D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, vol.3, issue.5, pp.577-685, 1989.
DOI : 10.1109/TPAMI.1984.4767596

L. Ambrosio and V. M. Tortorelli, Approximation of functional depending on jumps by elliptic functional via t-convergence, Communications on Pure and Applied Mathematics, vol.17, issue.8, pp.999-1036, 1990.
DOI : 10.1080/01621459.1987.10478393

L. Ambrosio and V. M. Tortorelli, On the approximation of free discontinuity problems, Boll. Un. Mat. Ital, vol.6, pp.105-123, 1992.

E. De-giorgi, M. Carriero, and A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Archive for Rational Mechanics and Analysis, vol.107, issue.4, pp.195-218, 1989.
DOI : 10.1007/978-1-4684-9486-0

L. Ambrosio, N. Fusco, and D. Pallara, Free Discontinuity Problems and Special Functions with Bounded Variation, 2000.
DOI : 10.1007/978-3-0348-8974-2_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

L. Condat, Discrete Total Variation: New Definition and Minimization, SIAM Journal on Imaging Sciences, vol.10, issue.3, pp.1258-1290, 2017.
DOI : 10.1137/16M1075247
URL : https://hal.archives-ouvertes.fr/hal-01309685

B. Bourdin and A. Chambolle, Implementation of an adaptive finite-element approximation of the Mumford-Shah functional, Numerische Mathematik, vol.85, issue.4, pp.609-646, 2000.
DOI : 10.1007/PL00005394

Z. Li, F. Malgouyres, and T. Zeng, Regularized Non-local Total Variation and Application in Image Restoration, Journal of Mathematical Imaging and Vision, vol.3, issue.3, pp.296-317, 2017.
DOI : 10.1137/090746379
URL : https://hal.archives-ouvertes.fr/hal-01342111

M. Foare, J. Lachaud, and H. Talbot, Image restoration and segmentation using the Ambrosio-Tortorelli functional and Discrete Calculus, 2016 23rd International Conference on Pattern Recognition (ICPR), 2016.
DOI : 10.1109/ICPR.2016.7899836
URL : https://hal.archives-ouvertes.fr/hal-01379993

H. Attouch, J. Bolte, P. Redont, and A. Soubeyran, Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-??ojasiewicz Inequality, Mathematics of Operations Research, vol.35, issue.2, pp.438-457, 2010.
DOI : 10.1287/moor.1100.0449

J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Proc. European Conference on Computer Vision, pp.459-494, 2014.
DOI : 10.1007/BF01584660
URL : https://hal.archives-ouvertes.fr/hal-00916090

N. Pustelnik, H. Wendt, P. Abry, and N. Dobigeon, Combining local regularity estimation and total variation optimization for scale-free texture segmentation, IEEE Transactions on Computational Imaging, vol.2, issue.4, pp.468-479, 2016.
DOI : 10.1109/TCI.2016.2594139

M. Serres, M. Zanota, R. Philippe, and V. Vidal, On the stability of Taylor bubbles inside a confined highly porous medium, International Journal of Multiphase Flow, vol.85, pp.157-163, 2016.
DOI : 10.1016/j.ijmultiphaseflow.2016.06.003