Sign preservation analysis of orthogonal greedy algorithms

Thi Thanh Nguyen (1) , Charles Soussen (2) , Jérôme Idier (3) , El-Hadi Djermoune (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 L2S - Laboratoire des signaux et systèmes
3 LS2N - Laboratoire des Sciences du Numérique de Nantes

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).

Mots clés: Greedy Algorithms; Orthogonal Matching Pursuit; Orthogonal Least Squares; Exact Recovery Condition; Mutual Coherence; Sparse Non-Negative Least Square Problems

Domaines: Traitement du signal et de l'image [eess.SP]

Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. Sign preservation analysis of orthogonal greedy algorithms. 2019. ⟨hal-01971697v1⟩