L. Abergel and . Moisan, Accelerated a-contrario detection of smooth trajectories, Proceedings of the 22nd European Signal Processing Conference (EU- SIPCO), pp.2200-2204, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00957747

R. Abergel and L. Moisan, Fast and accurate evaluation of a generalized incomplete gamma function, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01329669

R. Abergel, C. Louchet, L. Moisan, and T. Zeng, Total Variation Restoration of Images Corrupted by Poisson Noise with Iterated Conditional Expectations, Proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp.178-190, 2015.
DOI : 10.1007/978-3-319-18461-6_15

URL : https://hal.archives-ouvertes.fr/hal-01275813

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, American Journal of Physics, vol.34, issue.2, 1964.
DOI : 10.1119/1.1972842

C. Aguerrebere, J. Delon, Y. Gousseau, and P. Musé, Study of the digital camera acquisition process and statistical modeling of the sensor raw data, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00733538

C. Akinlar and C. Topal, EDCircles: A real-time circle detector with a false detection control, Pattern Recognition, vol.46, issue.3, pp.725-740, 2013.
DOI : 10.1016/j.patcog.2012.09.020

A. Aldroubi, M. Unser, and M. Eden, Cardinal spline filters: Stability and convergence to the ideal sinc interpolator, Signal Processing, vol.28, issue.2, pp.127-138, 1992.
DOI : 10.1016/0165-1684(92)90030-Z

A. Almansa, V. Caselles, G. Haro, and B. Rougé, Restoration and Zoom of Irregularly Sampled, Blurred, and Noisy Images by Accurate Total Variation Minimization with Local Constraints, Multiscale Modeling & Simulation, vol.5, issue.1, pp.235-272, 2006.
DOI : 10.1137/050634086

F. Alter, S. Durand, and J. Froment, Adapted Total Variation for Artifact Free Decompression of JPEG Images, Journal of Mathematical Imaging and Vision, vol.25, issue.9, pp.199-211, 2005.
DOI : 10.1007/s10851-005-6467-9

URL : https://hal.archives-ouvertes.fr/hal-00712138

K. J. Arrow, L. Hurwicz, and H. Uzawa, Studies in linear and non-linear programming, 1958.

J. Aujol and A. Chambolle, Dual Norms and Image Decomposition Models, International Journal of Computer Vision, vol.19, issue.3, pp.85-104, 2005.
DOI : 10.1023/B:JMIV.0000011320.81911.38

URL : https://hal.archives-ouvertes.fr/inria-00071453

J. Aujol and C. Dossal, Stability of Over-Relaxations for the Forward-Backward Algorithm, Application to FISTA, SIAM Journal on Optimization, vol.25, issue.4, pp.2408-2433, 2015.
DOI : 10.1137/140994964

URL : https://hal.archives-ouvertes.fr/hal-01163432

J. F. Aujol, G. Aubert, L. Blanc-féraud, and A. Chambolle, Image Decomposition into a Bounded Variation Component and an Oscillating Component, Journal of Mathematical Imaging and Vision, vol.15, issue.3, pp.71-88, 2005.
DOI : 10.1023/B:JMIV.0000011320.81911.38

URL : https://hal.archives-ouvertes.fr/hal-00202001

S. D. Babacan, R. Molina, and A. K. Katsaggelos, Total variation super resolution using a variational approach, 2008 15th IEEE International Conference on Image Processing, pp.641-644, 2008.
DOI : 10.1109/ICIP.2008.4711836

Y. Bar-shalom, On hierarchical tracking for the real world, IEEE Transactions on Aerospace and Electronic Systems, vol.42, issue.3, pp.846-850, 2006.
DOI : 10.1109/TAES.2006.248192

Y. Bar-shalom, T. Fortmann, and M. Scheffe, Sonar tracking of multiple targets using joint probabilistic data association, IEEE Journal of Oceanic Engineering, vol.8, issue.3, pp.173-184, 1983.

