L. Adams and J. Ortega, A multi-color SOR method for parallel computation

M. Afonso, J. Bioucas-dias, and M. Figueiredo, Fast Image Recovery Using Variable Splitting and Constrained Optimization, IEEE Transactions on Image Processing, vol.19, issue.9, pp.2345-2356, 2010.
DOI : 10.1109/TIP.2010.2047910

URL : http://arxiv.org/abs/0910.4887

J. Alvarez, M. Esclarin, J. Lefebure, and . Sanchez, A pde model for computing the optical flow, XVI congreso de ecuaciones diferenciales y aplicaciones, pp.1349-1356, 1999.

R. Aubert, P. Deriche, and . Kornprobst, Computing Optical Flow via Variational Techniques, SIAM Journal on Applied Mathematics, vol.60, issue.1, pp.156-182, 1999.
DOI : 10.1137/S0036139998340170

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

A. and P. Kornprobst, A Mathematical Study of the Relaxed Optical Flow Problem in the Space BV (?), SIAM Journal on Mathematical Analysis, vol.30, issue.8, p.1282, 1999.

A. and P. Kornprobst, Mathematical problems in image processing, 2006.

J. Backus, Can programming be liberated from the von Neumann style?: a functional style and its algebra of programs, Communications of the ACM, vol.21, issue.8, pp.613-641, 1978.
DOI : 10.1145/359576.359579

S. Baker, D. Scharstein, J. Lewis, S. Roth, M. Black et al., A database and evaluation methodology for optical flow, p.69, 2009.

R. Bayt and K. Breuer, Fabrication and testing of micron-sized cold-gas thrusters, Micropropulsion for Small Spacecraft, p.381, 2000.

D. Bertsekas, W. Hager, and O. , Mangasarian : Nonlinear programming, p.45, 1999.

M. J. Black, Anandan : Robust dynamic motion estimation over time, IEEE computer society conference on computer vision and patern recognition, pp.296-302, 1991.
DOI : 10.1109/cvpr.1991.139705

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

M. Black, Robust incremental optical flow, Thèse de doctorat, 1992.

M. Black and P. Anandan, The Robust Estimation of Multiple Motions: Parametric and Piecewise-Smooth Flow Fields, Computer Vision and Image Understanding, vol.63, issue.1, pp.75-104, 1996.
DOI : 10.1006/cviu.1996.0006

M. Blanc-feraud, T. Barlaud, and . Gaidon, Motion estimation involving discontinuities in multiresolution scheme, Optical Engineering, vol.32, issue.7, pp.1475-1509, 1993.
DOI : 10.1117/12.138647

F. Bornemann and P. Deuflhard, The cascadic multigrid method for elliptic problems, Numerische Mathematik, vol.75, issue.2, pp.135-152, 1996.
DOI : 10.1007/s002110050234

L. Bregman, The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming* 1. USSR computational mathematics and mathematical physics, pp.200-217, 1967.

J. Brossard, P. Monnier, F. Barricau, Y. L. Vandernoot, F. Sant et al., Le Besnerais : Principles and Applications of Particle Image Velocimetry, AerospaceLab, vol.1, issue.1, p.12, 2009.

A. Bruhn, J. Weickert, C. Feddern, T. Kohlberger, and C. , Variational optical flow computation in real time, IEEE Transactions on Image Processing, vol.14, issue.5, pp.608-615, 2005.
DOI : 10.1109/TIP.2005.846018

A. Bruhn, J. Weickert, T. Kohlberger, and C. , A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods, International Journal of Computer Vision, vol.44, issue.2, pp.257-277, 2006.
DOI : 10.1007/s11263-006-6616-7

A. Bruhn, J. Weickert, and C. , Schnörr : Lucas/kanade meets horn/schunck : Combining local and global optic flow methods, International Journal of Computer Vision, vol.61, pp.211-231, 2005.

A. Chambolle, Pock : A first-order primal-dual algorithm for convex problems with applications to imaging, p.47, 2010.

A. Chambolle, An algorithm for total variation minimization and applications, J. Math. Imaging Vis, vol.20, issue.12, pp.89-97, 2004.

