Nearfield Acoustic Holography using sparsity and compressive sampling principles

Abstract : Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions, new regularization schemes can be developed, based on the sparsity of the normal velocity of the plate in a well-designed basis, i.e. the possibility to approximate it as a weighted sum of few elementary basis functions. In particular, these new techniques can handle discontinuities of the velocity field at the boundaries, which can be problematic with standard techniques. This comes at the cost of a higher computational complexity to solve the associated optimization problem, though it remains easily tractable with out-of-the-box software. Furthermore, this sparsity framework allows us to take advantage of the concept of Compressive Sampling: under some conditions on the sampling process (here, the design of a random array, which can be numerically and experimentally validated), it is possible to reconstruct the sparse signals with significantly less measurements (i.e., microphones) than classically required. After introducing the different concepts, this paper presents numerical and experimental results of NAH with two plate geometries, and compares the advantages and limitations of these sparsity-based techniques over standard Tikhonov regularization.


https://hal.inria.fr/hal-00720129
Contributeur : Rémi Gribonval <>
Soumis le : mardi 24 juillet 2012 - 10:19:45
Dernière modification le : vendredi 13 janvier 2017 - 14:18:44
Document(s) archivé(s) le : jeudi 25 octobre 2012 - 02:21:09

Fichiers

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

Identifiants

  • HAL Id : hal-00720129, version 1
  • ARXIV : 1207.5618

Citation

Gilles Chardon, Laurent Daudet, Antoine Peillot, François Ollivier, Nancy Bertin, et al.. Nearfield Acoustic Holography using sparsity and compressive sampling principles. Journal of the Acoustical Society of America, Acoustical Society of America, 2012, <http://scitation.aip.org/JASA>. <hal-00720129>

Partager

Métriques

Consultations de
la notice

1429

Téléchargements du document

900