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Décomposition Modale Empirique : Contribution à la Modélisation Mathématique et Application en Traitement du Signal et de l'Image

Abstract : The EMD technique is a new tool for representing non linear and non-stationary signal as a sum of components called Intrinsic Mode Functions (IMF). The EMD decomposition can be compared with a wavelet one. However the main limit of the use of this method is lack of theoretical basis. There wasn't existence or convergence results before this work. In this work we replace within EMD algorithm, the mean envelope detection of a signal by asymptotic solutions of Partial Differential Equations (PDE) systems . Thus by a variational method, we prove the convergence of the algorithm and establish the IMF existence result. The orthogonality property of EMD algorithm is also studied on appropriate space. Two novel applications in signal and image processing are presented : intermittency and mode mixing extractions by Thikonov regularization, and restoration by EMD shrinkage. Finally the model can be a starting point of a study of the unicity of EMD decomposition.
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https://tel.archives-ouvertes.fr/tel-00878354
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Submitted on : Wednesday, October 30, 2013 - 1:34:21 AM
Last modification on : Friday, October 4, 2019 - 1:29:55 AM
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  • HAL Id : tel-00878354, version 1

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Oumar Niang. Décomposition Modale Empirique : Contribution à la Modélisation Mathématique et Application en Traitement du Signal et de l'Image. Equations aux dérivées partielles [math.AP]. Université Paris XII Val de Marne, 2007. Français. ⟨tel-00878354⟩

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