A. Beck and M. Teboulle, Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems, IEEE Transactions on Image Processing, vol.18, issue.11, pp.2419-2434, 2009.
DOI : 10.1109/TIP.2009.2028250

A. Beck and M. Teboulle, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM Journal on Imaging Sciences, vol.2, issue.1, pp.183-202, 2009.
DOI : 10.1137/080716542

R. Bellman, The theory of dynamic programming, Bulletin of the American Mathematical Society, vol.60, issue.6, pp.503-515, 1954.
DOI : 10.1090/S0002-9904-1954-09848-8

J. Berclaz, F. Fleuret, E. Turetken, and P. Fua, Multiple Object Tracking Using K-Shortest Paths Optimization, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.33, issue.9, pp.1806-1819, 2011.
DOI : 10.1109/TPAMI.2011.21

URL : http://cvlab.epfl.ch/publications/publications/2011/BerclazFTF11.pdf

G. P. Bhattacharjee, Algorithm AS 32: The Incomplete Gamma Integral, Applied Statistics, vol.19, issue.3, pp.285-287, 1970.
DOI : 10.2307/2346339

G. Blanchet and L. Moisan, An explicit sharpness index related to global phase coherence, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.1065-1068, 2012.
DOI : 10.1109/ICASSP.2012.6288070

URL : https://hal.archives-ouvertes.fr/hal-00662374

M. Bleicher and P. Nicolini, Large extra dimensions and small black holes at the LHC, Journal of Physics: Conference Series, p.12008, 2010.
DOI : 10.1088/1742-6596/237/1/012008

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

K. Bredies, K. Kunisch, and T. Pock, Total Generalized Variation, SIAM Journal on Imaging Sciences, vol.3, issue.3, pp.492-526, 2010.
DOI : 10.1137/090769521

URL : http://gpu4vision.icg.tugraz.at/papers/2009/pock_tgv.pdf

T. Briand and J. Vacher, Linear filtering : From the continuous spectral definition to the numerical computations. IPOL preprint, 2015.

A. Buades, B. Coll, and J. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024

URL : https://hal.archives-ouvertes.fr/hal-00271141

C. J. Cannon and I. M. Vardavas, The effect of redistribution on the emission peaks from chromospheric-type stellar atmospheres, Astronomy and Astrophysics, vol.32, p.85, 1974.

V. Caselles, A. Chambolle, and M. Novaga, Total variation in imaging, Handbook of Mathematical Methods in Imaging, pp.1455-1499, 2015.

A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical imaging and vision, vol.20, issue.12, pp.89-97, 2004.

A. Chambolle, Total variation minimization and a class of binary mrf models. In Energy minimization methods in computer vision and pattern recognition, pp.136-152, 2005.

A. Chambolle and C. Dossal, On the Convergence of the Iterates of the ???Fast Iterative Shrinkage/Thresholding Algorithm???, Journal of Optimization Theory and Applications, vol.155, issue.2, pp.968-982, 2015.
DOI : 10.1007/978-1-4419-9467-7

A. Chambolle and T. Pock, A First-Order Primal-Dual Algorithm for Convex Problems with??Applications to Imaging, Journal of Mathematical Imaging and Vision, vol.60, issue.5, pp.120-145, 2011.
DOI : 10.1007/978-3-540-74936-3_22

URL : https://hal.archives-ouvertes.fr/hal-00490826

A. Chambolle, V. Caselles, D. Cremers, M. Novaga, and T. Pock, An introduction to total variation for image analysis. Theoretical foundations and numerical methods for sparse recovery, pp.263-340, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00437581

A. Chambolle, S. E. Levine, and B. J. Lucier, An Upwind Finite-Difference Method for Total Variation???Based Image Smoothing, SIAM Journal on Imaging Sciences, vol.4, issue.1, pp.277-299, 2011.
DOI : 10.1137/090752754

A. Chambolle, V. Duval, G. Peyré, and C. Poon, Geometric properties of solutions to the total variation denoising problem, Inverse Problems, vol.33, issue.1, 2016.
DOI : 10.1088/0266-5611/33/1/015002

URL : https://hal.archives-ouvertes.fr/hal-01323720

T. F. Chan and S. Esedoglu, Function Approximation, SIAM Journal on Applied Mathematics, vol.65, issue.5, pp.1817-1837, 2005.
DOI : 10.1137/040604297

T. F. Chan and C. Wong, Total variation blind deconvolution, IEEE Transactions on Image Processing, vol.7, issue.3, pp.370-375, 1998.
DOI : 10.1109/83.661187

T. F. Chan, A. Marquina, and P. Mulet, High-Order Total Variation-Based Image Restoration, SIAM Journal on Scientific Computing, vol.22, issue.2, pp.503-516, 2000.
DOI : 10.1137/S1064827598344169

T. F. Chan, A. M. Yip, and F. E. Park, Simultaneous total variation image inpainting and blind deconvolution, International Journal of Imaging Systems and Technology, vol.8, issue.1, pp.92-102, 2005.
DOI : 10.1007/978-1-4615-3980-3

B. W. Char, On Stieltjes's continued fraction for the gamma function, Mathematics of Computation, vol.34, issue.150, pp.547-551, 1980.

