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 HerzetConnect in order to contact the contributor Submitted on : Friday, November 30, 2012 - 3:57:06 PM Last modification on : Wednesday, April 27, 2022 - 3:49:07 AM Long-term archiving on: : Friday, March 1, 2013 - 3:56:34 AM