Mathematical Programming

, Volume 127, Issue 1, pp 89–122 | Cite as

Verifiable conditions of 1-recovery for sparse signals with sign restrictions

  • Anatoli Juditsky
  • Fatma Kılınç Karzan
  • Arkadi Nemirovski
Full Length Paper Series B


We propose necessary and sufficient conditions for a sensing matrix to be “s-semigood” – to allow for exact 1-recovery of sparse signals with at most s nonzero entries under sign restrictions on part of the entries. We express error bounds for imperfect 1-recovery in terms of the characteristics underlying these conditions. These characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse 1-recovery and thus efficiently computable upper bounds on those s for which a given sensing matrix is s-semigood. We examine the properties of proposed verifiable sufficient conditions, describe their limits of performance and provide numerical examples comparing them with other verifiable conditions from the literature.

Mathematics Subject Classification (2000)

90C90 90C05 90C22 62J05 


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Copyright information

© Springer and Mathematical Optimization Society 2010

Authors and Affiliations

  • Anatoli Juditsky
    • 1
  • Fatma Kılınç Karzan
    • 2
  • Arkadi Nemirovski
    • 2
  1. 1.LJK, Université J. FourierGrenoble Cedex 9France
  2. 2.Georgia Institute of TechnologyAtlantaUSA

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