Exact recovery analysis of non-negative 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

It is well-known that Orthogonal Matching Pursuit (OMP) recovers the exact support of K-sparse signals under the condition μ < 1/(2K − 1) where μ denotes the mutual coherence of the dictionary. In this communication, we show that under the same condition and if the unknown K-sparse signal is non-negative, the weights of the atoms selected by OMP are non-negative at any of the first K iterations. Therefore, the generalized version of OMP to the non-negative setting (NNOMP) identifies with OMP, which allows us to establish an exact recovery analysis of NNOMP under the mutual coherence condition. We further establish a similar analysis of the non-negative extension of Orthogonal Least Squares (OLS), and discuss open issues related to the elaboration of weakened guarantees as compared to mutual coherence guarantees.

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

Thi Thanh Nguyen, Charles Soussen, Jérôme Idier, El-Hadi Djermoune. Exact recovery analysis of non-negative orthogonal greedy algorithms. International Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques, iTWIST 2020, Dec 2020, Nantes, France. ⟨hal-03083627⟩