M. A. Chaudhry and S. M. Zubair, On a class of incomplete gamma functions with applications, 2001.

D. Chetverikov and J. Verestoy, Feature Point Tracking for Incomplete Trajectories, Computing, vol.62, issue.4, pp.321-338, 1999.
DOI : 10.1007/s006070050027

R. T. Collins, Multitarget data association with higher-order motion models, 2012 IEEE Conference on Computer Vision and Pattern Recognition, pp.1744-1751, 2012.
DOI : 10.1109/CVPR.2012.6247870

P. L. Combettes, Iterative construction of the resolvent of a sum of maximal monotone operators, Journal of Convex Analysis, vol.16, issue.4, pp.727-748, 2009.

P. L. Combettes and J. Pesquet, Proximal splitting methods in signal processing In Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011.

P. L. Combettes and V. R. Wajs, Signal Recovery by Proximal Forward-Backward Splitting, Multiscale Modeling & Simulation, vol.4, issue.4, pp.1168-1200, 2005.
DOI : 10.1137/050626090

URL : https://hal.archives-ouvertes.fr/hal-00017649

L. Condat, Discrete Total Variation: New Definition and Minimization, SIAM Journal on Imaging Sciences, vol.10, issue.3, 2016.
DOI : 10.1137/16M1075247

URL : https://hal.archives-ouvertes.fr/hal-01309685

J. W. Cooley and J. W. Tukey, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, vol.19, issue.90, pp.297-301, 1965.
DOI : 10.1090/S0025-5718-1965-0178586-1

B. Coulange and L. Moisan, An aliasing detection algorithm based on suspicious colocalizations of Fourier coefficients, 2010 IEEE International Conference on Image Processing, pp.2013-2016, 2010.
DOI : 10.1109/ICIP.2010.5651195

URL : https://hal.archives-ouvertes.fr/hal-00497406

I. Csiszar, Why least squares and maximum entropy? an axiomatic approach to inference for linear inverse problems. The annals of statistics, pp.2032-2066, 1991.

A. Cuyt, F. Backeljauw, and C. Bonan-hamada, Continued Fractions for Special Functions: Handbook and Software, 2008.
DOI : 10.1137/050629203

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering, IEEE Transactions on Image Processing, vol.16, issue.8, pp.2080-2095, 2007.
DOI : 10.1109/TIP.2007.901238

J. Darbon and M. Sigelle, Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization, Journal of Mathematical Imaging and Vision, vol.2, issue.4, pp.261-276, 2006.
DOI : 10.1007/s10851-006-8803-0

I. Daubechies, M. Defrise, and C. Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Communications on Pure and Applied Mathematics, vol.58, issue.11, pp.1413-1457, 2004.
DOI : 10.1002/0471221317

C. Deledalle, F. Tupin, and L. Denis, Poisson NL means: Unsupervised non local means for Poisson noise, 2010 IEEE International Conference on Image Processing, pp.801-804, 2010.
DOI : 10.1109/ICIP.2010.5653394

URL : https://hal.archives-ouvertes.fr/hal-00957982

A. Desolneux, When the a contrario approach becomes generative, International Journal of Computer Vision, vol.27, issue.2, pp.46-65, 2016.
DOI : 10.1023/A:1007925832420

A. Desolneux and F. Doré, An Anisotropic A Contrario Framework for the Detection of Convergences in Images, Journal of Mathematical Imaging and Vision, vol.3, issue.1, pp.32-56, 2016.
DOI : 10.1016/S1361-8415(99)80016-4

A. Desolneux, L. Moisan, and J. Morel, Meaningful alignments, International Journal of Computer Vision, vol.40, issue.1, pp.7-23, 2000.
DOI : 10.1023/A:1026593302236

A. Desolneux, L. Moisan, and J. Morel, Edge detection by Helmholtz principle, Journal of Mathematical Imaging and Vision, vol.14, issue.3, pp.271-284, 2001.
DOI : 10.1023/A:1011290230196

URL : https://hal.archives-ouvertes.fr/hal-00170793

A. Desolneux, L. Moisan, and J. Morel, Maximal meaningful events and applications to image analysis, Annals of Statistics, pp.1822-1851, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00170777

A. Desolneux, L. Moisan, and J. Morel, From Gestalt Theory to Image Analysis . A Probabilistic Approach, Interdisciplinary Applied Mathematics, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00259077

M. Dimiccoli, J. Jacob, and L. Moisan, Particle detection and tracking in fluorescence time-lapse imaging: a contrario approach, Machine Vision and Applications, pp.511-527, 2016.
DOI : 10.1109/ICIP.2007.4379564

URL : https://hal.archives-ouvertes.fr/hal-01386816

F. Doré, Convergences de structures linéaires dans les images: modélisation stochastique et applications en imagerie médicale, 2014.

