Approximation of functions over redundant dictionaries using coherence
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On Lebesgue-type inequalities for greedy approximation
Journal of Approximation Theory
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Journal of Approximation Theory
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We show that the Orthogonal Greedy Algorithm (OGA) for dictionaries in a Hilbert space with small coherence M performs almost as well as the best m-term approximation for all signals with sparsity close to the best theoretically possible threshold m=12(M^-^1+1) by proving a Lebesgue-type inequality for arbitrary signals. Additionally, we present a dictionary with coherence M and a 12(M^-^1+1)-sparse signal for which OGA fails to pick up any atoms from the support, showing that the above threshold is sharp. We also show that the Pure Greedy Algorithm (PGA) matches the rate of convergence of the best m-term approximation beyond the saturation limit of m^-^1^2.