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Estimation de fonctions géométriques et déconvolution

Abstract : The presented work is divided into three parts. At first, we show that the formalism of model selection allows to bound the decay rate of the estimation error of a thresholding estimator in an orthogonal basis bandlettes of a noisy image (Gaussian additive noise) for a set of geometrically regular images. This rate is optimal up to a logarithmic factor for functions of regularity C_alpha outside C_alpha curves. In a second step, we show that a similar approach can also achieve an optimal estimator for the inversion of the tomography operator on the same class of functions. In the third part we analyze the 1D sparse spike deconvolution by l_1 minimization and show that a minimum distance between the spikes, depending on the filter, ensures that l_1 minimization provides exact reconstruction.
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Contributor : Charles Dossal Connect in order to contact the contributor
Submitted on : Wednesday, August 28, 2013 - 10:36:41 PM
Last modification on : Tuesday, October 19, 2021 - 11:05:45 PM
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  • HAL Id : tel-00855128, version 1



Charles Dossal. Estimation de fonctions géométriques et déconvolution. Statistiques [math.ST]. Ecole Polytechnique X, 2005. Français. ⟨tel-00855128⟩



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