Skip to Main content Skip to Navigation
Theses

Modèles AM-FM et Approche par Équations aux Dérivées Partielles de la Décomposition Modale Empirique pour l'Analyse des Signaux et des Images

Abstract : This work is addressed to signal and image analysis based on the empirical mode decomposition (EMD) and AM-FM models. In the first part of the thesis, a theoretical study of the 1D and 2D EMD is proposed. To do that, upper and lower envelopes are locally modeled with continuous operators. The local mean of envelopes is then computed in a more convenient way, such that the 1D and 2D sifting iterations are now well approximated by the resolutions of well posed partial differential equations (PDE). In addition, we provide theoretical justifications and carry out analytical characterizations of 1D and 2D empirical modes. This theoretical work enlightens important aspects of the EMD that were stated only in an intuitive way or based on controlled numerical simulations. In that way, we provide mathematical contributions on the method, which is originally defined just as an algorithm, and for which the main criticism remains the lack of a theoretical framework. Finally, new EMD algorithms are proposed and associated PDE are numerically solved, both in 1D and 2D. Our PDE-based approaches are illustrated with various signal and image examples. The second part deals with AM-FM image modeling. AM-FM models decompose images into components. In one hand, we have the local texture contrast (AM). On the other, we have the image geometry (FM). We first propose some improvements in wideband image demodulation techniques. Secondly, image demodulation based on 2D higher order differential energy operators (2D HODEO) are explored and better image demodulation algorithms are introduced. A practical application to sonar images' segmentation is also proposed. Our approaches are illustrated with various images and results are compared to the DESA (Discrete Energy Separation Algorithm) and the analytical image-based approach.
Complete list of metadatas

Cited literature [144 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-00464849
Contributor : El Hadji Diop <>
Submitted on : Thursday, March 18, 2010 - 10:48:31 AM
Last modification on : Friday, July 17, 2020 - 2:53:33 PM
Long-term archiving on: : Friday, October 19, 2012 - 10:10:20 AM

Identifiers

  • HAL Id : tel-00464849, version 1

Citation

El Hadji Samba Diop. Modèles AM-FM et Approche par Équations aux Dérivées Partielles de la Décomposition Modale Empirique pour l'Analyse des Signaux et des Images. Traitement du signal et de l'image [eess.SP]. Université Rennes 1, 2009. Français. ⟨tel-00464849⟩

Share

Metrics

Record views

724

Files downloads

931