Joint K-Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares

@article{Soussen2013JointKA,
  title={Joint K-Step Analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares},
  author={Charles Soussen and R{\'e}mi Gribonval and J{\'e}r{\^o}me Idier and C{\'e}dric Herzet},
  journal={IEEE Transactions on Information Theory},
  year={2013},
  volume={59},
  pages={3158-3174}
}
Tropp's analysis of orthogonal matching pursuit (OMP) using the exact recovery condition (ERC) is extended to a first exact recovery analysis of orthogonal least squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most k iterations where k denotes the support cardinality. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never… 

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