De l'utilisation des noyaux maxitifs en traitement de l'information

Kevin Loquin 1
1 ICAR - Image & Interaction
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : In this thesis, we propose and develop new methods in statistics and in signal and image processing based upon possibility theory. These new methods are adapted from usual data processing tools. They aim at handling the defects of the usual methods coming from the user's lack of knowledge in the modeling of the observed phenomenon. The precise, punctual outputs of the usual methods become interval, hence imprecise, outputs. The interval outputs thus obtained consistently reflect the arbitrariness in the choice of the parameters of the usual methods.
Many algorithms in signal processing and in statistics use, more or less explicitly, the expectation operator associated to a probabilistic representation of the neighborhood of a point, which we call summative kernel. Thus, we group many data processing methods together under the name of summative extraction of information. Among these methods, there are measure modeling, linear filtering, sampling, interpolation and derivation processes of digital signals, probability density and cumulative distribution functions estimators,...
As an alternative to the summative extraction method, we present the maxitive extraction of information that uses the Choquet integral operator associated to a possibilistic representation of the neighborhood of a point, which we call maxitive kernel. The lack of knowledge on the summative kernel is handled by the fact that a maxitive kernel encodes a family of summative kernels. Moreover, the interval output of the maxitive extraction method is the set of the punctual outputs of the summative extraction methods obtained with the summative kernels encoded by the chosen maxitive kernel. On top of this theoretical justification, we present a series of applications of the maxitive extraction method in statistics and signal processing, which constitutes a toolbox, left to be enriched and used on real cases.
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Kevin Loquin. De l'utilisation des noyaux maxitifs en traitement de l'information. Traitement du signal et de l'image [eess.SP]. Université Montpellier II - Sciences et Techniques du Languedoc, 2008. Français. ⟨tel-00356477v2⟩

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