• DocumentCode
    1517006
  • Title

    Stable Recovery of Sparse Signals and an Oracle Inequality

  • Author

    Cai, Tony Tony ; Wang, Lie ; Xu, Guangwu

  • Author_Institution
    Dept. of Stat., Univ. of Pennsylvania, Philadelphia, PA, USA
  • Volume
    56
  • Issue
    7
  • fYear
    2010
  • fDate
    7/1/2010 12:00:00 AM
  • Firstpage
    3516
  • Lastpage
    3522
  • Abstract
    This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise.
  • Keywords
    Gaussian noise; signal processing; Gaussian noise; oracle inequality; sparse signal recovery; stable recovery; Compressed sensing; Dictionaries; Gaussian noise; Image reconstruction; Mathematics; Noise level; Signal processing; Sparse matrices; Statistics; Vectors; $ell _{1}$ minimization; compressed sensing; mutual incoherence; oracle inequality; sparse recovery;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2010.2048506
  • Filename
    5484999