudzb73db3_q7n7MXmxnu1_2HrX3njzvfVjvf33T-751Rptv-PP12VqxNUot4vAnGMVhmkbS4ameSF24tptGhhlEPLBCPbGFLmNQXKDHIpBGnEYxLiiPDcoXmPLAts5qo63lVnJOm5SJiYOagLahT01XpFx3Uhlg6Mcx9WhcmxiopHk3z4DTdByTC5zYNa5dLpTULP4XHzSHH4Xzf-WY0I5iOY9rXtBGV-6vJhfB018JLxWPz289BLvY |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=%E5%9F%BA%E4%BA%8E%E4%BC%BC%E9%9B%B6%E8%8C%83%E6%95%B0%E5%92%8C%E6%B7%B7%E5%90%88%E4%BC%98%E5%8C%96%E7%9A%84%E5%8E%8B%E7%BC%A9%E6%84%9F%E7%9F%A5%E4%BF%A1%E5%8F%B7%E5%BF%AB%E9%80%9F%E9%87%8D%E6%9E%84%E7%AE%97%E6%B3%95&rft.jtitle=%E8%87%AA%E5%8A%A8%E5%8C%96%E5%AD%A6%E6%8A%A5&rft.au=%E4%BC%8D%E9%A3%9E%E4%BA%91&rft.au=%E5%91%A8%E8%B7%83%E6%B5%B7&rft.au=%E7%AB%A5%E5%B3%B0&rft.date=2014&rft.pub=%E5%8E%A6%E9%97%A8%E5%A4%A7%E5%AD%A6%E6%B0%B4%E5%A3%B0%E9%80%9A%E4%BF%A1%E4%B8%8E%E6%B5%B7%E6%B4%8B%E4%BF%A1%E6%81%AF%E6%8A%80%E6%9C%AF%E6%95%99%E8%82%B2%E9%83%A8%E9%87%8D%E7%82%B9%E5%AE%9E%E9%AA%8C%E5%AE%A4+%E5%8E%A6%E9%97%A8+361005&rft.issn=0254-4156&rft.issue=10&rft.spage=2145&rft.epage=2150&rft_id=info:doi/10.3724%2FSP.J.1004.2014.02145&rft.externalDocID=zdhxb201410008 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F90250X%2F90250X.jpg http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fwww.wanfangdata.com.cn%2Fimages%2FPeriodicalImages%2Fzdhxb%2Fzdhxb.jpg |