Spike detection from inaccurate samplings

Jean-Marc Azaïs (1) , Yohann de Castro (2) , Fabrice Gamboa (1, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Probabilités et Statistique
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

This article investigates the super-resolution phenomenon using the celebrated statistical estimator LASSO in the complex valued measure framework. More precisely, we study the recovery of a discrete measure (spike train) from few noisy observations (Fourier samples, moments, Stieltjes transformation...). In particular, we provide an explicit quantitative localization of the spikes. Moreover, our analysis is based on the Rice method and provide an upper bound on the supremum of white noise perturbation in the measure space.

Mots clés: Super-resolution; LASSO; Signed measure; Bregman divergence; Semidefinite programming; Compressed Sensing.

Mots clés: Compressed Sensing

Domaines: Théorie [stat.TH]; Statistiques [math.ST]

Jean-Marc Azaïs, Yohann de Castro, Fabrice Gamboa. Spike detection from inaccurate samplings. 2013. ⟨hal-00780808v1⟩