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.
https://hal.inria.fr/hal-00759433
Contributor : Cédric Herzet
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Submitted on : Friday, November 30, 2012 - 3:57:06 PM
Last modification on : Monday, September 2, 2019 - 2:20:10 PM
Long-term archiving on : Friday, March 1, 2013 - 3:56:34 AM
