THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS*

doi:10.1007/s10473-024-0509-0

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1787-1800.doi: 10.1007/s10473-024-0509-0

THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*

Yifang yang, Jinping wang^†

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

收稿日期:2023-02-16 修回日期:2024-06-06 出版日期:2024-10-25 发布日期:2024-10-22
通讯作者: †Jinping WANG, E-mail,: wangjinping@nbu.edu.cn
作者简介:Yifang yang, E-mail,: 2458224497@qq.com
基金资助:
Natural Science Foundation of China (62071262) and the K. C. Wong Magna Fund at Ningbo University.

THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*

Yifang yang, Jinping wang^†

School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China

Received:2023-02-16 Revised:2024-06-06 Online:2024-10-25 Published:2024-10-22
Contact: †Jinping WANG, E-mail,: wangjinping@nbu.edu.cn
About author:Yifang yang, E-mail,: 2458224497@qq.com
Supported by:
Natural Science Foundation of China (62071262) and the K. C. Wong Magna Fund at Ningbo University.

摘要/Abstract

摘要： In this paper, we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit (BgOMP) algorithm in the $l_2$-bounded noise case. Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal, if the sensing matrix satisfies the the block restricted isometry property (block-RIP), then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations. Furthermore, we conjecture that this condition is sharp.

关键词: compressed sensing, strongly-decaying, block sparse signal, block generalized OMP, block-RIP

Abstract: In this paper, we reconstruct strongly-decaying block sparse signals by the block generalized orthogonal matching pursuit (BgOMP) algorithm in the $l_2$-bounded noise case. Under some restraints on the minimum magnitude of the nonzero elements of the strongly-decaying block sparse signal, if the sensing matrix satisfies the the block restricted isometry property (block-RIP), then arbitrary strongly-decaying block sparse signals can be accurately and steadily reconstructed by the BgOMP algorithm in iterations. Furthermore, we conjecture that this condition is sharp.

Key words: compressed sensing, strongly-decaying, block sparse signal, block generalized OMP, block-RIP

中图分类号:

35B10

Yifang yang, Jinping wang. THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*[J]. 数学物理学报(英文版), 2024, 44(5): 1787-1800.

Yifang yang, Jinping wang. THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1787-1800.

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THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*

THE STABLE RECONSTRUCTION OF STRONGLY-DECAYING BLOCK SPARSE SIGNALS^*

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