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无约束的$\ell_{2,1}$-分析法重构冗余紧框架下分块稀疏信号的条件

刘洋铄, 刘宏宇, 葛焕敏   

  1. 北京体育大学体育工程学院, 北京 100084
  • 收稿日期:2021-02-02 修回日期:2021-07-17 出版日期:2022-04-20 发布日期:2022-04-20
  • 通讯作者: 葛焕敏,Email:gehuanmin@163.com.
  • 基金资助:
    国家自然科学基金(11901037),北京体育大学大学生创新创业训练计划项目(2018)资助课题.

刘洋铄, 刘宏宇, 葛焕敏. 无约束的$\ell_{2,1}$-分析法重构冗余紧框架下分块稀疏信号的条件[J]. 系统科学与数学, 2022, 42(3): 509-527.

LIU Yangshuo, LIU Hongyu, GE Huanmin. The Condition for the Recovery of Block Sparse Signal Based on Redundant Tight Frame via the Unconstrained $\ell_{2,1}$-Analysis Method[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(3): 509-527.

The Condition for the Recovery of Block Sparse Signal Based on Redundant Tight Frame via the Unconstrained $\ell_{2,1}$-Analysis Method

LIU Yangshuo, LIU Hongyu, GE Huanmin   

  1. School of Sports Engineering, Beijing Sport University, Beijing 100084
  • Received:2021-02-02 Revised:2021-07-17 Online:2022-04-20 Published:2022-04-20
文章主要利用分块稀疏信号的凸分解技术分析无约束的$\ell_{2,1}$-分析模型,建立无约束的$\ell_{2,1}$-分析法重构冗余紧框架下分块稀疏信号的条件,其条件基于紧框架下的限制等距性质.首先,利用分块稀疏信号的凸分解技术建立两个重要技术引理.其次,基于发展的两个技术引理建立无约束的$\ell_{2,1}$-分析法恢复冗余紧框架下分块稀疏信号新的恢复条件,其条件基于紧框架下的限制等距性质,改进了现存最好的恢复条件.最后,设计数值实验,说明无约束的$\ell_{2,1}$-分析法重构冗余紧框架下分块稀疏信号的性能.
In this paper, we mainly apply the convex decomposition of block sparse signals to analyse the unconstrained $\ell_{2,1}$-analysis model and develop the condition for the recovery of block sparse signals based on redundant tight frames via the unconstrained $\ell_{2,1}$-analysis method, which is based on restricted isometry property under tight frame. We first develop two significant lemmas based on the convex decomposition theory. Second, we build the weak condition based on restricted isometry property under tight frame for the recovery of block sparse signals based on redundant tight frames via the unconstrained $\ell_{2,1}$-analysis method. Last, numerical experiments is established to verify the recovery performance of the unconstrained $\ell_{2,1}$-analysis method.

MR(2010)主题分类: 

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[1] 王忠梅,许克明,张焕水. 不确定量测联合信号重构的稳定性[J]. 系统科学与数学, 2014, 34(10): 1244-1251.
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