Non-Negative Orthogonal Greedy Algorithms

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

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

Orthogonal greedy algorithms are popular sparse signal reconstruction algorithms. Their principle is to select atoms one by one. A series of unconstrained least-squares subproblems of gradually increasing size is solved to compute the approximation coefficients, which is efficiently performed using a fast recursive update scheme. When dealing with non-negative sparse signal reconstruction, a series of non-negative least-squares subproblems have to be solved. Fast implementation becomes tricky since each subproblem does not have a closed-form solution anymore. Recently, non-negative extensions of the classical orthogonal matching pursuit and orthogonal least squares algorithms were proposed, using slow (i.e., non-recursive) or recursive but inexact implementations. In this paper, we revisit these algorithms in a unified way. We define a class of non-negative orthogonal algorithms and exhibit their structural properties. We propose a fast and exact implementation based on the active-set resolution of non-negative least-squares and exploiting warm start initializations. The algorithms are assessed in terms of accuracy and computational complexity for a sparse spike deconvolution problem. We also present an application to near-infrared spectra decomposition.

Mots clés: orthogonal greedy algorithms; sparse reconstruction; non-negativity; non-negative least-squares; active-set algorithms

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

Thi Thanh Nguyen, Jérôme Idier, Charles Soussen, El-Hadi Djermoune. Non-Negative Orthogonal Greedy Algorithms. 2019. ⟨hal-02049424v1⟩