D. Béréziat and I. Herlin, Solving ill-posed image processing problems using data assimilation, Numerical Algorithms, vol.52, issue.2, pp.219-252, 2011.

R. H. Byrd, P. Lu, and J. Nocedal, A Limited Memory Algorithm for Bound Constrained Optimization, SIAM Journal on Scientific Computing, vol.16, issue.5, pp.1190-1208, 1995.
DOI : 10.1137/0916069

T. Corpetti, E. Mémin, and P. Prez, Dense estimation of fluid flows, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, issue.3, pp.365-380, 2002.
DOI : 10.1109/34.990137

URL : https://hal.archives-ouvertes.fr/hal-00329724

P. Courtier, J. Thépaut, and A. Hollingsworth, A strategy for operational implementation of 4d-var, using and

J. D. Adamo, N. Papadakis, E. Mémin, and A. G. , Variational assimilation of POD low-order dynamical systems, Journal of Turbulence, vol.8, issue.9, pp.1-22, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00596160

P. Dérian, P. Héas, C. Herzet, and E. Mémin, Top: Sun et al method Middle: using the full model Bottom: our estimation Wavelets to reconstruct turbulence multifractals from experimental image sequences, Figure 10. Result on real data 7th International Symposium on Turbulence and Shear Flow Phenomena, p.7, 2011.

P. Dérian, P. Héas, C. Herzet, and E. Mémin, Wavelets and optical flow motion estimation, Numerical Mathematics: Theory, Methods and Applications, 2012.

I. Herlin and K. Drifi, Learning reduced models for motion estimation on long temporal image sequences, 2012 IEEE International Geoscience and Remote Sensing Symposium, 2012.
DOI : 10.1109/IGARSS.2012.6351591

URL : https://hal.archives-ouvertes.fr/hal-00730515

C. Homescu, L. R. Petzold, and R. Serban, Error estimation for reduced-order models of dynamical systems, SIAM Journal of Numerical Analysis, vol.43, issue.41, pp.693-1714, 2005.

B. Horn and B. Schunk, 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

S. K. Harouna, P. Dérian, P. Héas, and E. Mémin, Divergence-free wavelets and high order regularization, International Journal of Computer Vision, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00646104

S. , K. Harouna, and V. Perrier, Effective construction of divergence-free wavelets on the square, Journal of Computational and Applied Mathematics, vol.240, pp.74-86, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00727038

F. , L. Dimet, and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus, pp.97-110, 1986.

J. Lions, Optimal Control of Systems Governed by Partial Differential Equations, 1971.
DOI : 10.1007/978-3-642-65024-6

N. Papadakis, T. Corpetti, and E. Mémin, Dynamically consistent optical flow estimation, 2007 IEEE 11th International Conference on Computer Vision
DOI : 10.1109/ICCV.2007.4408889

URL : https://hal.archives-ouvertes.fr/hal-00596200

M. Restelli, L. Bonaventura, and R. Sacco, A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows, Journal of Computational Physics, vol.216, issue.1, pp.195-215, 2006.
DOI : 10.1016/j.jcp.2005.11.030

D. Sun, S. Roth, and M. Black, Secrets of optical flow estimation and their principles, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.2432-2439, 2010.
DOI : 10.1109/CVPR.2010.5539939

D. Suter, Motion estimation and vector splines, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition CVPR-94, pp.939-942, 1994.
DOI : 10.1109/CVPR.1994.323929

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.57.4768

O. Titaud, A. Vidard, I. Souopgui, and F. Dimet, Assimilation of image sequences in numerical models, Tellus A: Dynamic Meteorology and Oceanography, vol.105, issue.8, pp.30-47, 2010.
DOI : 10.1111/j.1600-0870.2009.00416.x

URL : https://hal.archives-ouvertes.fr/inria-00332815

E. and V. Hólm, Lectures notes on assimilation algorithms European Centre for Medium- Range Weather Forecasts Reading, 2008.