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            <title xml:lang="en">APPROACHING THE TWO INFINITE BY ELECTROMAGNETIC WAVES ELEMENTARY GEOMETRIC STRUCTURES OF DIGITAL ELECTROMAGNETIC INFORMATION Statistical characterization of the digital measurement of spatio-Doppler and polarimetric fluctuations of the radar electromagnetic wave</title>
            <title xml:lang="fr">APPROCHER LES DEUX INFINIS PAR LES ONDES ELECTROMAGNETIQUES LES STRUCTURES GÉOMÉTRIQUES ÉLÉMENTAIRES DE L'INFORMATION DIGITALE ÉLECTROMAGNÉTIQUE Caractérisation statistique de la mesure digitale des fluctuations spatio-Doppler et polarimétrique de l'onde électromagnétique radar</title>
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                <forename type="first">Frédéric</forename>
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                <title xml:lang="en">APPROACHING THE TWO INFINITE BY ELECTROMAGNETIC WAVES ELEMENTARY GEOMETRIC STRUCTURES OF DIGITAL ELECTROMAGNETIC INFORMATION Statistical characterization of the digital measurement of spatio-Doppler and polarimetric fluctuations of the radar electromagnetic wave</title>
                <title xml:lang="fr">APPROCHER LES DEUX INFINIS PAR LES ONDES ELECTROMAGNETIQUES LES STRUCTURES GÉOMÉTRIQUES ÉLÉMENTAIRES DE L'INFORMATION DIGITALE ÉLECTROMAGNÉTIQUE Caractérisation statistique de la mesure digitale des fluctuations spatio-Doppler et polarimétrique de l'onde électromagnétique radar</title>
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                    <forename type="first">Frédéric</forename>
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                <term xml:lang="en">radar clutter</term>
                <term xml:lang="en">unsupervised classification</term>
                <term xml:lang="en">Information Geometry</term>
                <term xml:lang="en">Statistical Fluctuations</term>
                <term xml:lang="en">Electromagnetic wave</term>
                <term xml:lang="fr">Fluctuation Statistique</term>
                <term xml:lang="fr">Géométrie de l'Information</term>
                <term xml:lang="fr">classification non-supervisée</term>
                <term xml:lang="fr">fouillis radar</term>
                <term xml:lang="fr">Radar</term>
                <term xml:lang="fr">Onde électromagnétique</term>
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              <p>The aim is to describe new geometric approaches to define the statistics of spatio-temporal and polarimetric measurements of the states of an electromagnetic wave, using the works of Maurice Fréchet, Jean-Louis Koszul and Jean-Marie Souriau, with in particular the notion of 'average' state of this digital measurement as a Fréchet barycentre in a metric space and a model derived from statistical mechanics to define and calculate a maximum density of entropy (extension of the notion of Gaussian) to describe the fluctuations of the electromagnetic wave. The article will illustrate these new tools with examples of radar application for Doppler, spatio-temporal and polarimetric measurement of the electromagnetic wave by introducing a distance on the covariance matrices of the electromagnetic digital signal, based on Fisher’s metric from Information Geometry.</p>
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              <p>Il s'agit de décrire de nouvelles approches géométriques pour définir les statistiques de mesures spatio-temporelles et polarimétrique des états d'une onde électromagnétique, en utilisant les travaux de Maurice Fréchet, Jean-Louis Koszul et Jean-Marie Souriau, avec en particulier la notion d'état « moyen » de cette mesure digitale comme barycentre de Fréchet dans un espace métrique et un modèle issu de la mécanique statistique pour définir et calculer une densité à maximum d'entropie (extension de la notion de gaussienne) pour décrire les fluctuations de l'onde électromagnétique. L'article illustrera ces outils nouveaux avec des exemples d'application en radar pour la mesure Doppler, spatio-temporelle et polarimétrique de l'onde électromagnétique en introduisant une distance sur les matrices de covariance du signal digital électromagnétique, basé sur la métrique de Fisher issue de la Géométrie de l'Information.</p>
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