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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