数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1721-1730.doi: 10.1016/S0252-9602(16)30101-1

• 论文 • 上一篇    下一篇

STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION

谌稳固1, 李亚玲2   

  1. 1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    2. Graduate School, China Academy of Engineering Physics§Beijing 100088, China
  • 收稿日期:2015-06-03 修回日期:2015-12-25 出版日期:2016-12-25 发布日期:2016-12-25
  • 作者简介:Wengu CHEN,E-mail:chenwg@iapcm.ac.cn;Yaling LI,E-mail:leeyaling@126.com
  • 基金资助:

    This work was supported by National Natural Science Foundation of China (11271050 and 11371183).

STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION

Wengu CHEN1, Yaling LI2   

  1. 1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
    2. Graduate School, China Academy of Engineering Physics§Beijing 100088, China
  • Received:2015-06-03 Revised:2015-12-25 Online:2016-12-25 Published:2016-12-25
  • Supported by:

    This work was supported by National Natural Science Foundation of China (11271050 and 11371183).

摘要:

This paper establishes a high order condition on the restricted isometry property adapted to a frame D (D-RIP) for the signal recovery. It is shown that if the measurement matrix A satisfies the D-RIP condition δtk<√(t-1)/(t) for t>1, then all signals f which are sparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y=Af+z in l2 and Dantzig selector bounded noise setting.

关键词: compressed sensing, D-restricted isometry property, tight frame

Abstract:

This paper establishes a high order condition on the restricted isometry property adapted to a frame D (D-RIP) for the signal recovery. It is shown that if the measurement matrix A satisfies the D-RIP condition δtk<√(t-1)/(t) for t>1, then all signals f which are sparse in terms of a tight frame D can be recovered stably or exactly via the l1-analysis model based on y=Af+z in l2 and Dantzig selector bounded noise setting.

Key words: compressed sensing, D-restricted isometry property, tight frame

中图分类号: 

  • 94A12