The Non Degenerate Source Condition: Support Robustness for Discrete and Continuous Sparse Deconvolution

Vincent Duval (1, 2) , Gabriel Peyré (1, 2)

1 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper, we study discrete and continuous versions of the LASSO in order to solve the deconvolution problem. We shed light on the Non Degenerate Source Condition, a property which yields support robustness for both the continuous and discrete problems. More precisely, we show that this property yields exact support recovery in the continuous case and the estimation of twice the number of spikes in the discrete case.

Mots clés: sparse regularization; deconvolution; total variation

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

Vincent Duval, Gabriel Peyré. The Non Degenerate Source Condition: Support Robustness for Discrete and Continuous Sparse Deconvolution. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Dec 2015, Cancun, Mexico. ⟨hal-01169371⟩