Team, Visitors, External Collaborators
Overall Objectives
Research Program
New Software and Platforms
New Results
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
PDF e-Pub


Bibliography

Publications of the year

Doctoral Dissertations and Habilitation Theses

[1]
A. Genevay.
Entropy-Regularized Optimal Transport for Machine Learning, PSL University, March 2019.
https://tel.archives-ouvertes.fr/tel-02319318

Articles in International Peer-Reviewed Journals

[2]
J.-D. Benamou, G. Carlier, M. Laborde.
An augmented Lagrangian approach to Wasserstein gradient flows and applications, in: ESAIM: Proceedings and Surveys, August 2019.
https://hal.archives-ouvertes.fr/hal-01245184
[3]
J.-D. Benamou, V. Duval.
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem, in: European Journal of Applied Mathematics, 2019, https://arxiv.org/abs/1710.05594, forthcoming. [ DOI : 10.1017/S0956792518000451 ]
https://hal.inria.fr/hal-01616842
[4]
J.-D. Benamou, T. Gallouët, F.-X. Vialard.
Second order models for optimal transport and cubic splines on the Wasserstein space, in: Foundations of Computational Mathematics, October 2019, https://arxiv.org/abs/1801.04144.
https://hal.archives-ouvertes.fr/hal-01682107
[5]
C. Boyer, A. Chambolle, Y. De Castro, V. Duval, F. De Gournay, P. Weiss.
On Representer Theorems and Convex Regularization, in: SIAM Journal on Optimization, May 2019, vol. 29, no 2, pp. 1260–1281, https://arxiv.org/abs/1806.09810. [ DOI : 10.1137/18M1200750 ]
https://hal.archives-ouvertes.fr/hal-01823135
[6]
C. Cancès, T. Gallouët, M. Laborde, L. Monsaingeon.
Simulation of multiphase porous media flows with minimizing movement and finite volume schemes, in: European Journal of Applied Mathematics, 2019, vol. 30, no 6, pp. 1123-1152. [ DOI : 10.1017/S0956792518000633 ]
https://hal.archives-ouvertes.fr/hal-01700952
[7]
S. Dallaporta, Y. De Castro.
Sparse Recovery from Extreme Eigenvalues Deviation Inequalities, in: ESAIM: Probability and Statistics, 2019, https://arxiv.org/abs/1604.01171 - 33 pages, 1 figure. [ DOI : 10.1051/ps/2018024 ]
https://hal.archives-ouvertes.fr/hal-01309439
[8]
Y. De Castro, F. Gamboa, D. Henrion, R. Hess, J. B. Lasserre.
Approximate Optimal Designs for Multivariate Polynomial Regression, in: Annals of Statistics, January 2019, vol. 47, no 1, pp. 127-155. [ DOI : 10.1214/18-AOS1683 ]
https://hal.laas.fr/hal-01483490
[9]
Q. Denoyelle, V. Duval, G. Peyré, E. Soubies.
The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy, in: Inverse Problems, 2019, https://arxiv.org/abs/1811.06416, forthcoming. [ DOI : 10.1088/1361-6420/ab2a29 ]
https://hal.archives-ouvertes.fr/hal-01921604
[10]
T. Gallouët, M. Laborde, L. Monsaingeon.
An unbalanced optimal transport splitting scheme for general advection-reaction-diffusion problems, in: ESAIM: Control, Optimisation and Calculus of Variations, 2019, vol. 25, no 8, https://arxiv.org/abs/1704.04541. [ DOI : 10.1051/cocv/2018001 ]
https://hal.archives-ouvertes.fr/hal-01508911
[11]
T. Gallouët, A. Natale, F.-X. Vialard.
Generalized compressible flows and solutions of the H(div) geodesic problem, in: Archive for Rational Mechanics and Analysis, 2020, https://arxiv.org/abs/1806.10825, forthcoming.
https://hal.archives-ouvertes.fr/hal-01815531
[12]
R. E. Gaunt, G. Mijoule, Y. Swan.
Some new Stein operators for product distributions, in: Brazilian Journal of Probability and Statistics, 2019, https://arxiv.org/abs/1901.11460 - 13 pages, forthcoming.
https://hal.archives-ouvertes.fr/hal-02017801
[13]
A. Natale, F.-X. Vialard.
Embedding Camassa-Holm equations in incompressible Euler, in: Journal of Geometric Mechanics, June 2019, https://arxiv.org/abs/1804.11080.
https://hal.archives-ouvertes.fr/hal-01781162
[14]
P. Pegon, F. Santambrogio, Q. Xia.
A fractal shape optimization problem in branched transport, in: Journal de Mathématiques Pures et Appliquées, March 2019, https://arxiv.org/abs/1709.01415.
https://hal.archives-ouvertes.fr/hal-01581675

International Conferences with Proceedings

[15]
J.-B. Courbot, E. Monfrini, V. Mazet, C. Collet.
