Numéro spécial : Génération aléatoire de conditions météorologiques
Image data assimilation with filtering methods
Journal de la société française de statistique, Volume 156 (2015) no. 1, pp. 169-179.

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.

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.

Keywords: Data assimilation, High dimension, Filtering methods
@article{JSFS_2015__156_1_169_0,
     author = {Cuzol, Anne and Marchand, Jean-Louis and M\'emin, Etienne},
     title = {Image data assimilation with filtering methods},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {169--179},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {156},
     number = {1},
     year = {2015},
     zbl = {1316.62138},
     language = {en},
     url = {http://www.numdam.org/item/JSFS_2015__156_1_169_0/}
}
TY  - JOUR
AU  - Cuzol, Anne
AU  - Marchand, Jean-Louis
AU  - Mémin, Etienne
TI  - Image data assimilation with filtering methods
JO  - Journal de la société française de statistique
PY  - 2015
DA  - 2015///
SP  - 169
EP  - 179
VL  - 156
IS  - 1
PB  - Société française de statistique
UR  - http://www.numdam.org/item/JSFS_2015__156_1_169_0/
UR  - https://zbmath.org/?q=an%3A1316.62138
LA  - en
ID  - JSFS_2015__156_1_169_0
ER  - 
%0 Journal Article
%A Cuzol, Anne
%A Marchand, Jean-Louis
%A Mémin, Etienne
%T Image data assimilation with filtering methods
%J Journal de la société française de statistique
%D 2015
%P 169-179
%V 156
%N 1
%I Société française de statistique
%G en
%F JSFS_2015__156_1_169_0
Cuzol, Anne; Marchand, Jean-Louis; Mémin, Etienne. Image data assimilation with filtering methods. Journal de la société française de statistique, Volume 156 (2015) no. 1, pp. 169-179. http://www.numdam.org/item/JSFS_2015__156_1_169_0/

[1] Avenel, C.; Mémin, E.; Pérez, P. Stochastic level set dynamics to track closed curves through image data, Journal of Mathematical Imaging and Vision, accepted for publication (2013) | Zbl

[2] Beyou, S.; Cuzol, A.; Gorthi, S.; Mémin, E. Weighted Ensemble Transform Kalman Filter for Image Assimilation, Tellus A, Volume 65 (2013) no. 18803

[3] Bishop, C.H.; Etherton, B.J.; Majumdar, S.J. Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects, Monthly weather review, Volume 129 (2001) no. 3, pp. 420-436

[4] Cuzol, A.; Hellier, P.; Mémin, E. A low dimensional fluid motion estimator, Int. Journ. on Computer Vision, Volume 75 (2007) no. 3, pp. 329-349

[5] Corpetti, T.; Héas, P.; Mémin, E.; Papadakis, N. Pressure image asimilation for atmospheric motion estimation, Tellus, Volume 61A (2009), pp. 160-178

[6] Cuzol, A.; Memin, E. A stochastic filtering technique for fluid flows velocity fields tracking, IEEE Trans. Pattern Analysis and Machine Intelligence, Volume 31 (2009) no. 7, pp. 1278-1293

[7] Corpetti, T.; Mémin, E. Stochastic uncertainty models for the luminance consistency assumption, IEEE Transaction on Image Processing, Volume 21 (2012) no. 2, pp. 481-493 | Zbl

[8] Cuzol, A.; Mémin, E. Monte Carlo fixed-lag smoothing in state-space models, Preprint, arXiv:1310.1267 (2013)

[9] Del Moral, P. Feynman-Kac Formulae Genealogical and Interacting Particle Systems with Applications, Springer, New York; Series: Probability and Applications, 2004 | Zbl

[10] Doucet, A.; Godsill, S.; Andrieu, C. On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, Volume 10 (2000) no. 3, pp. 197-208

[11] Delyon, B.; Hu, Y. Simulation of conditioned diffusions and applications to parameter estimation, Stochastic Processes and Applications, Volume 116 (2006), pp. 1660-1675 | Zbl

[12] Evensen, G. The ensemble Kalman filter, theoretical formulation and practical implementation, Ocean Dynamics, Volume 53 (2003) no. 4, pp. 343-367

[13] Evensen, G. Sequential data assimilation with a non linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., Volume 99 (C5) (1994) no. 10, pp. 143-162

[14] Franzke, C.; Majda, A. Low-Order Stochastic Mode Reduction for a Prototype Atmospheric GCM, J. Atmos. Sci., Volume 63 (2005), pp. 457-479

[15] Gordon, N.J.; Salmond, D.J.; Smith, A.F.M. Novel approach to non-linear/non-Gaussian Bayesian state estimation, IEEE Processing-F, Volume 140 (1993) no. 2

[16] Houtekamer, P. L.; Mitchell, H.L. Data Assimilation Using an Ensemble Kalman Filter Technique, Monthly Weather Review, Volume 126 (1998) no. 3, pp. 796-811

[17] Kalman, R.E. A new approach to linear filtering and prediction problems, Transactions of the ASME - Journal of Basic Engineering, Volume 82 (1960), pp. 35-45

[18] Le Gland, F.; Monbet, V.; Tran, V. D. Large sample asymptotics for the ensemble Kalman filter, Handbook on Nonlinear Filtering (Crisan, D.; Rozovskii, B., eds.), Oxford University Press, 2011, pp. 598-631 | Zbl

[19] Marchand, J.L. Conditionnement de processus markoviens, IRMAR, Université de Rennes I (2012) (Ph. D. Thesis)

[20] Marchand, J. L. Conditioning diffusions with respect to partial observations, Preprint, arXiv:1105.1608 (2013)

[21] Mémin, E. Fluid flow dynamics under location uncertainty, Geophysical & Astrophysical Fluid Dynamics (2013) (accepted for publication) | HAL

[22] Majda, A.; Timofeyev, I.; Eijnden, E. Vanden Models for stochastic climate prediction, PNAS (1999) | Zbl

[23] Ott, E.; Hunt, B.R.; Szunyogh, I.; Zimin, A.V.; E.J. Kostelich, M. Corazza; Kalnay, E.; Patil, D.J.; Yorke, J. A. A local ensemble Kalman filter for atmospheric data assimilation, Tellus, Volume 56A (2004), pp. 415-428

[24] Papadakis, N.; Mémin, E.; Cuzol, A.; Gengembre, N. Data assimilation with the weighted ensemble Kalman filter, Tellus Series A: Dynamic Meteorology and Oceanography, Volume 62 (2010) no. 5, pp. 673-697

[25] Snyder, C; Bengtsson, T.; Bickel, P.; Anderson, J. Obstacles to High-Dimensional Particle Filtering, Monthly Weather Review (2008)

[26] Titaud, O.; Vidard, A.; Souopgui, I.; Dimet, F.-X. Le Assimilation of image sequences in numerical models, Tellus A, Volume 62 (2010) no. 1, pp. 30-47

[27] Van Leeuwen, P. J. Nonlinear data assimilation in geosciences: an extremely efficient particle filter, Quarterly Journal of the Royal Meteorological Society, Volume 136 (2010) no. 653, pp. 1991-1999