Greed is Fine: on Finding Sparse Zeros of Hilbert Operators

François-Xavier Dupé (1)

1 QARMA - éQuipe d'AppRentissage de MArseille

We propose an generalization of the classical Orthogonal Matching Pursuit (OMP) algorithm for finding sparse zeros of Hilbert operator. First we introduce a new condition called the restricted diagonal deviation property which allow us to analysis of the consistency of the estimated support and vector. Secondly when using a perturbed version of the operator, we show that a partial recovery of the support is possible and remain possible even if some of the steps of the algorithm are inexact. Finally we discuss about the links between recent works on other version of OMP.

Mots clés: Consistency analysis; Greedy Algorithm; Orthogonal Matching Pursuit

Domaines: Traitement du signal et de l'image [eess.SP]; Apprentissage [cs.LG]

François-Xavier Dupé. Greed is Fine: on Finding Sparse Zeros of Hilbert Operators. 2015. ⟨hal-01120059v2⟩