Triplet markov trees for image segmentation, in: SSP 2018: IEEE Workshop on Statistical Signal Processing, Fribourg-en-Brisgau, Germany, 2018 IEEE Statistical Signal Processing Workshop (SSP), IEEE Computer Society, 2019, pp. 233-237. [ DOI : 10.1109/SSP.2018.8450841 ]
https://hal.archives-ouvertes.fr/hal-01815562

Conferences without Proceedings

[16]
J. M. Fadili, G. Garrigos, J. Malick, G. Peyré.
Model Consistency for Learning with Mirror-Stratifiable Regularizers, in: International Conference on Artificial Intelligence and Statistics (AISTATS), Naha, Japan, April 2019.
https://hal.archives-ouvertes.fr/hal-01988309

Other Publications

[17]
J.-M. Azaïs, Y. De Castro.
Multiple Testing and Variable Selection along Least Angle Regression's path, July 2019, https://arxiv.org/abs/1906.12072 - 39 pages, 7 figures.
https://hal.archives-ouvertes.fr/hal-02170476
[18]
J.-D. Benamou, G. Carlier, S. D. Marino, L. Nenna.
An entropy minimization approach to second-order variational mean-field games, September 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01848370
[19]
C. Cancès, T. Gallouët, G. Todeschi.
A variational finite volume scheme for Wasserstein gradient flows, July 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02189050
[20]
J.-B. Courbot, V. Duval, B. Legras.
Sparse analysis for mesoscale convective systems tracking, February 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02010436
[21]
S. Di Marino, A. Natale, R. Tahraoui, F.-X. Vialard.
Metric completion of Diff([0,1]) with the H1 right-invariant metric, June 2019, https://arxiv.org/abs/1906.09139 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02161686
[22]
V. Duval.
An Epigraphical Approach to the Representer Theorem, December 2019, https://arxiv.org/abs/1912.13224 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02424908
[23]
G. Mijoule, G. Reinert, Y. Swan.
Stein operators, kernels and discrepancies for multivariate continuous distributions, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02420874
[24]
A. Natale, G. Todeschi.
TPFA Finite Volume Approximation of Wasserstein Gradient Flows, January 2020, https://arxiv.org/abs/2001.07005 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02444833
References in notes
[25]
I. Abraham, R. Abraham, M. Bergounioux, G. Carlier.
Tomographic reconstruction from a few views: a multi-marginal optimal transport approach, in: Preprint Hal-01065981, 2014.
[26]
Y. Achdou, V. Perez.
Iterative strategies for solving linearized discrete mean field games systems, in: Netw. Heterog. Media, 2012, vol. 7, no 2, pp. 197–217.
http://dx.doi.org/10.3934/nhm.2012.7.197
[27]
M. Agueh, G. Carlier.
Barycenters in the Wasserstein space, in: SIAM J. Math. Anal., 2011, vol. 43, no 2, pp. 904–924.
[28]
F. Alter, V. Caselles, A. Chambolle.
Evolution of Convex Sets in the Plane by Minimizing the Total Variation Flow, in: Interfaces and Free Boundaries, 2005, vol. 332, pp. 329–366.
[29]
F. R. Bach.
Consistency of the Group Lasso and Multiple Kernel Learning, in: J. Mach. Learn. Res., June 2008, vol. 9, pp. 1179–1225.
http://dl.acm.org/citation.cfm?id=1390681.1390721
[30]
F. R. Bach.
Consistency of Trace Norm Minimization, in: J. Mach. Learn. Res., June 2008, vol. 9, pp. 1019–1048.
http://dl.acm.org/citation.cfm?id=1390681.1390716
[31]
H. H. Bauschke, P. L. Combettes.
A Dykstra-like algorithm for two monotone operators, in: Pacific Journal of Optimization, 2008, vol. 4, no 3, pp. 383–391.
[32]
M. F. Beg, M. I. Miller, A. Trouvé, L. Younes.
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms, in: International Journal of Computer Vision, February 2005, vol. 61, no 2, pp. 139–157.
http://dx.doi.org/10.1023/B:VISI.0000043755.93987.aa
[33]
M. Beiglbock, P. Henry-Labordère, F. Penkner.
Model-independent bounds for option prices mass transport approach, in: Finance and Stochastics, 2013, vol. 17, no 3, pp. 477-501.
http://dx.doi.org/10.1007/s00780-013-0205-8
[34]
G. Bellettini, V. Caselles, M. Novaga.
The Total Variation Flow in RN, in: J. Differential Equations, 2002, vol. 184, no 2, pp. 475–525.