J. Douglas and H. H. Rachford, On the numerical solution of heat conduction problems in two and three space variables. Transactions of the, pp.421-439, 1956.

Y. Drori, S. Sabach, and M. Teboulle, A simple algorithm for a class of nonsmooth convex???concave saddle-point problems, Operations Research Letters, vol.43, issue.2, pp.209-214, 2015.
DOI : 10.1016/j.orl.2015.02.001

J. Eckstein and D. Bertsekas, On the Douglas???Rachford splitting method and the proximal point algorithm for maximal monotone operators, Mathematical Programming, vol.29, issue.1, pp.293-318, 1992.
DOI : 10.2140/pjm.1970.33.209

I. Ekeland and R. Témam, Convex Analysis and Variational Problems, Society for Industrial and Applied Mathematics (SIAM), vol.28, 1999.
DOI : 10.1137/1.9781611971088

G. Facciolo, A. Almansa, J. Aujol, and V. Caselles, Irregular to Regular Sampling, Denoising, and Deconvolution, Multiscale Modeling & Simulation, vol.7, issue.4, pp.1574-1608, 2009.
DOI : 10.1137/080719443

URL : https://hal.archives-ouvertes.fr/hal-00988783

J. M. Fadili and G. Peyré, Total Variation Projection With First Order Schemes, IEEE Transactions on Image Processing, vol.20, issue.3, pp.657-669, 2011.
DOI : 10.1109/TIP.2010.2072512

URL : https://hal.archives-ouvertes.fr/hal-00380491

M. A. Figueiredo and J. M. Bioucas-dias, Restoration of Poissonian Images Using Alternating Direction Optimization, IEEE Transactions on Image Processing, vol.19, issue.12, pp.3133-3145, 2010.
DOI : 10.1109/TIP.2010.2053941

F. Fleuret, J. Berclaz, R. Lengagne, and P. Fua, Multicamera People Tracking with a Probabilistic Occupancy Map, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.2, pp.267-282, 2008.
DOI : 10.1109/TPAMI.2007.1174

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE, vol.93, issue.2, pp.216-231, 2005.
DOI : 10.1109/JPROC.2004.840301

W. Fullerton, Algorithm 435: modified incomplete gamma function [S14], Communications of the ACM, vol.15, issue.11, pp.993-995, 1972.
DOI : 10.1145/355606.361891

D. Gabay and B. Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation, Computers & Mathematics with Applications, vol.2, issue.1, pp.17-40, 1976.
DOI : 10.1016/0898-1221(76)90003-1

W. Gautschi, A Computational Procedure for Incomplete Gamma Functions, ACM Transactions on Mathematical Software, vol.5, issue.4, pp.466-481, 1979.
DOI : 10.1145/355853.355863

W. Gautschi, The incomplete gamma functions since tricomi, Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, Accademia Nazionale dei Lincei, pp.203-237, 1998.

P. Getreuer, Linear Methods for Image Interpolation, Image Processing On Line, vol.1, 2011.
DOI : 10.5201/ipol.2011.g_lmii

G. Gilboa, A Spectral Approach to Total Variation, Proceedings of the 4th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp.36-47, 2013.
DOI : 10.1007/978-3-642-38267-3_4

R. Glowinski and P. L. Tallec, Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, SIAM, vol.9, 1989.
DOI : 10.1137/1.9781611970838

Y. Gousseau and J. Morel, Are Natural Images of Bounded Variation?, SIAM Journal on Mathematical Analysis, vol.33, issue.3, pp.634-648, 2001.
DOI : 10.1137/S0036141000371150

B. Grosjean and L. Moisan, A-contrario Detectability of Spots in??Textured Backgrounds, Journal of Mathematical Imaging and Vision, vol.68, issue.2, pp.313-337, 2009.
DOI : 10.1259/bjr.71.851.10434911

URL : https://hal.archives-ouvertes.fr/hal-00534713

F. Guichard and F. Malgouyres, Total variation based interpolation, Proceedings of the 9th European Signal Processing Conference (EUSIPCO), pp.1741-1744, 1998.

