On the jump set of solutions of the total variation flow
Rendiconti del Seminario Matematico della Università di Padova, Tome 130 (2013), p. 155-168
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consulter le site de la revue
@article{RSMUP_2013__130__155_0,
     author = {Caselles, V. and Jalalzai, K. and Novaga, M.},
     title = {On the jump set of solutions of the total variation flow},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {130},
     year = {2013},
     pages = {155-168},
     zbl = {1284.49043},
     mrnumber = {3148636},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2013__130__155_0}
}
Caselles, V.; Jalalzai, K.; Novaga, M. On the jump set of solutions of the total variation flow. Rendiconti del Seminario Matematico della Università di Padova, Tome 130 (2013) pp. 155-168. http://www.numdam.org/item/RSMUP_2013__130__155_0/

[1] F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in R N . Math. Ann., 332 (2) (2005), pp. 329-366. | MR 2178065

[2] L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime. Scuola Normale Superiore, Pisa, 1997. | MR 1736268

[3] L. Ambrosio - N. Fusco - D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs XVIII, Clarendon Press, 2000. | MR 1857292

[4] F. Andreu - C. Ballester - V. Caselles - J. M. Mazón, Minimizing total variation flow. Differential Integral Equations, 14 (3) (2001), pp. 321-360. | MR 1799898

[5] F. Andreu - C. Ballester - V. Caselles - J. M. Mazón, The Dirichlet problem for the total variation flow. Journal Functional Analysis, 180 (2001), pp. 347-403. | MR 1814993

[6] F. Andreu - V. Caselles - J. M. Mazón, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Birkhaüser Verlag, 2004. | MR 2033382

[7] G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl., 135 (1983), pp. 293-318. | MR 750538

[8] G. Bellettini - V. Caselles - M. Novaga, The total variation flow in R N . J. Differential Equations, 184 (2) (2002), pp. 475-525. | MR 1929886

[9] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam, 1973. | MR 348562

[10] V. Caselles - A. Chambolle - M. Novaga, The discontinuity set of solutions of the TV denoising problem and some extensions. Multiscale modeling & simulation, 6 (3) (2007), pp. 879-894. | MR 2368971

[11] V. Caselles - A. Chambolle - M. Novaga, Total Variation in Imaging. Handbook of Mathematical Methods in Imaging, Springer Verlag, 2010, pp. 1016-1057.

[12] A. Chambolle - V. Caselles - D. Cremers - M. Novaga - T. Pock, An introduction to Total Variation for Image Analysis. In Theoretical Foundations and Numerical Methods for Sparse Recovery, De Gruyter, Radon Series Comp. Appl. Math., vol. 9 (2010), pp. 263-340. | MR 2731599

[13] V. Caselles - A. Chambolle - M. Novaga, Regularity for solutions of the total variation denoising problem. Rev. Mat. Iberoamericana, 27 (1) (2011), pp. 233-252. | MR 2815736

[14] A. Chambolle - P.-L. Lions, Image recovery via total variation minimization and related problems. Numer. Math., 76 (1997), pp. 167-188. | MR 1440119

[15] A. Chambolle, An algorithm for mean curvature motion. Interfaces Free Bound., 6 (2) (2004), pp. 195-218. | MR 2079603

[16] T. F. Chan - G. H. Golub - P. Mulet, A nonlinear primal-dual method for total variation based image restoration. SIAM J. Sci. Computing, 20 (1999), pp. 1964-1977. | MR 1694649

[17] M. G. Crandall - T. M. Liggett, Generation of Semigroups of Nonlinear Transformations on General Banach Spaces, Amer. J. Math., 93 (1971), pp. 265-298. | MR 287357

[18] K. Jalalzai, Regularization of inverse problems in image processing. PhD Thesis, École Polytechnique, Palaiseau, Mars 2012.

[19] L. Rudin - S. Osher - E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D, 60 (1992), pp. 259-268.

[20] W. P. Ziemer, Weakly Differentiable Functions, GTM 120, Springer Verlag, 1989. | MR 1014685