Coherence-based Partial Exact Recovery Condition for OMP/OLS
Information Theory
2012-12-03 v1 math.IT
Data Analysis, Statistics and Probability
Computation
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.
Cite
@article{arxiv.1211.7283,
title = {Coherence-based Partial Exact Recovery Condition for OMP/OLS},
author = {Cedric Herzet and Charles Soussen and Jerome Idier and Remi Gribonval},
journal= {arXiv preprint arXiv:1211.7283},
year = {2012}
}