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JAT
2007

On Lebesgue-type inequalities for greedy approximation

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On Lebesgue-type inequalities for greedy approximation
We study the efficiency of greedy algorithms with regard to redundant dictionaries in Hilbert spaces. We obtain upper estimates for the errors of the Pure Greedy Algorithm and the Orthogonal Greedy Algorithm in terms of the best m-term approximations. We call such estimates the Lebesgue-type inequalities. We prove the Lebesgue-type inequalities for dictionaries with special structure. We assume that the dictionary has a property of mutual incoherence (the coherence parameter of the dictionary is small). We develop a new technique that, in particular, allowed us to get rid of an extra factor m1/2 in the Lebesgue-type inequality for the Orthogonal Greedy Algorithm. © 2007 Elsevier Inc. All rights reserved.
David L. Donoho, Michael Elad, Vladimir N. Temlyak
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where JAT
Authors David L. Donoho, Michael Elad, Vladimir N. Temlyakov
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