I. I. Guseinov and B. A. Mamedov, Evaluation of Incomplete Gamma Functions Using Downward Recursion and Analytical Relations, Journal of Mathematical Chemistry, vol.36, issue.4, pp.341-346, 2004.
DOI : 10.1023/B:JOMC.0000044521.18885.d3

J. G. Hills, Effect of binary stars on the dynamical evolution of stellar clusters. II - Analytic evolutionary models, The Astronomical Journal, vol.80, pp.1075-1080, 1975.
DOI : 10.1086/111842

P. J. Huber, Robust Estimation of a Location Parameter, The Annals of Mathematical Statistics, vol.35, issue.1, pp.73-101, 1964.
DOI : 10.1214/aoms/1177703732

P. J. Huber, Robust regression: asymptotics, conjectures and Monte Carlo. The Annals of Statistics, pp.799-821, 1973.
DOI : 10.1214/aos/1176342503

W. B. Jones and W. J. Thron, Continued fractions: analytic theory and applications . Number 11 in Encyclopedia of mathematics and its applications, 1980.

R. Kannan and C. K. Krueger, Advanced analysis: on the real line, 2012.
DOI : 10.1007/978-1-4613-8474-8

Z. Khan, T. Balch, and F. Dellaert, MCMC-based particle filtering for tracking a variable number of interacting targets, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), issue.11, pp.271805-1819, 2005.

L. Kissel, R. H. Pratt, and S. C. Roy, Rayleigh scattering by neutral atoms, 100 eV to 10 MeV, Physical Review A, vol.155, issue.5, 1970.
DOI : 10.1016/0029-554X(78)90531-1

M. Lai, B. Lucier, and J. Wang, The Convergence of a Central-Difference Discretization of Rudin-Osher-Fatemi Model for Image Denoising, Proceedings of the 2nd International Conference on Scale Space and Variational Methods in Computer Vision (SSVM), pp.514-526, 2009.
DOI : 10.1016/0167-2789(92)90242-F

C. Lanczos, A Precision Approximation of the Gamma Function, Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, vol.1, issue.1, pp.86-96, 1964.
DOI : 10.1137/0701008

A. Leclaire and L. Moisan, No-Reference Image Quality Assessment and Blind Deblurring with Sharpness Metrics Exploiting Fourier Phase Information, Journal of Mathematical Imaging and Vision, vol.19, issue.12, pp.145-172, 2015.
DOI : 10.1109/TIP.2010.2052820

URL : https://hal.archives-ouvertes.fr/hal-00933628

W. J. Lentz, Generating Bessel functions in Mie scattering calculations using continued fractions, Applied Optics, vol.15, issue.3, pp.668-671, 1976.
DOI : 10.1364/AO.15.000668

V. Linetsky, PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY, Mathematical Finance, vol.11, issue.1, pp.255-282, 2006.
DOI : 10.1007/978-3-642-56634-9

C. Louchet and L. Moisan, Total variation denoising using posterior expectation, Proceedings of the 16th European Signal Processing Conference (EUSIPCO), pp.1-5, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00258849

C. Louchet and L. Moisan, Posterior Expectation of the Total Variation Model: Properties and Experiments, SIAM Journal on Imaging Sciences, vol.6, issue.4, pp.2640-2684, 2013.
DOI : 10.1137/120902276

URL : https://hal.archives-ouvertes.fr/hal-00764175

C. Louchet and L. Moisan, Total variation denoising using iterated conditional expectation, Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), pp.1592-1596, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01214735

D. G. Lowe, Perceptual Organization and Visual Recognition, volume 5 of The Kluwer International Series in Engineering and Computer Science, 1985.

D. Luenberger and Y. Ye, Linear and nonlinear programming, 1984.
DOI : 10.1007/978-3-319-18842-3

F. Malgouyres and F. Guichard, Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis, SIAM Journal on Numerical Analysis, vol.39, issue.1, pp.1-37, 2001.
DOI : 10.1137/S0036142999362286

S. Masnou and J. Morel, Level lines based disocclusion, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269), pp.259-263, 1998.
DOI : 10.1109/ICIP.1998.999016

W. Metzger, Gesetze des sehens, 1975.

Y. Meyer, Oscillating patterns in image processing and nonlinear evolution equations: the fifteenth Dean Jacqueline B. Lewis memorial lectures, 2001.
DOI : 10.1090/ulect/022

W. Miled, J. Pesquet, and M. Parent, A Convex Optimization Approach for Depth Estimation Under Illumination Variation, IEEE Transactions on Image Processing, vol.18, issue.4, pp.813-830, 2009.
DOI : 10.1109/TIP.2008.2011386

URL : https://hal.archives-ouvertes.fr/hal-00692900

L. Moisan, How to discretize the Total Variation of an image?, the 6th International Congress on Industrial Applied Mathematics Proceedings in Applied Mathematics and Mechanics, pp.1041907-1041908, 2007.
DOI : 10.1002/j.1538-7305.1948.tb01338.x

URL : https://hal.archives-ouvertes.fr/hal-00624503

L. Moisan, Periodic Plus Smooth Image Decomposition, Journal of Mathematical Imaging and Vision, vol.4, issue.1, pp.161-179, 2011.
DOI : 10.1109/NSSMIC.2005.1596801

URL : https://hal.archives-ouvertes.fr/hal-00388020

J. Moreau, Inf-convolution des fonctions numériques sur un espace vectoriel, Comptes Rendus de l'Academie des Sciences de Paris, pp.125-129, 1963.