[35]
J.-D. Benamou, Y. Brenier.
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, in: Numer. Math., 2000, vol. 84, no 3, pp. 375–393.
http://dx.doi.org/10.1007/s002110050002
[36]
J.-D. Benamou, Y. Brenier.
Weak existence for the semigeostrophic equations formulated as a coupled Monge-Ampère/transport problem, in: SIAM J. Appl. Math., 1998, vol. 58, no 5, pp. 1450–1461.
[37]
J.-D. Benamou, G. Carlier.
Augmented Lagrangian algorithms for variational problems with divergence constraints, in: JOTA, 2015.
[38]
J.-D. Benamou, G. Carlier, N. Bonne.
An Augmented Lagrangian Numerical approach to solving Mean-Fields Games, Inria, December 2013, 30 p.
http://hal.inria.fr/hal-00922349
[39]
J.-D. Benamou, G. Carlier, M. Cuturi, L. Nenna, G. Peyré.
Iterative Bregman Projections for Regularized Transportation Problems, in: SIAM J. Sci. Comp., 2015, to appear.
[40]
J.-D. Benamou, G. Carlier, Q. Mérigot, É. Oudet.
Discretization of functionals involving the Monge-Ampère operator, HAL, July 2014.
https://hal.archives-ouvertes.fr/hal-01056452
[41]
J.-D. Benamou, F. Collino, J.-M. Mirebeau.
Monotone and Consistent discretization of the Monge-Ampère operator, in: arXiv preprint arXiv:1409.6694, 2014, to appear in Math of Comp.
[42]
J.-D. Benamou, B. D. Froese, A. Oberman.
Two numerical methods for the elliptic Monge-Ampère equation, in: M2AN Math. Model. Numer. Anal., 2010, vol. 44, no 4, pp. 737–758.
[43]
J.-D. Benamou, B. D. Froese, A. Oberman.
Numerical solution of the optimal transportation problem using the Monge–Ampere equation, in: Journal of Computational Physics, 2014, vol. 260, pp. 107–126.
[44]
F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio.
Numerical approximation of continuous traffic congestion equilibria, in: Netw. Heterog. Media, 2009, vol. 4, no 3, pp. 605–623.
[45]
M. Benning, M. Burger.
Ground states and singular vectors of convex variational regularization methods, in: Meth. Appl. Analysis, 2013, vol. 20, pp. 295–334.
[46]
B. Berkels, A. Effland, M. Rumpf.
Time discrete geodesic paths in the space of images, in: Arxiv preprint, 2014.
[47]
J. Bigot, T. Klein.
Consistent estimation of a population barycenter in the Wasserstein space, in: Preprint arXiv:1212.2562, 2012.
[48]
A. Blanchet, P. Laurençot.
The parabolic-parabolic Keller-Segel system with critical diffusion as a gradient flow in Rd,d3, in: Comm. Partial Differential Equations, 2013, vol. 38, no 4, pp. 658–686.
http://dx.doi.org/10.1080/03605302.2012.757705
[49]
J. Bleyer, G. Carlier, V. Duval, J.-M. Mirebeau, G. Peyré.
A Γ Convergence Result for the Upper Bound Limit Analysis of Plates, in: ESAIM: Mathematical Modelling and Numerical Analysis, January 2016, vol. 50, no 1, pp. 215–235. [ DOI : 10.1051/m2an/2015040 ]
https://www.esaim-m2an.org/articles/m2an/abs/2016/01/m2an141087/m2an141087.html
[50]
N. Bonneel, J. Rabin, G. Peyré, H. Pfister.
Sliced and Radon Wasserstein Barycenters of Measures, in: Journal of Mathematical Imaging and Vision, 2015, vol. 51, no 1, pp. 22–45.
http://hal.archives-ouvertes.fr/hal-00881872/
[51]
U. Boscain, R. Chertovskih, J.-P. Gauthier, D. Prandi, A. Remizov.
Highly corrupted image inpainting through hypoelliptic diffusion, Preprint CMAP, 2014.
http://hal.archives-ouvertes.fr/hal-00842603/
[52]
G. Bouchitté, G. Buttazzo.
Characterization of optimal shapes and masses through Monge-Kantorovich equation, in: J. Eur. Math. Soc. (JEMS), 2001, vol. 3, no 2, pp. 139–168.
http://dx.doi.org/10.1007/s100970000027
[53]
L. Brasco, G. Carlier, F. Santambrogio.
Congested traffic dynamics, weak flows and very degenerate elliptic equations, in: J. Math. Pures Appl. (9), 2010, vol. 93, no 6, pp. 652–671.
