Méthodes d'identification sous contraintes de non-négativité : application au filtrage adaptatif et à l'analyse d'images hyperspectrales
Auteur / Autrice : | Jie Chen |
Direction : | Paul Honeine, Cédric Richard |
Type : | Thèse de doctorat |
Discipline(s) : | Optimisation et sûreté des systèmes |
Date : | Soutenance en 2013 |
Etablissement(s) : | Troyes |
Ecole(s) doctorale(s) : | Ecole doctorale Sciences pour l'Ingénieur (Troyes, Aube) |
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Mots clés contrôlés
Résumé
In many real-life phenomena, due to the inherent physical characteristics of systems under investigation, non-negativity is a desired constraint that can be imposed on the parameters to estimate. The objective of this thesis is to investigate theories and algorithms for system identification under side constraints, in particular the non-negativity constraint and sum-toone constraint over the vector of parameters to estimate. The first part of the thesis addresses the problem of online system identification subject to non-negativity constraints. The Non-negative Least-Mean-Square algorithm (NNLMS) and its variants are proposed. The stochastic behavior of these algorithms in non-stationnary environments is analytically studied. Finally, an extension of this approach allows us to derive an LMS-type algorithm with L1-norm regularization The second part of the thesis focuses on a specific system identification problem — nonlinear spectral unmixing, with non-negativity and sum-to-one constraints. We formulate a new kernel-based paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra, with additive nonlinear fluctuations defined in a reproducing kernel Hilbert space. A kernel-based algorithm, based on multi-kernel learning, is proposed to determine the fractional abundances of pure materials subject to constraints. Finally, the spatial correlation between spectral signatures of neighboring pixels is used as prior information to improve the performance