Numéro spécial : Génération aléatoire de conditions météorologiques
Image data assimilation with filtering methods
[Méthodes de filtrage pour l’assimilation de données image]
Journal de la société française de statistique, Tome 156 (2015) no. 1, pp. 169-179.

Dans cet article nous décrivons plusieurs techniques d’assimilation de données images formulées dans le cadre d’un problème de filtrage stochastique non linéaire. Nous prônons l’utilisation de filtres hybrides couplant des filtres de Kalman d’ensemble et les filtres particulaires. La première famille de filtres, bien que déficiente d’un point de vue théorique puisqu’elle ne converge pas vers les moments de la distribution de filtrage cible, a montré son efficacité pour des problèmes d’assimilation de données en très grande dimension. La seconde en revanche, bien posée théoriquement, est confrontée à d’importantes difficultés pratiques en grande dimension. Nous listons brièvement les principes gouvernant la construction de ces filtres, ainsi que leur avantages et défauts. Quelques résultats comparatifs entre ces différentes techniques sont donnés dans le cas du filtrage d’un écoulement turbulent 2D.

In this paper we describe several techniques formulated within the stochastic filtering framework for image data assimilation issues. We advocate here the use of hybrid methods between ensemble Kalman methods and particle filters. The former family, despite being theoretically deficient in the sense that it does not in general converge towards the sought-after filtering moments, has demonstrated to be very efficient in practice for high dimensional space filtering issues. At the opposite, the latter are theoretically well posed but face strong practical difficulties in high dimensional spaces. We list here briefly the principal ideas of the underlying hybrid filters, their qualities and their drawbacks. Some comparison results between those different techniques are provided for the filtering of a 2D turbulent flow.

Keywords: Data assimilation, High dimension, Filtering methods
Mot clés : Assimilation de données, Grande dimension, Méthodes de filtrage 
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Cuzol, Anne; Marchand, Jean-Louis; Mémin, Etienne. Image data assimilation with filtering methods. Journal de la société française de statistique, Tome 156 (2015) no. 1, pp. 169-179. http://archive.numdam.org/item/JSFS_2015__156_1_169_0/

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