[54]
L. M. Bregman.
The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, in: USSR computational mathematics and mathematical physics, 1967, vol. 7, no 3, pp. 200–217.
[55]
Y. Brenier.
Generalized solutions and hydrostatic approximation of the Euler equations, in: Phys. D, 2008, vol. 237, no 14-17, pp. 1982–1988.
http://dx.doi.org/10.1016/j.physd.2008.02.026
[56]
Y. Brenier.
Décomposition polaire et réarrangement monotone des champs de vecteurs, in: C. R. Acad. Sci. Paris Sér. I Math., 1987, vol. 305, no 19, pp. 805–808.
[57]
Y. Brenier.
Polar factorization and monotone rearrangement of vector-valued functions, in: Comm. Pure Appl. Math., 1991, vol. 44, no 4, pp. 375–417.
http://dx.doi.org/10.1002/cpa.3160440402
[58]
Y. Brenier, U. Frisch, M. Henon, G. Loeper, S. Matarrese, R. Mohayaee, A. Sobolevski.
Reconstruction of the early universe as a convex optimization problem, in: Mon. Not. Roy. Astron. Soc., 2003, vol. 346, pp. 501–524.
http://arxiv.org/pdf/astro-ph/0304214.pdf
[59]
M. Bruveris, L. Risser, F.-X. Vialard.
Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups, in: Multiscale Modeling & Simulation, 2012, vol. 10, no 4, pp. 1344-1368.
[60]
M. Burger, M. DiFrancesco, P. Markowich, M. T. Wolfram.
Mean field games with nonlinear mobilities in pedestrian dynamics, in: DCDS B, 2014, vol. 19.
[61]
M. Burger, M. Franek, C. Schonlieb.
Regularized regression and density estimation based on optimal transport, in: Appl. Math. Res. Expr., 2012, vol. 2, pp. 209–253.
[62]
M. Burger, S. Osher.
A guide to the TV zoo, in: Level-Set and PDE-based Reconstruction Methods, Springer, 2013.
[63]
G. Buttazzo, C. Jimenez, É. Oudet.
An optimization problem for mass transportation with congested dynamics, in: SIAM J. Control Optim., 2009, vol. 48, no 3, pp. 1961–1976.
[64]
H. Byrne, D. Drasdo.
Individual-based and continuum models of growing cell populations: a comparison, in: Journal of Mathematical Biology, 2009, vol. 58, no 4-5, pp. 657-687.
[65]
L. A. Caffarelli.
The regularity of mappings with a convex potential, in: J. Amer. Math. Soc., 1992, vol. 5, no 1, pp. 99–104.
http://dx.doi.org/10.2307/2152752
[66]
L. A. Caffarelli, S. A. Kochengin, V. Oliker.
On the numerical solution of the problem of reflector design with given far-field scattering data, in: Monge Ampère equation: applications to geometry and optimization (Deerfield Beach, FL, 1997), Providence, RI, Contemp. Math., Amer. Math. Soc., 1999, vol. 226, pp. 13–32.
http://dx.doi.org/10.1090/conm/226/03233
[67]
C. CanCeritoglu.
Computational Analysis of LDDMM for Brain Mapping, in: Frontiers in Neuroscience, 2013, vol. 7.
[68]
C. Cancès, T. Gallouët, L. Monsaingeon.
Incompressible immiscible multiphase flows in porous media: a variational approach, in: Analysis & PDE, 2017, vol. 10, no 8, pp. 1845–1876. [ DOI : 10.2140/apde.2017.10.1845 ]
https://hal.archives-ouvertes.fr/hal-01345438
[69]
E. Candes, M. Wakin.
An Introduction to Compressive Sensing, in: IEEE Signal Processing Magazine, 2008, vol. 25, no 2, pp. 21–30.
[70]
E. J. Candès, C. Fernandez-Granda.
Super-Resolution from Noisy Data, in: Journal of Fourier Analysis and Applications, 2013, vol. 19, no 6, pp. 1229–1254.
[71]
E. J. Candès, C. Fernandez-Granda.
Towards a Mathematical Theory of Super-Resolution, in: Communications on Pure and Applied Mathematics, 2014, vol. 67, no 6, pp. 906–956.
[72]
P. Cardaliaguet, G. Carlier, B. Nazaret.
Geodesics for a class of distances in the space of probability measures, in: Calc. Var. Partial Differential Equations, 2013, vol. 48, no 3-4, pp. 395–420.
[73]
G. Carlier.
A general existence result for the principal-agent problem with adverse selection, in: J. Math. Econom., 2001, vol. 35, no 1, pp. 129–150.
