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Approximation des signaux: approches variationnelles et modèles aléatoires

Abstract : A probabilistic model and a variational method are being studied for sparse approximation.
The variational method use a L2 data term regularized by a mixed norm. These mixed norms are used to structure the sparsity. The resulted functionals can be minimized by iterative algorithms which convergence is proved. These mixed norms give estimates by "generalized thresholding operators". These operators are then modified to localize them or to introduce more persistence.
The probabilistic one uses a model a priori of signals as sparse random series of waveforms, with random coefficients chosen in an union of two orthonormal basis. The pdf of these coefficients involve two levels of randomness : the position in the time-frequency space, and the value. The study of analysis coefficients allows us to estimate the time-frequency maps by classification. The signal is then estimated by an orthogonal projection on these maps, and one obtains a decomposition into two layers and a residual.
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Contributor : Matthieu Kowalski Connect in order to contact the contributor
Submitted on : Monday, December 15, 2008 - 8:13:35 PM
Last modification on : Sunday, June 26, 2022 - 12:17:59 AM
Long-term archiving on: : Thursday, October 11, 2012 - 1:50:36 PM


  • HAL Id : tel-00347441, version 1



Matthieu Kowalski. Approximation des signaux: approches variationnelles et modèles aléatoires. Mathématiques [math]. Université de Provence - Aix-Marseille I, 2008. Français. ⟨tel-00347441⟩



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