F. Champagnat, A. Plyer, G. Le-besnerais, B. Leclaire, S. Davoust et al., Accelerating PIV computation speed using highly parallel iterative correlation maximization algorithm. To appear in Experiments in fluids Sant : How to calculate dense PIV vector fields at video rates, Proceedings of 8th International Symposium on Particle Image Velocimetry -PIV09, p.20, 2009.
DOI : 10.1007/s00348-011-1054-x

T. Chan and P. Mulet, On the Convergence of the Lagged Diffusivity Fixed Point Method in Total Variation Image Restoration, SIAM Journal on Numerical Analysis, vol.36, issue.2, pp.354-367, 1999.
DOI : 10.1137/S0036142997327075

G. Chapman, R. Jost, . Van-der, and . Pas, Using OpenMP : portable shared memory parallel programming, p.56, 2008.

I. Cohen, Nonlinear variational method for optical flow computation, Proceeding of the 8th SCIA, pp.523-530, 1993.
URL : https://hal.archives-ouvertes.fr/inria-00615717

E. Corpetti, P. Mémin, and . Pérez, Dense estimation of fluid flows. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.24, issue.3, pp.365-380, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00329724

D. Corpetti, G. Heitz, E. Arroyo, A. S. Mémin, and . Cruz, Fluid experimental flow estimation based on an optical-flow scheme, Experiments in Fluids, vol.10, issue.5, pp.80-97, 2006.
DOI : 10.1007/s00348-005-0048-y

URL : https://hal.archives-ouvertes.fr/halshs-00008138

J. Dongarra, Preface: Basic Linear Algebra Subprograms Technical (Blast) Forum Standard, International Journal of High Performance Computing Applications, vol.16, issue.1, pp.1-111, 2002.
DOI : 10.1177/10943420020160010101

J. Eckstein and D. , Bertsekas : On the Douglas?Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, pp.293-318, 1992.

G. Elsinga, F. Scarano, and B. Wieneke, Tomographic particle image velocimetry, Experiments in Fluids, vol.28, issue.7, pp.933-947, 2006.
DOI : 10.1007/s00348-006-0212-z

. Esser, Applications of Lagrangian-based alternating direction methods and connections to split, Bregman. CAM report, vol.9, pp.31-47, 2009.

F. Fezzani, G. L. Champagnat, and . Besnerais, Clarifying the implementation of warping in the combined local global method for optic flow computation, 18th European Signal Processing Conference (EUSIPCO), pp.1321-1325, 2010.

D. Geman and G. Reynolds, Constrained restoration and the recovery of discontinuities . Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.14, issue.3, pp.367-383, 1992.

D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Transactions on Image Processing, vol.4, issue.7, pp.932-946, 1995.
DOI : 10.1109/83.392335

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

T. Goldstein and S. Osher, The Split Bregman Method for L1-Regularized Problems, SIAM Journal on Imaging Sciences, vol.2, issue.2, pp.323-343, 2009.
DOI : 10.1137/080725891

G. Golub and C. Van-loan, Matrix computations, p.38, 1996.

J. Grewenig and . Weickert, Bruhn : From box filtering to fast explicit diffusion, Pattern Recognition, pp.533-542, 2010.
DOI : 10.1007/978-3-642-15986-2_54

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

P. Gwosdek, H. Zimmer, S. Grewenig, A. Bruhn, and J. Weickert, A Highly Efficient GPU Implementation for Variational Optic Flow Based on the Euler-Lagrange Framework, Proc. 2010 ECCV Workshop on Computer Vision with GPUs, p.12, 2010.
DOI : 10.1007/978-3-642-35740-4_29

D. Heitz, P. Héas, E. Mémin, and J. Carlier, Dynamic consistent correlation-variational approach for robust optical flow estimation, Experiments in Fluids, vol.28, issue.3, pp.595-608, 2008.
DOI : 10.1007/s00348-008-0567-4

URL : https://hal.archives-ouvertes.fr/hal-00914361

D. Heitz, E. Mémin, and C. Schnörr, Variational fluid flow measurements from image sequences: synopsis and perspectives, Experiments in Fluids, vol.28, issue.4, pp.369-393, 2010.
DOI : 10.1007/s00348-009-0778-3

