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Réduction de dimension en statistique et application en imagerie hyper-spectrale

Robin Girard 1 
1 SMS - Statistique et Modélisation Stochatisque
LJK - Laboratoire Jean Kuntzmann
Abstract : This thesis deals with high dimensional statistical analysis. We focus on three different problems motivated by medical applications : curve classification, pixel classification and clustering in hyperspectral images. Our approaches are deeply linked with statistical testing procedures (multiple testing, minimax testing, robust testing, and functional testing) and learning theory. Both are introduced in the first part of this thesis. The second part focuses on classification of High dimensional Gaussian data. Our approach is based on a dimensionality reduction, and we show practical and theorical results. In the third and last part of this thesis we focus on hyperspectral image segmentation. We first propose a pixel classification algorithm based on multi-scale analysis, penalised maximum likelihood and feature selection. We give theorical results and simulations for this algorithm. We then propose a pixel clustering algorithm. It involves wavelet decomposition of observations in each pixel, smoothing with a growing region algorithm and frontier extraction based on a voting scheme.
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Submitted on : Monday, April 27, 2009 - 6:09:58 PM
Last modification on : Friday, March 25, 2022 - 11:09:30 AM
Long-term archiving on: : Thursday, June 10, 2010 - 10:02:11 PM

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Robin Girard. Réduction de dimension en statistique et application en imagerie hyper-spectrale. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2008. Français. ⟨tel-00379179⟩

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