Emergent Mind
Coherence-based Partial Exact Recovery Condition for OMP/OLS
(1211.7283)
Published Nov 30, 2012
in
cs.IT
,
math.IT
,
physics.data-an
,
and
stat.CO
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 \mu of the dictionary and relaxes Tropp's well-known condition \mu<1/(2k-1) to the case where OMP/OLS have a partial knowledge of the support.
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