URL : https://hal.archives-ouvertes.fr/hal-00456162

B. K. Horn and B. G. , Determining optical flow, Artificial Intelligence, vol.17, issue.1-3, pp.185-203, 1981.
DOI : 10.1016/0004-3702(81)90024-2

M. Huang, Y. Ng, and . Wen, A Fast Total Variation Minimization Method for Image Restoration, Multiscale Modeling & Simulation, vol.7, issue.2, pp.774-817, 2008.
DOI : 10.1137/070703533

. Huber, Robust Regression: Asymptotics, Conjectures and Monte Carlo, The Annals of Statistics, vol.1, issue.5, pp.799-821, 1973.
DOI : 10.1214/aos/1176342503

URL : http://projecteuclid.org/download/pdf_1/euclid.aos/1176342503

J. Idier, Convex half-quadratic criteria and interacting auxiliary variables for image restoration, IEEE Transactions on Image Processing, vol.10, issue.7, pp.1001-1009, 2001.
DOI : 10.1109/83.931094

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

T. Kohlberger, C. Schnorr, A. Bruhn, and J. Weickert, Domain decomposition for variational optical-flow computation, IEEE Transactions on Image Processing, vol.14, issue.8, pp.1125-1137, 2005.
DOI : 10.1109/TIP.2005.849778

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

A. Kumar and A. Tannenbaum, Optical flow: a curve evolution approach, IEEE Transactions on Image Processing, vol.5, issue.4, pp.598-610, 1996.
DOI : 10.1109/83.491336

L. Besnerais and F. Champagnat, Dense optical flow by iterative local window registration, IEEE International Conference on Image Processing 2005, p.26, 2005.
DOI : 10.1109/ICIP.2005.1529706

L. Besnerais, F. Champagnat, A. Plyer, R. Fezzani, B. Leclaire et al., Advenced processing methods for image-based displacement measurement, Aerospace Lab, vol.1, issue.1, p.38, 2009.

B. Leclaire, Y. L. Sant, S. Davoust, G. L. Besnerais, and F. Champagnat, Folki-spiv : a new, ultra-fast approach for stereo piv, p.94, 2011.

B. Lecordier and J. , Westerweel : The EUROPIV synthetic image generator (SIG) In Particle image velocimetry : recent improvements, Proceedings of the EUROPIV, p.20, 2004.

P. Lions, On the Schwarz alternating method I. Domain decomposition methods for partial differential equations, pp.1-41, 1988.

B. D. Lucas and T. Kanade, An iterative image registration technique with an application to stereo vision, Seventh international joint conference on artificial intelligence, pp.674-679, 1981.

E. Mémin and P. , 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, 1944.
DOI : 10.1109/83.668027

H. H. Nagel and W. Enkelmann, An Investigation of Smoothness Constraints for the Estimation of Displacement Vector Fields from Image Sequences, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.8, issue.5, pp.565-593, 1986.
DOI : 10.1109/TPAMI.1986.4767833

J. Nocedal and S. Wright, Numerical optimization, p.45, 1999.
DOI : 10.1007/b98874

C. Nvidia, Compute Unified Device Architecture Programming Guide, p.65, 2007.

C. Nvidia, Tuning CUDA Applications for FERMI, p.65, 2010.

N. Papenberg, A. Bruhn, T. Brox, S. Didas, and J. Weickert, Highly Accurate Optic Flow Computation with Theoretically Justified Warping, International Journal of Computer Vision, vol.14, issue.3, pp.141-158, 2006.
DOI : 10.1007/s11263-005-3960-y

M. Pilgrim, Dive into Python, Apress, p.52, 2004.
DOI : 10.1007/978-1-4302-0700-9

G. Quenot, J. Pakleza, and T. Kowalewski, Particle image velocimetry with optical flow, Experiments in Fluids, vol.25, issue.3, pp.177-189, 1998.
DOI : 10.1007/s003480050222

URL : https://hal.archives-ouvertes.fr/hal-00953823

M. Raffel, C. Willert, and S. Wereley, Particle image velocimetry : a practical guide, p.14, 2007.
DOI : 10.1007/978-3-662-03637-2

L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, vol.60, issue.1-4, pp.259-268, 1992.
DOI : 10.1016/0167-2789(92)90242-F

