Block sparse compressed sensing with frames: Null space property and <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mi mathvariant="bold-italic">l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>/</mo><msub><mrow><mi mathvariant="bold-italic">l</mi></mrow><mrow><mi mathvariant="bold-italic">q</mi></mrow></msub><mo stretchy="false">(</mo><mn mathvariant="normal">0</mn><mo>&lt;</mo><mi mathvariant="bold-italic">q</mi><mo>≤</mo><mn mathvariant="normal">1</mn><mo stretchy="false">)</mo></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/5095B941-6DD0-42a6-B7B6-E1F5356EBF8D-M001.jpg"><?fx-imagestate width="36.15266418" height="7.28133297"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/5095B941-6DD0-42a6-B7B6-E1F5356EBF8D-M001c.jpg"><?fx-imagestate width="36.15266418" height="7.28133297"?></graphic></alternatives></inline-formula>-synthesis

WU Fengong; ZHONG Penghong; QIN Yuehai

doi:10.13471/j.cnki.acta.snus.ZR20240295

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Block sparse compressed sensing with frames: Null space property and

l_{2} / l_{q} (0 < q \leq 1)

-synthesis

Research articles | 更新时间：2025-11-14

- Block sparse compressed sensing with frames: Null space property and $l_{2} / l_{q} (0 < q \leq 1)$ -synthesis
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 3, Pages: 173-182(2025)
- 作者机构：
  
  广东第二师范学院数学系，广东广州 510303
- 作者简介：
  
  WU Fengong（wufengong@gdei.edu.cn）
  ZHONG Penghong（zhongpenghong@gdei.edu.cn ）
  [ "QIN Yuehai（haiqy2000@gdei.edu.cn）" ]
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240295
  CLC： O224
- Received：05 October 2024，
  
  Accepted：22 February 2025，
  
  Published Online：07 May 2025，
  
  Published：25 May 2025
- 稿件说明：
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吴焚供,钟澎洪,覃跃海.框架下组稀疏非凸压缩感知问题：零空间性质与l2/lq (0<q≤1)-综合法[J].中山大学学报(自然科学版)(中英文),2025,64(03):173-182.

WU Fengong,ZHONG Penghong,QIN Yuehai.Block sparse compressed sensing with frames: Null space property and l2/lq(0<q≤1)-synthesis[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(03):173-182.
吴焚供,钟澎洪,覃跃海.框架下组稀疏非凸压缩感知问题：零空间性质与l2/lq (0<q≤1)-综合法[J].中山大学学报(自然科学版)(中英文),2025,64(03):173-182. DOI： 10.13471/j.cnki.acta.snus.ZR20240295.

WU Fengong,ZHONG Penghong,QIN Yuehai.Block sparse compressed sensing with frames: Null space property and l2/lq(0<q≤1)-synthesis[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(03):173-182. DOI： 10.13471/j.cnki.acta.snus.ZR20240295.

Block sparse compressed sensing with frames: Null space property and

l_{2} / l_{q} (0 < q \leq 1)

-synthesis

PDF Download

摘要

研究了基于

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497422&type=

4.06400013

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497408&type=

20.06599998

-综合法重构框架下具有组稀疏结构信号的重构条件及理论性能. 我们定义了一个框架意义下的新的零空间性质，称为

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497409&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497424&type=

2.20133328

-NSP

，并证明了测量矩阵满足

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497409&type=

2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497424&type=

2.20133328

-NSP

性质是

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497425&type=

3.21733332

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497411&type=

4.99533367

-综合法精确重构框架下组稀疏信号的充要条件. 更进一步地，我们还证明了该零空间性质还是保障

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497425&type=

3.21733332

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497411&type=

4.99533367

-综合法稳定重构框架下组稀疏信号的充要条件，并刻画了稳定重构的理论表现. 从现有研究文献来看，这是第一个保障

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497425&type=

3.21733332

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497411&type=

4.99533367

-综合法稳定重构框架下组稀疏信号的充要条件.

Abstract

This paper explores the recovery of block sparse signals in frame-based settings using the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497356&type=

3.80999994

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497377&type=

5.67266655

-synthesis technique (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497357&type=

3.47133350

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497372&type=

16.17133331

). We propose a new null space property

referred to as block

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497378&type=

2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497393&type=

2.53999996

-NSP

which is based on the dictionary

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497404&type=

2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497394&type=

2.53999996

. We establish that matrices adhering to the block

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497404&type=

2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497394&type=

2.53999996

-NSP

condition are both necessary and sufficient for the exact recovery of block sparse signals via

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497395&type=

3.80999994

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497420&type=

5.67266655

-synthesis. Additionally

this condition is essential for the stable recovery of signals that are block-compressible with respect to

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497404&type=

2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497394&type=

2.53999996

. This

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2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497394&type=

2.53999996

-NSP

property is identified as the first complete condition for successful signal recovery using

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497421&type=

3.80999994

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497380&type=

5.67266655

-synthesis. Furthermore

we assess the theoretical efficacy of the

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497397&type=

3.80999994

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497407&type=

5.67266655

-synthesis method under conditions of measurement noise.

关键词

Keywords

references

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⁰

Block sparse compressed sensing with frames: Null space property and l2/lq(0<q≤1)-synthesis

DOI：10.13471/j.cnki.acta.snus.ZR20240295

摘要

Abstract

关键词

Keywords

references

Block sparse compressed sensing with frames: Null space property and $l_{2} / l_{q} (0 < q \leq 1)$ -synthesis