R. J. Adrian, Particle-Imaging Techniques for Experimental Fluid Mechanics, Annual Review of Fluid Mechanics, vol.23, issue.1, pp.261-304, 1991.
DOI : 10.1146/annurev.fl.23.010191.001401

L. Alvarez, J. Esclarin, M. Lefbure, and J. Snchez, A PDE model for computing the optical flow, XVI congreso de ecuaciones diferenciales y aplicaciones, pp.21-24, 1999.

D. Béréziat and I. Herlin, Solving ill-posed Image Processing problems using Data Assimilation, Numerical Algorithms, vol.14, issue.7, pp.219-252, 2011.
DOI : 10.1007/s11075-010-9383-z

M. J. Black and P. Anandan, Robust dynamic motion estimation over time, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.3-6, 1991.
DOI : 10.1109/CVPR.1991.139705

K. A. Brewster, Phase-Correcting Data Assimilation and Application to Storm-Scale Numerical Weather Prediction. Part I: Method Description and Simulation Testing, Monthly Weather Review, vol.131, issue.3, pp.480-492, 2003.
DOI : 10.1175/1520-0493(2003)131<0480:PCDAAA>2.0.CO;2

K. A. Brewster, Phase-Correcting Data Assimilation and Application to Storm-Scale Numerical Weather Prediction. Part II: Application to a Severe Storm Outbreak, Monthly Weather Review, vol.131, issue.3, pp.493-507, 2003.
DOI : 10.1175/1520-0493(2003)131<0493:PCDAAA>2.0.CO;2

E. Candes and D. Donoho, singularities, Communications on Pure and Applied Mathematics, vol.9, issue.7, pp.219-266, 2004.
DOI : 10.1002/cpa.10116

E. Candes and D. Donoho, Continuous curvelet transform, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.162-197, 2005.
DOI : 10.1016/j.acha.2005.02.003

E. Candes and D. Donoho, Continuous curvelet transform, Applied and Computational Harmonic Analysis, vol.19, issue.2, pp.198-222, 2005.
DOI : 10.1016/j.acha.2005.02.004

E. Candes, L. Demanet, D. Donoho, Y. , and L. , Fast discrete curvelet transforms, Multiscale Model, pp.861-899, 2006.

D. Chapelle, M. Fragu, V. Mallet, and P. Moireau, Fundamental principles of data assimilation underlying the Verdandi library: applications to biophysical model personalization within euHeart, Medical & Biological Engineering & Computing, vol.4, issue.7, pp.1221-1233, 2013.
DOI : 10.1007/s11517-012-0969-6
URL : https://hal.archives-ouvertes.fr/hal-00760887

A. Cohen, Ondelettes et traitement numérique du signal, 1992.

R. R. Coifman, L. Auslander, T. Kailath, and S. K. Mitter, Wavelet Analysis and Signal Processing, pp.59-68, 1990.
DOI : 10.1007/978-1-4684-6393-4_5

F. Ovidio, V. Taillandier, I. Taupier-letage, and M. , L: Lagrangian validation of the mediterranean mean dynamic topography by extraction of tracer frontal structures, Mercator Ocean Quart. Newslett, vol.32, pp.24-32, 2009.

G. Evensen, Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics, Journal of Geophysical Research, vol.109, issue.Part 4, pp.10143-10162, 1994.
DOI : 10.1029/94JC00572

M. Farge, Wavelet Transforms and their Applications to Turbulence, Annual Review of Fluid Mechanics, vol.24, issue.1, pp.395-457, 1992.
DOI : 10.1146/annurev.fl.24.010192.002143
URL : https://hal.archives-ouvertes.fr/hal-01299264

J. Flór and I. Eames, Dynamcis of monopolar vortices on a topographic beta-plane, J. Fluid Mech, vol.456, pp.353-376, 2002.

L. Gaultier, J. Verron, J. Brankart, O. Titaud, and P. Brasseur, On the inversion of submesoscale tracer fields to estimate the surface ocean circulation, Journal of Marine Systems, vol.126, pp.33-42, 2013.
DOI : 10.1016/j.jmarsys.2012.02.014

S. Gorthi, S. Beyou, T. Corpetti, and E. Memin, Multiscale Weighted Ensemble Kalman Filter for Fluid Flow Estimation, International Conference on Scale Space and Variational Methods in Computer Vision (SSVM'11)
DOI : 10.1007/978-3-642-24785-9_63
URL : https://hal.archives-ouvertes.fr/hal-00694975

G. Haller, Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D: Nonlinear Phenomena, vol.149, issue.4, pp.248-277, 2001.
DOI : 10.1016/S0167-2789(00)00199-8

G. Haller, A variational theory of hyperbolic Lagrangian Coherent Structures, Physica D: Nonlinear Phenomena, vol.240, issue.7, pp.574-598, 2011.
DOI : 10.1016/j.physd.2010.11.010

G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence www.nonlin-processes-geophys.net, Physica D Nonlin. Processes Geophys, vol.1472215, issue.22, pp.352-370, 2000.

F. Dimet, Toward the assimilation of images
URL : https://hal.archives-ouvertes.fr/hal-00769826

I. Herlin, E. Huot, J. Berroir, L. Dimet, F. Korotaev et al., Estimation of a motien field on satellite images from a simplified ocean circulation model, ICIP International Conference on Image Processing, pp.8-11, 2006.