P. Ruhnau, T. Kohlberger, and C. Schnörr, Variational optical flow estimation for particle image velocimetry, Experiments in Fluids, vol.14, issue.1, pp.21-32, 2005.
DOI : 10.1007/s00348-004-0880-5

P. Ruhnau and C. Schnörr, Optical Stokes flow estimation: an imaging-based control approach, Experiments in Fluids, vol.15, issue.3, pp.61-78, 2007.
DOI : 10.1007/s00348-006-0220-z

P. Ruhnau, A. Stahl, and C. Schnörr, Variational estimation of experimental fluid flows with physics-based spatio-temporal regularization, Measurement Science and Technology, vol.18, issue.3, pp.755-94, 2007.
DOI : 10.1088/0957-0233/18/3/027

Y. Saad, Iterative methods for sparse linear systems, Society for Industrial Mathematics, vol.38, p.40, 2003.
DOI : 10.1137/1.9780898718003

F. Scarano and M. Riethmuller, Advances in iterative multigrid PIV image processing, Experiments in Fluids, vol.29, issue.7, pp.51-60, 2000.
DOI : 10.1007/s003480070007

S. Setzer, Split Bregman algorithm, Douglas-Rachford splitting and frame shrinkage . Scale space and variational methods in computer vision, pp.464-476, 2009.
DOI : 10.1007/978-3-642-02256-2_39

M. Stanislas, K. Okamoto, C. J. Kähler, and J. Westerweel, Main results of the Second International PIV Challenge, Experiments in Fluids, vol.23, issue.9, pp.170-191, 2005.
DOI : 10.1007/s00348-005-0951-2

URL : https://hal.archives-ouvertes.fr/hal-00137843

F. Steinbruecker, T. Pock, and D. Cremers, Advanced data terms for variational optic flow estimation, Vision, Modeling, and Visualization Workshop, p.47, 2009.

. 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=

T. and C. Wu, Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. Scale Space and Variational Methods in Computer Vision, pp.502-513, 2009.

A. Tikhonov, On the stability of inverse problems, CR (Dokl.) Acad. Sci. URSS, n. Ser, pp.176-179, 1943.

. Tistarelli, Computation of coherent optical flow by using multiple constraints, Proceedings of IEEE International Conference on Computer Vision, pp.263-268, 1995.
DOI : 10.1109/ICCV.1995.466776

O. Tretiak, Pastor : Velocity estimation from image sequences with second order differential operators, International Conference on pattern recognition, pp.16-19, 1984.

C. Vogel and M. Oman, Iterative Methods for Total Variation Denoising, SIAM Journal on Scientific Computing, vol.17, issue.1, pp.227-238, 1996.
DOI : 10.1137/0917016

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

J. Wang, W. Yang, Y. Yin, and . Zhang, A New Alternating Minimization Algorithm for Total Variation Image Reconstruction, SIAM Journal on Imaging Sciences, vol.1, issue.3, pp.248-272, 2008.
DOI : 10.1137/080724265

J. Weickert and C. , Schnorr : 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

M. Werlberger, W. Trobin, T. Pock, A. Wedel, D. Cremers et al., Anisotropic Huber-L1 Optical Flow, Procedings of the British Machine Vision Conference 2009, pp.43-44, 2009.
DOI : 10.5244/C.23.108

P. Wesseling, An introduction to multigrid methods, p.92, 1991.

J. Westerweel and F. Nieuwstadt, Performance tests on 3-dimensional velocity measurements with a two-camera digital particle-image velocimeter, Laser Anemometry-Advances and Applications, pp.349-355, 1991.

Y. Yamamoto and T. Uemura, Robust particle image velocimetry using gradient method with upstream difference and downstream difference, Experiments in Fluids, vol.6, issue.Suppl.1, pp.659-670, 2009.
DOI : 10.1007/s00348-008-0591-4

I. Yavneh, A Multilevel Nonlinear Method, SIAM Journal on Scientific Computing, vol.28, issue.1, pp.24-46, 2006.
DOI : 10.1137/040613809

C. Zach, T. Pock, and H. Bischof, A duality based approach for realtime tv- l1 optical flow, Pattern Recognition (Proc. DAGM), pp.214-223, 2007.