[74]
G. Carlier, V. Chernozhukov, A. Galichon.
Vector Quantile Regression, Arxiv 1406.4643, 2014.
[75]
G. Carlier, M. Comte, I. Ionescu, G. Peyré.
A Projection Approach to the Numerical Analysis of Limit Load Problems, in: Mathematical Models and Methods in Applied Sciences, 2011, vol. 21, no 6, pp. 1291–1316. [ DOI : doi:10.1142/S0218202511005325 ]
http://hal.archives-ouvertes.fr/hal-00450000/
[76]
G. Carlier, X. Dupuis.
An iterated projection approach to variational problems under generalized convexity constraints and applications, In preparation, 2015.
[77]
G. Carlier, C. Jimenez, F. Santambrogio.
Optimal Transportation with Traffic Congestion and Wardrop Equilibria, in: SIAM Journal on Control and Optimization, 2008, vol. 47, no 3, pp. 1330-1350.
[78]
G. Carlier, T. Lachand-Robert, B. Maury.
A numerical approach to variational problems subject to convexity constraint, in: Numer. Math., 2001, vol. 88, no 2, pp. 299–318.
http://dx.doi.org/10.1007/PL00005446
[79]
G. Carlier, A. Oberman, É. Oudet.
Numerical methods for matching for teams and Wasserstein barycenters, in: M2AN, 2015, to appear.
[80]
J. A. Carrillo, S. Lisini, E. Mainini.
Uniqueness for Keller-Segel-type chemotaxis models, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, no 4, pp. 1319–1338.
http://dx.doi.org/10.3934/dcds.2014.34.1319
[81]
V. Caselles, A. Chambolle, M. Novaga.
The discontinuity set of solutions of the TV denoising problem and some extensions, in: Multiscale Modeling and Simulation, 2007, vol. 6, no 3, pp. 879–894.
[82]
F. A. C. C. Chalub, P. A. Markowich, B. Perthame, C. Schmeiser.
Kinetic models for chemotaxis and their drift-diffusion limits, in: Monatsh. Math., 2004, vol. 142, no 1-2, pp. 123–141.
http://dx.doi.org/10.1007/s00605-004-0234-7
[83]
A. Chambolle, T. Pock.
On the ergodic convergence rates of a first-order primal-dual algorithm, in: Preprint OO/2014/09/4532, 2014.
[84]
G. Charpiat, G. Nardi, G. Peyré, F.-X. Vialard.
Finsler Steepest Descent with Applications to Piecewise-regular Curve Evolution, Preprint hal-00849885, 2013.
http://hal.archives-ouvertes.fr/hal-00849885/
[85]
S. S. Chen, D. L. Donoho, M. A. Saunders.
Atomic decomposition by basis pursuit, in: SIAM journal on scientific computing, 1999, vol. 20, no 1, pp. 33–61.
[86]
P. Choné, H. V. J. Le Meur.
Non-convergence result for conformal approximation of variational problems subject to a convexity constraint, in: Numer. Funct. Anal. Optim., 2001, vol. 22, no 5-6, pp. 529–547.
http://dx.doi.org/10.1081/NFA-100105306
[87]
C. Cotar, G. Friesecke, C. Kluppelberg.
Density Functional Theory and Optimal Transportation with Coulomb Cost, in: Communications on Pure and Applied Mathematics, 2013, vol. 66, no 4, pp. 548–599.
http://dx.doi.org/10.1002/cpa.21437
[88]
M. J. P. Cullen, W. Gangbo, G. Pisante.
The semigeostrophic equations discretized in reference and dual variables, in: Arch. Ration. Mech. Anal., 2007, vol. 185, no 2, pp. 341–363.
http://dx.doi.org/10.1007/s00205-006-0040-6
[89]
M. J. P. Cullen, J. Norbury, R. J. Purser.
Generalised Lagrangian solutions for atmospheric and oceanic flows, in: SIAM J. Appl. Math., 1991, vol. 51, no 1, pp. 20–31.
[90]
M. Cuturi.
Sinkhorn Distances: Lightspeed Computation of Optimal Transport, in: Proc. NIPS, C. J. C. Burges, L. Bottou, Z. Ghahramani, K. Q. Weinberger (editors), 2013, pp. 2292–2300.
[91]
E. J. Dean, R. Glowinski.
Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type, in: Comput. Methods Appl. Mech. Engrg., 2006, vol. 195, no 13-16, pp. 1344–1386.
