Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations

Yoann Isaac 1, 2 Quentin Barthélemy 3 Cédric Gouy-Pailler 1 Michèle Sebag 4, 2 Jamal Atif 5
1 LADIS - Laboratoire d'analyse des données et d'intelligence des systèmes
DM2I - Département Métrologie Instrumentation & Information : DRT/LIST/DM2I
2 TAU - TAckling the Underspecified
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This paper addresses the structurally constrained sparse decomposition of multi-dimensional signals onto overcomplete families of vectors, called dictionaries. The contribution of the paper is threefold. Firstly, a generic spatio-temporal regularization term is designed and used together with the standard ℓ1ℓ1 regularization term to enforce a sparse decomposition preserving the spatio-temporal structure of the signal. Secondly, an optimization algorithm based on the split Bregman approach is proposed to handle the associated optimization problem, and its convergence is analyzed. Our well-founded approach yields same accuracy as the other algorithms at the state of the art, with significant gains in terms of convergence speed. Thirdly, the empirical validation of the approach on artificial and real-world problems demonstrates the generality and effectiveness of the method. On artificial problems, the proposed regularization subsumes the Total Variation minimization and recovers the expected decomposition. On the real-world problem of electro-encephalography brainwave decomposition, the approach outperforms similar approaches in terms of P300 evoked potentials detection, using structured spatial priors to guide the decomposition.
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01448305
Contributeur : Christine Okret-Manville <>
Soumis le : vendredi 27 janvier 2017 - 17:11:28
Dernière modification le : jeudi 7 février 2019 - 14:28:09

Lien texte intégral

Identifiants

Citation

Yoann Isaac, Quentin Barthélemy, Cédric Gouy-Pailler, Michèle Sebag, Jamal Atif. Multi-dimensional signal approximation with sparse structured priors using split Bregman iterations. Signal Processing, Elsevier, 2017, 130, pp.389-402. 〈10.1016/j.sigpro.2016.07.013〉. 〈hal-01448305〉

Partager

Métriques

Consultations de la notice

520