Sparse signal reconstruction for nonlinear models via piecewise rational optimization - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Signal Processing Année : 2021

Sparse signal reconstruction for nonlinear models via piecewise rational optimization

Résumé

We propose a method to reconstruct sparse signals degraded by a nonlinear distortion and acquired at a limited sampling rate. Our method formulates the reconstruction problem as a nonconvex minimization of the sum of a data fitting term and a penalization term. In contrast with most previous works which settle for approximated local solutions, we seek for a global solution to the obtained challenging nonconvex problem. Our global approach relies on the so-called Lasserre relaxation of polynomial optimization. We here specifically include in our approach the case of piecewise rational functions, which makes it possible to address a wide class of nonconvex exact and continuous relaxations of the l0 penalization function. Additionally, we study the complexity of the optimization problem. It is shown how to use the structure of the problem to lighten the computational burden efficiently. Finally, numerical simulations illustrate the benefits of our method in terms of both global optimality and signal reconstruction.
Fichier principal
Vignette du fichier
main.pdf (647.53 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02972442 , version 1 (20-10-2020)
hal-02972442 , version 2 (04-12-2020)

Identifiants

Citer

Arthur Marmin, Marc Castella, Jean-Christophe Pesquet, Laurent Duval. Sparse signal reconstruction for nonlinear models via piecewise rational optimization. Signal Processing, 2021, 179, pp.107835. ⟨10.1016/j.sigpro.2020.107835⟩. ⟨hal-02972442v2⟩
341 Consultations
177 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More