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Coherence-based Partial Exact Recovery Condition for OMP/OLS

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Abstract

We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the scenario where OMP/OLS have selected good atoms during the first l iterations (l < k) and derive a new sufficient and worst-case necessary condition for their success in k steps. Our result is based on the coherence of the dictionary and relaxes Tropp's well-known condition < 1=(2k 1) to the case where OMP/OLS have a partial knowledge of the support.
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Dates and versions

hal-00759433 , version 1 (30-11-2012)

Identifiers

  • HAL Id : hal-00759433 , version 1

Cite

Cedric Herzet, Charles Soussen, Jérôme Idier, Rémi Gribonval. Coherence-based Partial Exact Recovery Condition for OMP/OLS. 2012. ⟨hal-00759433⟩
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