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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

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.

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

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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