W. Hinterberger, O. Scherzer, C. Schnörr, and J. Weickert, ANALYSIS OF OPTICAL FLOW MODELS IN THE FRAMEWORK OF THE CALCULUS OF VARIATIONS, Numerical Functional Analysis and Optimization, vol.2, issue.1-2, pp.69-89, 2002.
DOI : 10.1023/A:1011286029287

R. N. Hoffman and C. Grassotti, A Technique for Assimilating SSM/I Observations of Marine Atmospheric Storms: Tests with ECMWF Analyses, Journal of Applied Meteorology, vol.35, issue.8, pp.1177-1188, 1996.
DOI : 10.1175/1520-0450(1996)035<1177:ATFASO>2.0.CO;2

R. N. Hoffman, Z. Liu, J. Louis, and C. Grassoti, Distortion Representation of Forecast Errors, Monthly Weather Review, vol.123, issue.9, pp.2758-2770, 1995.
DOI : 10.1175/1520-0493(1995)123<2758:DROFE>2.0.CO;2

B. K. Horn and B. G. Schunck, Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.185.1651

E. Huot, T. Isambert, I. Herlin, J. Berroir, and G. Korotaev, Data Assimilation of Satellite Images Within an Oceanographic Circulation Model, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, pp.14-19, 2006.
DOI : 10.1109/ICASSP.2006.1660330
URL : https://hal.archives-ouvertes.fr/inria-00604108

G. Korotaev, E. Huot, L. Dimet, F. Herlin, I. Stanichny et al., Analysis of the black sea surface currents retrieved from space imagery, Rapport du 38ème Congrès de la Commission Internationale pour l'Exploration Scientifique de la mer Méditerranée, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00627839

G. Lapeyre, Characterization of finite-time Lyapunov exponents and vectors in two-dimensional turbulence, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.12, issue.3, pp.688-698, 2002.
DOI : 10.1063/1.1499395
URL : https://hal.archives-ouvertes.fr/hal-00310234

L. Dimet, F. Talagrand, and O. , Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus A, vol.109, issue.2, pp.97-110, 1986.
DOI : 10.1111/j.1600-0870.1986.tb00459.x

F. Lekien, C. Coulliette, A. J. Mariano, E. H. Ryan, L. K. Shay et al., Pollution release tied to invariant manifolds: A case study for the coast of Florida, Physica D: Nonlinear Phenomena, vol.210, issue.1-2, pp.1-20, 2005.
DOI : 10.1016/j.physd.2005.06.023

J. Ma, A. Antoniadis, L. Dimet, and F. , Curvelet-Based Snake for Multiscale Detection and Tracking of Geophysical Fluids, IEEE Transactions on Geoscience and Remote Sensing, vol.44, issue.12
DOI : 10.1109/TGRS.2006.885017
URL : https://hal.archives-ouvertes.fr/hal-00171444

J. Ma, M. Y. Hussaini, O. V. Vasilyev, L. Dimet, and F. , Multiscale geometric analysis of turbulence by curvelets, Physics of Fluids, vol.21, issue.7, p.75104, 2009.
DOI : 10.1063/1.3177355
URL : https://hal.archives-ouvertes.fr/inria-00391872

S. G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.7, pp.674-693, 1989.
DOI : 10.1109/34.192463

E. Mémin and P. Perez, Dense estimation and object-based segmentation of the optical flow with robust techniques, IEEE Transactions on Image Processing, vol.7, issue.5, pp.703-719, 1998.
DOI : 10.1109/83.668027

H. Nagel, Constraints for the estimation of displacement vector elds from image sequences, Eighth International Joint Conference on Articial Intelligence, pp.945-951, 1983.

N. Papadakis and E. Mémin, Variational Assimilation of Fluid Motion from Image Sequence, SIAM Journal on Imaging Sciences, vol.1, issue.4, pp.343-363, 2008.
DOI : 10.1137/080713896
URL : https://hal.archives-ouvertes.fr/hal-00596149

S. Ravela, K. Emanuel, and D. Mclaughlin, Data assimilation by field alignment, Physica D: Nonlinear Phenomena, vol.230, issue.1-2, pp.127-145, 2007.
DOI : 10.1016/j.physd.2006.09.035

S. Ravela, J. Marshall, C. Hill, A. Wong, and S. Stransky, A realtime observatory for laboratory simulation of planetary flows, Experiments in Fluids, vol.12, issue.6, pp.915-925, 2010.
DOI : 10.1007/s00348-009-0752-0

C. Schnörr, Segmentation of visual motion by minimizing convex non-quadratic functionals, Proceedings of 12th International Conference on Pattern Recognition, pp.9-13, 1994.
DOI : 10.1109/ICPR.1994.576391

J. Serra, Image Analysis and Mathematical Morphology: Theoretical Advances, Image Analysis and Mathematical Morphology, 1988.

D. Suter, Motion estimation and vector splines, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94, pp.21-23, 1994.
DOI : 10.1109/CVPR.1994.323929

A. N. Tikhonov, Regularization of incorrectly posed problems, Soviet Math, vol.4, pp.1624-1627, 1963.

O. Titaud, A. Vidard, I. Souopgui, L. Dimet, and F. , Assimilation of image sequences in numerical models, pp.30-47, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00332815

O. Titaud, J. Brankart, and J. Verron, On the use of finite-time Lyapunov exponents and vectors for direct assimilation of tracer images into ocean models, pp.1038-1051, 2011.

J. Weickert and C. Schnörr, A theoretical framework for convex regularizers in PDE-based computation of image motion, International Journal of Computer Vision, vol.45, issue.3, pp.245-264, 2001.
DOI : 10.1023/A:1013614317973