J. Moreau, Proximité et dualité dans un espace hilbertien Bulletin de la Société mathématique de France, pp.273-299, 1965.

Y. Moreno, R. Pastor-satorras, and A. Vespignani, Epidemic outbreaks in complex heterogeneous networks, The European Physical Journal B, vol.26, issue.4, pp.521-529, 2002.
DOI : 10.1140/epjb/e20020122

Y. Nesterov, A method of solving a convex programming problem with convergence rate, Soviet Mathematics Doklady, pp.372-376, 1983.

Y. Nesterov, Introductory Lectures on Convex Optimization, volume 87 of Applied Optimization, 2004.

Y. Nesterov, Smooth minimization of non-smooth functions, Mathematical Programming, vol.269, issue.1, pp.127-152, 2005.
DOI : 10.1007/s10107-004-0552-5

A. Newson, A. Almansa, M. Fradet, Y. Gousseau, and P. Pérez, Video Inpainting of Complex Scenes, SIAM Journal on Imaging Sciences, vol.7, issue.4, pp.1993-2019, 2014.
DOI : 10.1137/140954933

URL : https://hal.archives-ouvertes.fr/hal-00937795

M. Nikolova, Local Strong Homogeneity of a Regularized Estimator, SIAM Journal on Applied Mathematics, vol.61, issue.2, pp.633-658, 2000.
DOI : 10.1137/S0036139997327794

M. Nikolova, Model distortions in Bayesian MAP reconstruction, Inverse Problems and Imaging, vol.1, issue.2, p.399, 2007.
DOI : 10.3934/ipi.2007.1.399

P. Ochs, Y. Chen, T. Brox, and T. Pock, iPiano: Inertial Proximal Algorithm for Nonconvex Optimization, SIAM Journal on Imaging Sciences, vol.7, issue.2, pp.1388-1419, 2014.
DOI : 10.1137/130942954

URL : http://arxiv.org/pdf/1404.4805

N. Parikh and S. Boyd, Proximal algorithms. Foundations and Trends in optimization, pp.123-231, 2013.
DOI : 10.1561/2400000003

URL : http://www.nowpublishers.com/article/DownloadSummary/OPT-003

T. Pock and A. Chambolle, Diagonal preconditioning for first order primal-dual algorithms in convex optimization, 2011 International Conference on Computer Vision, pp.1762-1769, 2011.
DOI : 10.1109/ICCV.2011.6126441

J. Preciozzi, P. Musé, A. Almansa, S. Durand, A. Khazaal et al., A Sparsity-Based Variational Approach for the Restoration of SMOS Images From L1A Data, Proceedings of the IEEE International Geoscience and Remote Sensing Symposium (IGARSS), pp.2487-2490, 2014.
DOI : 10.1109/TGRS.2017.2654864

URL : https://hal.archives-ouvertes.fr/hal-01341839

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C: the art of scientific computing, 1992.

M. Primet, Probabilistic methods for point tracking and biological image analysis, p.5, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00669220

M. Primet and L. Moisan, Point tracking: an a-contrario approach, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00675083

G. R. Pugh, An analysis of the Lanczos gamma approximation, 2004.

J. Rabin, J. Delon, and Y. Gousseau, A Statistical Approach to the Matching of Local Features, SIAM Journal on Imaging Sciences, vol.2, issue.3, pp.931-958, 2009.
DOI : 10.1137/090751359

URL : https://hal.archives-ouvertes.fr/hal-00168285

H. Raguet, J. M. Fadili, and G. Peyré, A Generalized Forward-Backward Splitting, SIAM Journal on Imaging Sciences, vol.6, issue.3, pp.1199-1226, 2013.
DOI : 10.1137/120872802

URL : https://hal.archives-ouvertes.fr/hal-00613637

K. Rangarajan and M. Shah, Establishing motion correspondence, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), pp.103-108, 1991.

