Science China Information Sciences

, Volume 57, Issue 4, pp 1–7 | Cite as

A new approach of conditions on δ 2s (Φ) for s-sparse recovery

  • YiGang Cen
  • RuiZhen Zhao
  • ZhenJiang Miao
  • LiHui Cen
  • LiHong Cui
Research Paper

Abstract

In this paper, we provide a unified expression to obtain the conditions on the restricted isometry constant δ 2s (Φ). These conditions cover the important results proposed by Candes et al. and each of them is a sufficient condition for sparse signal recovery. In the noiseless case, when δ 2s (Φ) satisfies any one of these conditions, the s-sparse signal can be exactly recovered via (l 1) constrained minimization.

Keywords

concentration of mutilated vector in kerΦ s-largest mutilated vector restricted isometry constant δ2s(Φ) exact recovery of s-sparse signals via (l1maximum value of single variable function 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • YiGang Cen
    • 1
  • RuiZhen Zhao
    • 1
  • ZhenJiang Miao
    • 1
  • LiHui Cen
    • 2
    • 3
  • LiHong Cui
    • 4
  1. 1.School of Computer & Information TechnologyBeijing Jiaotong UniversityBeijingChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina
  3. 3.Key Laboratory of System Control and Information Processing, Ministry of EducationShanghaiChina
  4. 4.Department of MathematicsBeijing University of Chemical TechnologyBeijingChina

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