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Theses

Théorie des Matrices Aléatoires pour l'Imagerie Hyperspectrale

Abstract : Hyperspectral imaging generates large data due to the spectral and spatial high resolution, as it is the case for more and more other kinds of applications. For hyperspectral imaging, the data complexity comes from the spectral and spatial heterogeneity, the non-gaussianity of the noise and other physical processes. Nevertheless, this complexity enhances the wealth of collected informations, that need to be processed with adapted methods. Random matrix theory and robust processes are here suggested for hyperspectral imaging application: the random matrix theory is adapted to large data and the robustness enables to better take into account the non-gaussianity of the data. This thesis aims to enhance the model order selection on a hyperspectral image and the unmixing problem. As the model order selection is concerned, three new algorithms are developped, and the last one, more robust, gives better performances. One financial application is also presented. As for the unmixing problem, three methods that take into account the peculierities of hyperspectral imaging are suggested. The random matrix theory is of great interest for hyperspectral image processing, as demonstrated in this thesis. Differents methods developped here can be applied to other field of signal processing requiring the processing of large data.
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Eugénie Terreaux. Théorie des Matrices Aléatoires pour l'Imagerie Hyperspectrale. Autre. Université Paris Saclay (COmUE), 2018. Français. ⟨NNT : 2018SACLC091⟩. ⟨tel-02009854⟩

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