| A perturbation analysis based on group sparse representation with orthogonal matching pursuit | |
| Liu, Chunyan2; Zhang, Feng1; Qiu, Wei3; Li, Chuan4; Leng, Zhenbei2 | |
| 2021-10 | |
| 发表期刊 | Journal of Inverse and Ill-Posed Problems
 |
| ISSN | 0928-0219 |
| EISSN | 1569-3945 |
| 卷号 | 29期号:5页码:653-674 |
| 摘要 | In this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block K-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of the nonzero elements of the block K-sparse signals, we prove that the support of the block K-sparse signals can be exactly recovered by the BOMP algorithm in the case of l(2) and l(2)/l(infinity) bounded total noise if A satisfies the BRIP of order K + 1 with delta(K+1) < 1/root vK + 1(1 +epsilon((K+1))(A))(2) + 1 (1 +epsilon((K+1))(A))(2) - 1. In addition, we also show that this is a sharp condition for exactly recovering any block K-sparse signal with the BOMP algorithm. Moreover, we also give the reconstruction upper bound of the error between the recovered block-sparse signal and the original block-sparse signal. In the noiseless and perturbed case, we also prove that the BOMP algorithm can exactly recover the block K-sparse signal under some constraints on the block K-sparse signal and delta(K+1) < 2 + root 2/2(1 +epsilon((K+1))(A))(2) - 1. Finally, we compare the actual performance of perturbed OMP and perturbed BOMP algorithm in the numerical study. We also present some numerical experiments to verify the main theorem by using the completely perturbed BOMP algorithm. |
| 关键词 | Compressed sensing block sparsity perturbation of measurement matrix block-restricted isometry property block orthogonal matching pursuit block Schur complement |
| DOI | 10.1515/jiip-2019-0043 |
| 收录类别 | SCIE |
| 语种 | 英语 |
| WOS研究方向 | Mathematics |
| WOS类目 | Mathematics, Applied ; Mathematics |
| WOS记录号 | WOS:000704191700002 |
| 出版者 | WALTER DE GRUYTER GMBH |
| 原始文献类型 | Article |
| 出版地 | BERLIN |
| 引用统计 | |
| 文献类型 | 期刊论文 |
| 条目标识符 | https://ir.cqcet.edu.cn/handle/39TD4454/3660 |
| 专题 | 重庆电子科技职业大学 |
| 作者单位 | 1.Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China; 2.ChongQing Normal Univ, Coll Math & Comp, Foreign Trade & Business Coll, Chongqing 401520, Peoples R China; 3.Chongqing Vocat Inst Engn, Sch Resources & Safety Engn, Chongqing 402260, Peoples R China; 4.ChongQing Normal Univ, Coll Big Data & Intelligence Engn, Foreign Trade & Business Coll, Chongqing 401520, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, Chunyan,Zhang, Feng,Qiu, Wei,et al. A perturbation analysis based on group sparse representation with orthogonal matching pursuit[J]. Journal of Inverse and Ill-Posed Problems,2021,29(5):653-674. |
| APA | Liu, Chunyan,Zhang, Feng,Qiu, Wei,Li, Chuan,&Leng, Zhenbei.(2021).A perturbation analysis based on group sparse representation with orthogonal matching pursuit.Journal of Inverse and Ill-Posed Problems,29(5),653-674. |
| MLA | Liu, Chunyan,et al."A perturbation analysis based on group sparse representation with orthogonal matching pursuit".Journal of Inverse and Ill-Posed Problems 29.5(2021):653-674. |
| 条目包含的文件 | 下载所有文件 | |||||
| 文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 | ||
| Liu-2021-A perturbat（996KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | 浏览 下载 | |
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
修改评论