[92]
V. Duval, G. Peyré.
Exact Support Recovery for Sparse Spikes Deconvolution, in: Foundations of Computational Mathematics, 2014, pp. 1-41.
http://dx.doi.org/10.1007/s10208-014-9228-6
[93]
V. Duval, G. Peyré.
Sparse regularization on thin grids I: the L asso, in: Inverse Problems, 2017, vol. 33, no 5, 055008 p. [ DOI : 10.1088/1361-6420/aa5e12 ]
http://stacks.iop.org/0266-5611/33/i=5/a=055008
[94]
J. Fehrenbach, J.-M. Mirebeau.
Sparse Non-negative Stencils for Anisotropic Diffusion, in: Journal of Mathematical Imaging and Vision, 2014, vol. 49, no 1, pp. 123-147.
http://dx.doi.org/10.1007/s10851-013-0446-3
[95]
C. Fernandez-Granda.
Support detection in super-resolution, in: Proc. Proceedings of the 10th International Conference on Sampling Theory and Applications, 2013, pp. 145–148.
[96]
A. Figalli, R. McCann, Y. Kim.
When is multi-dimensional screening a convex program?, in: Journal of Economic Theory, 2011.
[97]
J.-B. Fiot, H. Raguet, L. Risser, L. D. Cohen, J. Fripp, F.-X. Vialard.
Longitudinal deformation models, spatial regularizations and learning strategies to quantify Alzheimer's disease progression, in: NeuroImage: Clinical, 2014, vol. 4, no 0, pp. 718 - 729. [ DOI : 10.1016/j.nicl.2014.02.002 ]
http://www.sciencedirect.com/science/article/pii/S2213158214000205
[98]
J.-B. Fiot, L. Risser, L. D. Cohen, J. Fripp, F.-X. Vialard.
Local vs Global Descriptors of Hippocampus Shape Evolution for Alzheimer's Longitudinal Population Analysis, in: Spatio-temporal Image Analysis for Longitudinal and Time-Series Image Data, Lecture Notes in Computer Science, Springer Berlin Heidelberg, 2012, vol. 7570, pp. 13-24.
http://dx.doi.org/10.1007/978-3-642-33555-6_2
[99]
U. Frisch, S. Matarrese, R. Mohayaee, A. Sobolevski.
Monge-Ampère-Kantorovitch (MAK) reconstruction of the eary universe, in: Nature, 2002, vol. 417, no 260.
[100]
B. D. Froese, A. Oberman.
Convergent filtered schemes for the Monge-Ampère partial differential equation, in: SIAM J. Numer. Anal., 2013, vol. 51, no 1, pp. 423–444.
[101]
A. Galichon, P. Henry-Labordère, N. Touzi.
A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Loopback options, in: submitted to Annals of Applied Probability, 2011.
[102]
W. Gangbo, R. McCann.
The geometry of optimal transportation, in: Acta Math., 1996, vol. 177, no 2, pp. 113–161.
http://dx.doi.org/10.1007/BF02392620
[103]
E. Ghys.
Gaspard Monge, Le mémoire sur les déblais et les remblais, in: Image des mathématiques, CNRS, 2012.
http://images.math.cnrs.fr/Gaspard-Monge,1094.html
[104]
O. Guéant, J.-M. Lasry, P.-L. Lions.
Mean field games and applications, in: Paris-Princeton Lectures on Mathematical Finance 2010, Berlin, Lecture Notes in Math., Springer, 2011, vol. 2003, pp. 205–266.
http://dx.doi.org/10.1007/978-3-642-14660-2_3
[105]
G. Herman.
Image reconstruction from projections: the fundamentals of computerized tomography, Academic Press, 1980.
[106]
D. D. Holm, J. T. Ratnanather, A. Trouvé, L. Younes.
Soliton dynamics in computational anatomy, in: NeuroImage, 2004, vol. 23, pp. S170–S178.
[107]
B. J. Hoskins.
The mathematical theory of frontogenesis, in: Annual review of fluid mechanics, Vol. 14, Palo Alto, CA, Annual Reviews, 1982, pp. 131–151.
[108]
R. Jordan, D. Kinderlehrer, F. Otto.
The variational formulation of the Fokker-Planck equation, in: SIAM J. Math. Anal., 1998, vol. 29, no 1, pp. 1–17.
[109]
W. Jäger, S. Luckhaus.
On explosions of solutions to a system of partial differential equations modelling chemotaxis, in: Trans. Amer. Math. Soc., 1992, vol. 329, no 2, pp. 819–824.
http://dx.doi.org/10.2307/2153966
[110]
L. Kantorovitch.
On the translocation of masses, in: C. R. (Doklady) Acad. Sci. URSS (N.S.), 1942, vol. 37, pp. 199–201.
[111]
E. Klann.
A Mumford-Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography, in: SIAM J. Imaging Sciences, 2011, vol. 4, no 4, pp. 1029–1048.
[112]
J.-M. Lasry, P.-L. Lions.
