Time-Frequency Energy Distributions Meet Compressed Sensing

Abstract : In the case of multicomponent signals with amplitude and frequency modulations, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum l1-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased.
Type de document :
Article dans une revue
IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2010, 58 (6), pp.2974-2982. 〈10.1109/TSP.2010.2044839〉
Liste complète des métadonnées

Littérature citée [42 références]  Voir  Masquer  Télécharger

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00475930
Contributeur : Pierre Borgnat <>
Soumis le : vendredi 23 avril 2010 - 13:16:32
Dernière modification le : jeudi 19 avril 2018 - 14:54:03
Document(s) archivé(s) le : lundi 22 octobre 2012 - 15:22:07

Fichier

IEEE_TSP_TFCS_double.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Patrick Flandrin, Pierre Borgnat. Time-Frequency Energy Distributions Meet Compressed Sensing. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2010, 58 (6), pp.2974-2982. 〈10.1109/TSP.2010.2044839〉. 〈ensl-00475930〉

Partager

Métriques

Consultations de la notice

363

Téléchargements de fichiers

764