D. Reid, An algorithm for tracking multiple targets, IEEE Transactions on Automatic Control, vol.24, issue.6, pp.843-854, 1979.
DOI : 10.1109/TAC.1979.1102177

W. Ring, Structural Properties of Solutions to Total Variation Regularization Problems, ESAIM: Modélisation Mathématique et Analyse Numérique, pp.799-810, 2000.
DOI : 10.1137/0917016

A. Robin, G. Mercier, G. Moser, and S. Serpico, An a-contrario approach for unsupervised change detection in radar images, 2009 IEEE International Geoscience and Remote Sensing Symposium, pp.240-243, 2009.
DOI : 10.1109/IGARSS.2009.5417327

A. Robin, L. Moisan, and S. Le-hégarat-mascle, An a-contrario approach for sub-pixel change detection in satellite imagery, IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), issue.11, pp.321977-1993, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00399698

R. T. Rockafellar, Convex analysis (Princeton mathematical series), p.49, 1970.

R. T. Rockafellar, Monotone Operators and the Proximal Point Algorithm, SIAM Journal on Control and Optimization, vol.14, issue.5, pp.877-898, 1976.
DOI : 10.1137/0314056

R. T. Rockafellar and R. Wets, Variational Analysis, 1998.
DOI : 10.1007/978-3-642-02431-3

B. Rougé and A. Seghier, <title>Nonlinear spectral extrapolation: new results and their application to spatial and medical imaging</title>, Neural, Morphological, and Stochastic Methods in Image and Signal Processing, pp.279-289, 1995.
DOI : 10.1117/12.216364

D. L. Ruderman, The statistics of natural images. Network: computation in neural systems, pp.517-548, 1994.

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

K. D. Schmidt, On the covariance of monotone functions of a random variable, Professoren des Inst. für Math. Stochastik, 2003.

A. Y. Schoene, Remark on ???Algorithm 435: Modified Incomplete Gamma Function [S14]???, ACM Transactions on Mathematical Software, vol.4, issue.3, pp.296-304, 1978.
DOI : 10.1145/355791.355803

S. Setzer, G. Steidl, and T. Teuber, Deblurring Poissonian images by split Bregman techniques, Journal of Visual Communication and Image Representation, vol.21, issue.3, pp.193-199, 2010.
DOI : 10.1016/j.jvcir.2009.10.006

URL : http://www.mathematik.uni-kl.de/uploads/tx_sibibtex/poisson_deblurring_elsevier_revised2.pdf

K. Shafique and M. Shah, A non-iterative greedy algorithm for multi-frame point correspondence, Proceedings Ninth IEEE International Conference on Computer Vision, pp.110-115, 2003.
DOI : 10.1109/ICCV.2003.1238321

L. Simon and J. Morel, Influence of Unknown Exterior Samples on Interpolated Values for Band-Limited Images, SIAM Journal on Imaging Sciences, vol.9, issue.1, pp.152-184, 2016.
DOI : 10.1137/140978338

URL : https://hal.archives-ouvertes.fr/hal-01287218

D. Strong and T. F. Chan, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Problems, vol.19, issue.6, pp.165-187, 2003.
DOI : 10.1088/0266-5611/19/6/059

P. Thévenaz, T. Blu, and M. Unser, Interpolation revisited [medical images application], IEEE Transactions on Medical Imaging, vol.19, issue.7, pp.739-758, 2000.
DOI : 10.1109/42.875199

I. Thompson, Algorithm 926, ACM Transactions on Mathematical Software, vol.39, issue.2, pp.1-14, 2013.
DOI : 10.1145/2427023.2427031

I. J. Thompson and A. R. Barnett, Coulomb and Bessel functions of complex arguments and order, Journal of Computational Physics, vol.64, issue.2, pp.490-509, 1986.
DOI : 10.1016/0021-9991(86)90046-X

F. G. Tricomi, Sulla funzione gamma incompleta, Annali di Matematica Pura ed Applicata, Series 4, vol.32, issue.1, pp.263-279, 1950.
DOI : 10.1007/978-3-662-01222-2

M. Unser, Ten good reasons for using spline wavelets, Optical Science, Engineering and Instrumentation'97 International Society for Optics and Photonics, pp.422-431, 1997.

