OPEN ACCESS
In this paper we address the problem of missing data interpolation in multi-modal geophysical satellite observation sequences. Main issues relate to the large percentage of missing data, from 20 % to 90 % for daily high-resolution observations; and the requirement forreconstructing fine-scale structures in accordance with the underlying turbulent dynamics. To solve the missing data interpolation problem, a variational data assimilation model is developped. Using synthetic and real ocean surface observations, numerical and qualitative evaluations demonstrate the relevance of two key components of the proposed model: the fusion of multimodal observations through a geometric front-driven constraint and the proposed variational assimilation setting using an advection-diffusion dynamical prior. Good reconstruction of highresolution geophysical observation sequences can then be achieved despite high percentage of missing data.
RÉSUMÉ
Cet article étudie l’estimation conjointe de données manquantes et de champs de déplacements dans des séquences multimodales d’observations satellitaires géophysiques. La complexité de la tâche est liée au taux élevé de données manquantes (entre 20 % et 90 %) pour des observations journalières de haute résolution et la reconstruction de structures fines en accord avec la dynamique sous-jacente. Nous avons développé une méthode basée sur l’assimilation variationnelle de données pour des séries multimodales et multirésolutions. A l’aide de données synthétiques et de données réelles de la surface océanique, une évaluation numé-rique et qualitative démontre l’apport de deux composantes-clés du modèle proposé : la fusion d’informations multimodales à partir d’une contrainte géométrique basée sur les structures frontales, et la méthode d’assimilation variationnelle utilisant comme a priori dynamique un modèle d’advection-diffusion. Les expérimentations conduites montrent que de bonnes performances de reconstruction sont obtenues pour les observations hautes résolutions en dépit du pourcentage élevé de données manquantes.
data assimilation, variational method, missing data interpolation, geophysical tracers dynamics, multimodal interpolation
MOTS-CLÉS
assimilation variationnelle de données, interpolation de données manquantes, inpainting
Arias P., Casselles V., Sapiro G. (2009). A variational framework for non-local image inpainting. International Conference on Energy Minimization Methods in Computer Vision and Patter Recognition, vol. 5681, p. 345-358.
Aujol J.-F., Ladja S., Masnou S. (2010). Exemplar-based inpainting from a variational point of view. SIAM Journal on Mathematical Analysis, vol. 42, no 3, p. 1246-1285.
Ba S. O., Corpetti T., Chapron B., Fablet R. (2010). Variational data assimilation for missing data interpolation in SST images. IEEE International Geoscience And Remote Sensing Symposium, p. 264-267.
Ba S. O., Corpetti T., Fablet R. (2012). Interpolation de données manquantes dans des séquences multi-modales d’images géophysiques satellitaires. Rencontres Francaises d’Intelligence Artificielle (RFIA).
Babacan S., Molina R., Katsaggelos X. (2009). Variational Bayesian super resolution. IEEE Transactions on Image Processing, vol. 20, no 4, p. 984-999.
Belkin I. M., , OReilly J. (2009). An algorithm for oceanic front detection in chlorophyll and SST satellite imagery. Journal of Marine Systems, vol. 78, no 3, p. 319-326.
Bennett A., Thorburn M. (1990). The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. Journal of Physical and Oceanography, p. 213-230.
Bertino L., Evensen G., Wackernagel H. (2003). Sequential data assimilation techniques in oceanography. International Statistical Review, vol. 71, no 2, p. 223-241.
Cheung V., Frey B. J., Jojic N. (2007). Video epitomes. International Journal on Computer Vision, vol. 1, p. 42- 49.
Gawarkiewicz G., Chapman D. (1991). Formation and maintenance of shelfbreak fronts in an unstratified flow. Journal of physical oceanography, vol. 21, no 8, p. 1225-1239.
Gejadze I., Honnorat M., Dimet F.-X. L., Monnier J. (2006). On variational data assimilation for 1D and 2D fluvial hydraulics. European Conf. on Mathematics for Industry, p. 361-365.
Glasner D., Bagon S., Irani M. (2009). Super-resolution from a single image. International Conference on Computer Vision, p. 349-356.
Hoyer J. L., Shea J. (2007). Optimal interpolation of sea surface temperature for the North Sea and Baltic sea. Journal of Marine Systems, vol. 65, no 1-4, p. 176-189.
Isern-Fontanet J., Chapron B., Lapyere G., Klein P. (2006). Potential use of microwave sea surface temperatures for the estimation of ocean currents. Geophys. Research Letter, vol. 33.
Ji J., Pan H., Liang Z. (2003). Further analysis of interpolation effects in mutual informationbased image registration. IEEE Transactions on Medical Imaging, vol. 22, no 9.
Lapeyre G., Klein P., Hua B. L. (2006). Oceanic restratification forced by surface frontogenesis. Journal of Physical Oceanography, vol. 36, p. 1577-1590.
Le Borgne P., Legendre G., Marsouin A. (2007). Operational SST retrieval from MetOp/AVHRR. EUMETSAT Conference.
Papadakis N., Corpetti T., Memin E. (2007). Dynamically consistent optical flow estimation. International Conference on Computer Vision, p. 1-7.
Papadakis N., Heas P., Memin E. (2007). Image assimilation for motion estimation of atmospheric layers with shallow-water model. Asian Conference on Computer Vision, p. 864-874.
Reynolds R., Smith T. M. (1994). Improved global sea surface temperature analyses using optimum interpolation. Journal of Climate, vol. 7, no 6, p. 929-948.
Solanki H. U., Dwivedi R. M., Nayak S., Somvanshi V. S., Gulati D. K., Pattnayak S. K. (2003). Fishery forecast using OCM chlorophyll concentration and AVHRR SST: validation results off Gujarat coast, India. International Journal of Remote Sensing, vol. 24, no 18.
Sukhtame J., Pierrehumbert R. (2002). Surface quasi geostrophic turbulence: The study of an active scalar. Chaos, vol. 12, no 2.
Talagrand O., Courtier P. (1987). Variational assimilation of meterological observations with the adjoint vorticity equation. Quarterly Journal of the Royal Meteorological Society, vol. 113, no 478, p. 1329-1347.
Tschumperlé D., Deriche R. (2005). Vector-valued image regularization with PDE’s : A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no 4, p. 506-517.
Ullman D. S., Cornillon P. C. (2000). Evaluation of front detection methods for satellite-derived SST data using in situ observations. Journal of Atmospheric and Oceanic Technology, vol. 17, no 12, p. 1667-1675.
Wentz F., Gentemmann C., Smith D., Chelton D. (2000). Satellite measurements of sea surface temperature through clouds. Science, vol. 288, p. 847-850.
Youzhuan D., Dongyang F., Zhihui W., Zhihua M., Juhong Z. (2008). Reconstruction of incomplete satellite oceanographic data sets based on EOF and Kriging methods. Conference on Image and Signal Processing for Remote Sensing.
Zheng X., Wei H. (2010). Analysis of chlorophyll concentration during the phytoplankton spring bloom in the Yellow Sea based on the MODIS data. International Conference on Life System Modeling and Intelligent Computing, vol. 6330, p. 254-261.