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Pré-Publication, Document De Travail Année : 2020

Sign preservation analysis of orthogonal greedy algorithms

Résumé

We bring a contribution to the exact recovery theory of a non-negative K-sparse vector from noisy linear measurements under the 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 for the first time an exact support recovery property based on mutual coherence for non-negative versions of OMP and OLS.
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Dates et versions

hal-01971697 , version 1 (07-01-2019)
hal-01971697 , version 2 (30-07-2020)
hal-01971697 , version 3 (24-02-2021)
hal-01971697 , version 4 (06-06-2021)
hal-01971697 , version 5 (20-07-2021)

Identifiants

  • HAL Id : hal-01971697 , version 2

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Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. Sign preservation analysis of orthogonal greedy algorithms. 2020. ⟨hal-01971697v2⟩
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