M. Unser, Sampling-50 years after Shannon, Proceedings of the IEEE, pp.569-587, 2000.
DOI : 10.1109/5.843002

M. Unser, A. Aldroubi, and M. Eden, Fast B-spline transforms for continuous image representation and interpolation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.3, pp.277-285, 1991.
DOI : 10.1109/34.75515

C. J. Veenman, M. J. Reinders, and E. Backer, Resolving motion correspondence for densely moving points, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.23, issue.1, pp.54-72, 2001.
DOI : 10.1109/34.899946

C. J. Veenman, M. J. Reinders, and E. Backer, Motion tracking as a constrained optimization problem, Pattern Recognition, vol.36, issue.9, pp.2049-2067, 2003.
DOI : 10.1016/S0031-3203(03)00037-2

J. Verestóy and D. Chetverikov, Experimental Comparative Evaluation of Feature Point Tracking Algorithms, Performance Characterization in Computer Vision, pp.167-178, 2000.
DOI : 10.1007/978-94-015-9538-4_14

L. Vese and S. J. Osher, Modeling textures with total variation minimization and oscillating patterns in image processing, Journal of Scientific Computing, vol.19, issue.1/3, pp.553-572, 2003.
DOI : 10.1023/A:1025384832106

L. A. Vese and S. J. Osher, Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions, Journal of Mathematical Imaging and Vision, vol.20, issue.1/2, pp.7-18, 2004.
DOI : 10.1023/B:JMIV.0000011316.54027.6a

URL : http://www.math.ucla.edu/~lvese/PAPERS/JMIVVeseOsher.pdf

C. R. Vogel and M. E. Oman, Fast, robust total variation-based reconstruction of noisy, blurred images, IEEE Transactions on Image Processing, vol.7, issue.6, pp.813-824, 1998.
DOI : 10.1109/83.679423

R. G. Von-gioi, J. Jakubowicz, J. Morel, and G. Randall, LSD: A Fast Line Segment Detector with a False Detection Control, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.4, pp.722-732, 2008.
DOI : 10.1109/TPAMI.2008.300

R. G. Von-gioi, J. Jakubowicz, J. Morel, and G. Randall, On Straight Line Segment Detection, Journal of Mathematical Imaging and Vision, vol.135, issue.2, pp.313-347, 2008.
DOI : 10.1007/978-1-4613-2551-2

J. Wang and B. J. Lucier, Error Bounds for Finite-Difference Methods for Rudin???Osher???Fatemi Image Smoothing, SIAM Journal on Numerical Analysis, vol.49, issue.2, pp.845-868, 2011.
DOI : 10.1137/090769594

P. Weiss, Algorithmes rapides d'optimisation convexe ApplicationsàApplicationsà la reconstruction d'images etàetà la détection de changements, 2008.

P. Weiss and L. Blanc-féraud, A proximal method for inverse problems in image processing, Proceedings of the 17th European Signal Processing Conference (EUSIPCO), pp.1374-1378, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00417712

P. Weiss, L. Blanc-féraud, and G. Aubert, Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.312047-2080, 2009.
DOI : 10.1137/070696143

URL : https://hal.archives-ouvertes.fr/inria-00166096

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, p.3, 2009.
DOI : 10.5244/C.23.108

M. Wertheimer, Untersuchungen zur Lehre von der Gestalt. II, Psychologische Forschung, vol.4, issue.1, pp.301-350, 1923.
DOI : 10.1007/BF00410640

S. Winitzki, Computing the Incomplete Gamma Function to Arbitrary Precision, Proceedings of the International Conference on Computational Science and Its Applications: Part I, ICCSA'03, pp.790-798, 2003.
DOI : 10.1007/3-540-44839-X_83

W. Research and I. , Generalized incomplete gamma function URL http://reference.wolfram.com/language/ref, Gamma.html, 1988.

W. Research and I. , Generalized incomplete gamma function, 1998.

G. Xia, J. Delon, and Y. Gousseau, Accurate Junction Detection and Characterization in Natural Images, International Journal of Computer Vision, vol.13, issue.9, pp.31-56, 2014.
DOI : 10.1016/0262-8856(95)98864-P

URL : https://hal.archives-ouvertes.fr/hal-00631609

L. P. Yaroslavsky, Signal sinc???interpolation: A fast computer algorithm, Bioimaging, vol.4, issue.4, pp.225-231, 1996.
DOI : 10.1002/1361-6374(199612)4:4<225::AID-BIO1>3.0.CO;2-G

K. Yosida, Functional Analysis Originally published as volume 123 in the series: Grundlehren der mathematischen Wissenschaften, 1968.

M. Zhu and T. Chan, An efficient primal-dual hybrid gradient algorithm for total variation image restoration, UCLA CAM Report, 2008.

W. P. Ziemer, Weakly differentiable functions: Sobolev spaces and functions of bounded variation, 2012.
DOI : 10.1007/978-1-4612-1015-3