An Active Curve Approach for Tomographic Reconstruction of Binary Radially Symmetric Objects, Numerical Mathematics and Advanced Applications, pp.663-670, 2008. ,
DOI : 10.1007/978-3-540-69777-0_79
URL : https://hal.archives-ouvertes.fr/hal-00084855
A variational method for tomographic reconstruction with few views, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00697218
Tomographic Reconstruction from a Few Views: A Multi-Marginal Optimal Transport Approach, Applied Mathematics & Optimization, vol.24, issue.1, pp.55-73, 2017. ,
DOI : 10.1007/978-3-319-20828-2
URL : https://hal.archives-ouvertes.fr/hal-01065981
A Penalization Approach for Tomographic Reconstruction of Binary Axially Symmetric Objects, Applied Mathematics and Optimization, vol.42, issue.5, pp.345-371, 2008. ,
DOI : 10.1007/s00245-008-9039-8
URL : https://hal.archives-ouvertes.fr/hal-00139494
Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis, vol.43, issue.2, pp.904-924, 2011. ,
DOI : 10.1137/100805741
URL : https://hal.archives-ouvertes.fr/hal-00637399
Functions of bounded variation and free discontinuity problems, Oxford mathematical monographs, 2000. ,
Stable inversion of the Abel integral equation of the first kind by means of orthogonal polynomials, Inverse Problems, vol.26, issue.10, p.28, 2010. ,
DOI : 10.1088/0266-5611/26/10/105005
A Range Description for the Planar Circular Radon Transform, SIAM Journal on Mathematical Analysis, vol.38, issue.2, pp.681-692, 2006. ,
DOI : 10.1137/050637492
URL : http://arxiv.org/pdf/math/0508082
Variational analysis in Sobolev and BV spaces, MPS/SIAM Series on Optimization Society for Industrial and Applied Mathematics (SIAM), vol.6, 2006. ,
DOI : 10.1137/1.9781611973488
Overview of computerized tomography with emphasis on future developments, Proc. IEEE 71, pp.356-297, 1983. ,
DOI : 10.1109/PROC.1983.12594
Benamou and Y. Brenier A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem, Numerische Mathematik, vol.84, issue.3, pp.375-393, 2000. ,
Iterative Bregman Projections for Regularized Transportation Problems, SIAM Journal on Scientific Computing, vol.37, issue.2, pp.1111-1138, 2015. ,
DOI : 10.1137/141000439
URL : https://hal.archives-ouvertes.fr/hal-01096124
A new relaxation method for a discrete image restoration problem, Journal of Convex Analysis, vol.17, issue.3, pp.861-883, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00345556
A relaxation approach for smooth tomographic reconstruction of binary axially symmetric objects, Pacific Journal of Optimization, vol.5, issue.1, pp.39-51, 2009. ,
A variational method using fractional order Hilbert spaces for tomographic reconstruction of blurred and noised binary images, Journal of Functional Analysis, vol.259, issue.9, pp.2296-2332, 2010. ,
DOI : 10.1016/j.jfa.2010.05.016
URL : https://hal.archives-ouvertes.fr/hal-00458340
Fractional-order variational numerical methods for tomographic reconstruction of binary images, preprint, https ,
3D tomographic reconstruction of binary images from cone beam projections: a fast level set approach, Proceedings IEEE International Symposium on Biomedical Imaging, pp.677-680, 2002. ,
DOI : 10.1109/ISBI.2002.1029348
An Extension Problem Related to the Fractional Laplacian, Communications in Partial Differential Equations, vol.32, issue.8, pp.1245-1260, 2007. ,
DOI : 10.1080/00036818308839425
Matching for teams, Economic Theory, vol.11, issue.1, pp.397-418, 2010. ,
DOI : 10.1007/978-4-431-53979-7_1
URL : https://hal.archives-ouvertes.fr/hal-00661901
Regularization by Functions of Bounded Variation and Applications to Image Enhancement, Applied Mathematics and Optimization, vol.40, issue.2, pp.229-257, 1999. ,
DOI : 10.1007/s002459900124
An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, vol.20, pp.1-2, 2004. ,
Tomographiè a partir d'un nombre limité de projections : régularisation par champs markovien, 1990. ,
Image reconstruction from projections, SPIE's international symposium on optics, imaging and instrumentation, 1994. ,
On the Gibbs phenomenon and its resolution, SIAM Rev, pp.644-668, 1997. ,
DOI : 10.1137/s0036144596301390
URL : http://dsec.pku.edu.cn/~tieli/notes/numer_anal/SIAMRev_39_644.pdf
A method for proving L p boundedness of singular Radon transforms in codimension one for 1 < p < ?, Duke Math, J, vol.108, issue.2, pp.363-393, 2001. ,
The Radon Transform, 1980. ,
Ranges of Radon transforms, Proc. Sympos, pp.63-70, 1982. ,
DOI : 10.1090/psapm/027/692054
On the range of the radon transform and its dual, Mathematische Annalen, vol.90, issue.1, pp.91-99, 1984. ,
DOI : 10.1007/978-1-4684-9928-5
Tomographic Reconstruction Of Axially Symmetric Objects From A Single Radiograph, 16th Intl Congress on High Speed Photography and Photonics, p.491, 1984. ,
DOI : 10.1117/12.967907
Image reconstruction from projections: the fundamentals of computerized tomography, 1980. ,
A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators, Inverse Problems, vol.23, issue.3, pp.987-1010, 2007. ,
DOI : 10.1088/0266-5611/23/3/009
URL : http://www.tu-chemnitz.de/mathematik/inverse_probleme/Aktuelle_Resultate/hkps.pdf
, Principles of Computerized Tomographic Imaging, 1988.
Discrete tomography for reconstruction from limited view angles in non-destructive testing, Proceedings of the Workshop on Discrete Tomography and its Applications, pp.455-474, 2005. ,
DOI : 10.1016/j.endm.2005.05.078
Reconstruction and Visualization of Planetary Nebulae, IEEE Transactions on Visualization and Computer Graphics, vol.11, issue.5, pp.485-496, 2005. ,
DOI : 10.1109/TVCG.2005.84
ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems, IEEE Transactions on Signal Processing, vol.52, issue.2, pp.418-433, 2004. ,
DOI : 10.1109/TSP.2003.821103
Exploiting the ranges of Radon transforms in tomography, Numerical treatment of inverse problems in differential and integral equations, Progr. Sci. Comput, vol.2, pp.290-303 ,
Localized Polynomial Frames on the Interval with Jacobi Weights, Journal of Fourier Analysis and Applications, vol.11, issue.5, pp.557-575, 2005. ,
DOI : 10.1007/s00041-005-4072-3
Theory, algorithms, and applications of level set methods for propagating interfaces, Acta Numerica, vol.11, pp.309-395, 1996. ,
DOI : 10.1007/BF00133570
, Ma¨?tineMa¨?tine Bergounioux Institut Denis Poisson -UMR 7013
, Université d'Orléans BP 6759 F-45067 Orléans Cedex
, France e-mail: maitine.bergounioux@univ-orleans
, Bruyères le Châtel, vol.12, 91680.
, Université d'Orléans BP 6759 F-45067 Orléans Cedex
, France e-mail: romain.abraham@univ-orleans
France e-mail: carlier@ceremade.dauphine.fr Erwan Le Pennec CMAP, ´ Ecole polytechnique, CNRS e-mail: erwan.le-pennec@polytechnique, 6) Laboratoire Jacques-Louis Lions, CNRS Inria, ´ equipe CAGE 4 place Jussieu, pp.75775-75791, 91128. ,