Mean field games, in: Jpn. J. Math., 2007, vol. 2, no 1, pp. 229–260.
http://dx.doi.org/10.1007/s11537-007-0657-8
[113]
J. Lasserre.
Global Optimization with Polynomials and the Problem of Moments, in: SIAM Journal on Optimization, 2001, vol. 11, no 3, pp. 796-817.
[114]
J. Lellmann, D. A. Lorenz, C. Schönlieb, T. Valkonen.
Imaging with Kantorovich-Rubinstein Discrepancy, in: SIAM J. Imaging Sciences, 2014, vol. 7, no 4, pp. 2833–2859.
[115]
A. S. Lewis.
Active sets, nonsmoothness, and sensitivity, in: SIAM Journal on Optimization, 2003, vol. 13, no 3, pp. 702–725.
[116]
B. Li, F. Habbal, M. Ortiz.
Optimal transportation meshfree approximation schemes for Fluid and plastic Flows, in: Int. J. Numer. Meth. Engng 83:1541–579, 2010, vol. 83, pp. 1541–1579.
[117]
G. Loeper.
A fully nonlinear version of the incompressible Euler equations: the semigeostrophic system, in: SIAM J. Math. Anal., 2006, vol. 38, no 3, pp. 795–823 (electronic).
[118]
G. Loeper, F. Rapetti.
Numerical solution of the Monge-Ampére equation by a Newton's algorithm, in: C. R. Math. Acad. Sci. Paris, 2005, vol. 340, no 4, pp. 319–324.
[119]
D. Lombardi, E. Maitre.
Eulerian models and algorithms for unbalanced optimal transport, in: Preprint hal-00976501, 2013.
[120]
C. Léonard.
A survey of the Schrödinger problem and some of its connections with optimal transport, in: Discrete Contin. Dyn. Syst., 2014, vol. 34, no 4, pp. 1533–1574.
http://dx.doi.org/10.3934/dcds.2014.34.1533
[121]
J. Maas, M. Rumpf, C. Schonlieb, S. Simon.
A generalized model for optimal transport of images including dissipation and density modulation, in: Arxiv preprint, 2014.
[122]
S. G. Mallat.
A wavelet tour of signal processing, Third, Elsevier/Academic Press, Amsterdam, 2009.
[123]
B. Maury, A. Roudneff-Chupin, F. Santambrogio.
A macroscopic crowd motion model of gradient flow type, in: Math. Models Methods Appl. Sci., 2010, vol. 20, no 10, pp. 1787–1821.
http://dx.doi.org/10.1142/S0218202510004799
[124]
M. I. Miller, A. Trouvé, L. Younes.
Geodesic Shooting for Computational Anatomy, in: Journal of Mathematical Imaging and Vision, March 2006, vol. 24, no 2, pp. 209–228.
http://dx.doi.org/10.1007/s10851-005-3624-0
[125]
J.-M. Mirebeau.
Adaptive, Anisotropic and Hierarchical cones of Discrete Convex functions, in: Preprint, 2014.
[126]
J.-M. Mirebeau.
Anisotropic Fast-Marching on Cartesian Grids Using Lattice Basis Reduction, in: SIAM Journal on Numerical Analysis, 2014, vol. 52, no 4, pp. 1573-1599.
[127]
Q. Mérigot.
A multiscale approach to optimal transport, in: Computer Graphics Forum, 2011, vol. 30, no 5, pp. 1583–1592.
[128]
Q. Mérigot, É. Oudet.
Handling Convexity-Like Constraints in Variational Problems, in: SIAM J. Numer. Anal., 2014, vol. 52, no 5, pp. 2466–2487.
[129]
N. Papadakis, G. Peyré, É. Oudet.
Optimal Transport with Proximal Splitting, in: SIAM Journal on Imaging Sciences, 2014, vol. 7, no 1, pp. 212–238. [ DOI : 10.1137/130920058 ]
http://hal.archives-ouvertes.fr/hal-00816211/
[130]
B. Pass, N. Ghoussoub.
Optimal transport: From moving soil to same-sex marriage, in: CMS Notes, 2013, vol. 45, pp. 14–15.
[131]
B. Pass.
Uniqueness and Monge Solutions in the Multimarginal Optimal Transportation Problem, in: SIAM Journal on Mathematical Analysis, 2011, vol. 43, no 6, pp. 2758-2775.
[132]
B. Perthame, F. Quiros, J. L. Vazquez.
The Hele-Shaw Asymptotics for Mechanical Models of Tumor Growth, in: Archive for Rational Mechanics and Analysis, 2014, vol. 212, no 1, pp. 93-127.
http://dx.doi.org/10.1007/s00205-013-0704-y
[133]
J. Petitot.
The neurogeometry of pinwheels as a sub-riemannian contact structure, in: Journal of Physiology-Paris, 2003, vol. 97, no 23, pp. 265–309.
