Sign preservation analysis of orthogonal greedy algorithms

Abstract : We bring a contribution to the exact recovery theory of a K-sparse vector in the noiseless setting under the standard condition mu < 1/(2K − 1), where mu denotes the mutual coherence. While it is known that Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) identify the true support in K iterations, we prove that the weights of the selected atoms have the correct sign in the best current approximation at any of the K iterations. Therefore, OMP and OLS identify with their sign-aware versions, which allows us to establish an exact support recovery property based on mutual coherence for non-negative versions of OMP and OLS).
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https://hal.archives-ouvertes.fr/hal-01971697
Contributor : Charles Soussen <>
Submitted on : Monday, January 7, 2019 - 11:52:45 AM
Last modification on : Friday, April 26, 2019 - 8:58:04 AM
Long-term archiving on : Monday, April 8, 2019 - 2:47:20 PM

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  • HAL Id : hal-01971697, version 1

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Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. Sign preservation analysis of orthogonal greedy algorithms. 2019. ⟨hal-01971697⟩

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