Matches in SemOpenAlex for { <https://semopenalex.org/work/W1491792074> ?p ?o ?g. }
Showing items 1 to 36 of
36
with 100 items per page.
- W1491792074 abstract "Resume – Nous traitons le probleme du debruitage spatial de l’estimation des parametres de lois statistiques grâce au flot geometrique nonlineaire de Laplace-Beltrami. Cet operateur , recemment introduit par N. Sochen et R. Kimmel [2] en traitement d’image, est etendu au cas d’un espace hybride forme des coordonnees spatiales (geometrie Euclidienne de la mesure) et des parametres des lois statistiques (geometrie de l’information de Chentsov dont la metrique est donnee par la matrice d’information de Fisher). Cet operateur EDP agissant intrinsequement sur la variete entropique possede la propriete de conserver les discontinuites, ce qui permet de lisser les estimateurs des parametres de lois statistiques de facon anisotrope. Nous appliquons ce formalisme au lissage spatial de parametres statistiques de processus autoregressifs via la metrique de Siegel, en deduisant l’expression des operateurs agissant sur les coefficients de reflexion qui permettent de lisser anisotropiquement des spectres Doppler. Que ce soit, pour la theorie des « Espaces d’Echelle », pour la metrique de Chentsov des densites gaussiennes, ou pour les modeles AR, le modele de geometrie hyperbolique de Poincare dans le disque unite semble jouer un role central. Abstract Our problem adresses the spatial denoising of statistical parameters estimation via the geometric non-linear Laplace-Beltrami Flow based on the embedding space geometry deduced from Information geometry. Input of our problem is a map W where Σ is a ndimensional Riemannian manifold and M → Σ : X is the embedding of this manifold in a space which is hybrid space of spatial coordinates and statistical parameters coordinates (Chentsov space of Information geometry deduced from Fisher metric). Then, our problem is solved viewing parameters space of Chentsov as embedding maps, that flow toward minimal surfaces.This spatial denoising, recently introduced by N.Sochen & R. Kimmel [2] in Image processing, and presently extended for spatial statistical parameters estimation denoising preserves discontinuities (The operator has the good behaviour that the projection is edge preserving.). After the definition of the Laplace-Beltrami flow for any statistical parameters space based on Fisher metric, we provide different applications for anisotropic spatial smoothing of Gaussian law parameters and reflection coefficient in Doppler analysis. In case of Doppler analysis, the hybrid space is the Embedding Siegel space. In all cases, Poincare’s hyperbolic geometry model in unit disk seems to play a central role." @default.
- W1491792074 created "2016-06-24" @default.
- W1491792074 creator A5015603088 @default.
- W1491792074 creator A5022828632 @default.
- W1491792074 creator A5056792252 @default.
- W1491792074 date "2003-01-01" @default.
- W1491792074 modified "2023-09-24" @default.
- W1491792074 title "Lissage anisotrope Doppler par extension de l'opérateur de diffusion de Laplace-Beltrami dans le cadre de la géométrie Riemannienne de l'information de Chentsov" @default.
- W1491792074 cites W107085514 @default.
- W1491792074 cites W1536988231 @default.
- W1491792074 cites W1543160960 @default.
- W1491792074 cites W2037900003 @default.
- W1491792074 cites W2066637591 @default.
- W1491792074 hasPublicationYear "2003" @default.
- W1491792074 type Work @default.
- W1491792074 sameAs 1491792074 @default.
- W1491792074 citedByCount "0" @default.
- W1491792074 crossrefType "journal-article" @default.
- W1491792074 hasAuthorship W1491792074A5015603088 @default.
- W1491792074 hasAuthorship W1491792074A5022828632 @default.
- W1491792074 hasAuthorship W1491792074A5056792252 @default.
- W1491792074 hasConcept C138885662 @default.
- W1491792074 hasConcept C15708023 @default.
- W1491792074 hasConcept C2524010 @default.
- W1491792074 hasConcept C33923547 @default.
- W1491792074 hasConceptScore W1491792074C138885662 @default.
- W1491792074 hasConceptScore W1491792074C15708023 @default.
- W1491792074 hasConceptScore W1491792074C2524010 @default.
- W1491792074 hasConceptScore W1491792074C33923547 @default.
- W1491792074 hasLocation W14917920741 @default.
- W1491792074 hasOpenAccess W1491792074 @default.
- W1491792074 hasPrimaryLocation W14917920741 @default.
- W1491792074 isParatext "false" @default.
- W1491792074 isRetracted "false" @default.
- W1491792074 magId "1491792074" @default.
- W1491792074 workType "article" @default.