[134]
G. Peyré.
Texture Synthesis with Grouplets, in: Pattern Analysis and Machine Intelligence, IEEE Transactions on, April 2010, vol. 32, no 4, pp. 733–746.
[135]
B. Piccoli, F. Rossi.
Generalized Wasserstein distance and its application to transport equations with source, in: Archive for Rational Mechanics and Analysis, 2014, vol. 211, no 1, pp. 335–358.
[136]
C. Poon.
Structure dependent sampling in compressed sensing: theoretical guarantees for tight frames, in: Applied and Computational Harmonic Analysis, 2015.
[137]
H. Raguet, J. Fadili, G. Peyré.
A Generalized Forward-Backward Splitting, in: SIAM Journal on Imaging Sciences, 2013, vol. 6, no 3, pp. 1199–1226. [ DOI : 10.1137/120872802 ]
http://hal.archives-ouvertes.fr/hal-00613637/
[138]
J.-C. Rochet, P. Choné.
Ironing, Sweeping and multi-dimensional screening, in: Econometrica, 1998.
[139]
L. Rudin, S. Osher, E. Fatemi.
Nonlinear total variation based noise removal algorithms, in: Physica D: Nonlinear Phenomena, 1992, vol. 60, no 1, pp. 259–268.
http://dx.doi.org/10.1016/0167-2789(92)90242-F
[140]
O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen.
Variational Methods in Imaging, Springer, 2008.
[141]
T. Schmah, L. Risser, F.-X. Vialard.
Left-Invariant Metrics for Diffeomorphic Image Registration with Spatially-Varying Regularisation, in: MICCAI (1), 2013, pp. 203-210.
[142]
T. Schmah, L. Risser, F.-X. Vialard.
Diffeomorphic image matching with left-invariant metrics, in: Fields Institute Communications series, special volume in memory of Jerrold E. Marsden, January 2014.
[143]
J. Solomon, F. de Goes, G. Peyré, M. Cuturi, A. Butscher, A. Nguyen, T. Du, L. Guibas.
Convolutional Wasserstein Distances: Efficient Optimal Transportation on Geometric Domains, in: ACM Transaction on Graphics, Proc. SIGGRAPH'15, 2015, to appear.
[144]
R. Tibshirani.
Regression shrinkage and selection via the Lasso, in: Journal of the Royal Statistical Society. Series B. Methodological, 1996, vol. 58, no 1, pp. 267–288.
[145]
A. Trouvé, F.-X. Vialard.
Shape splines and stochastic shape evolutions: A second order point of view, in: Quarterly of Applied Mathematics, 2012.
[146]
S. Vaiter, M. Golbabaee, J. Fadili, G. Peyré.
Model Selection with Piecewise Regular Gauges, in: Information and Inference, 2015, to appear.
http://hal.archives-ouvertes.fr/hal-00842603/
[147]
F.-X. Vialard, L. Risser, D. Rueckert, C. Cotter.
Diffeomorphic 3D Image Registration via Geodesic Shooting Using an Efficient Adjoint Calculation, in: International Journal of Computer Vision, 2012, vol. 97, no 2, pp. 229-241.
http://dx.doi.org/10.1007/s11263-011-0481-8
[148]
F.-X. Vialard, L. Risser.
Spatially-Varying Metric Learning for Diffeomorphic Image Registration: A Variational Framework, in: Medical Image Computing and Computer-Assisted Intervention MICCAI 2014, Lecture Notes in Computer Science, Springer International Publishing, 2014, vol. 8673, pp. 227-234.
[149]
C. Villani.
Topics in optimal transportation, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2003, vol. 58, xvi+370 p.
[150]
C. Villani.
Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2009, vol. 338, xxii+973 p, Old and new.
http://dx.doi.org/10.1007/978-3-540-71050-9
[151]
X.-J. Wang.
On the design of a reflector antenna. II, in: Calc. Var. Partial Differential Equations, 2004, vol. 20, no 3, pp. 329–341.
http://dx.doi.org/10.1007/s00526-003-0239-4
[152]
B. Wirth, L. Bar, M. Rumpf, G. Sapiro.
A continuum mechanical approach to geodesics in shape space, in: International Journal of Computer Vision, 2011, vol. 93, no 3, pp. 293–318.
[153]
J. Wright, Y. Ma, J. Mairal, G. Sapiro, T. S. Huang, S. Yan.
Sparse representation for computer vision and pattern recognition, in: Proceedings of the IEEE, 2010, vol. 98, no 6, pp. 1031–1044.