On the jump set of solutions of the total variation flow
V. Caselles; K. Jalalzai; M. Novaga
Rendiconti del Seminario Matematico della Università di Padova (2013)
- Volume: 130, page 155-168
- ISSN: 0041-8994
Access Full Article
topHow to cite
topCaselles, V., Jalalzai, K., and Novaga, M.. "On the jump set of solutions of the total variation flow." Rendiconti del Seminario Matematico della Università di Padova 130 (2013): 155-168. <http://eudml.org/doc/275131>.
@article{Caselles2013,
author = {Caselles, V., Jalalzai, K., Novaga, M.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {total variation flow; jump set; image denoising; nonlinear parabolic equations; functions of bounded variation},
language = {eng},
pages = {155-168},
publisher = {Seminario Matematico of the University of Padua},
title = {On the jump set of solutions of the total variation flow},
url = {http://eudml.org/doc/275131},
volume = {130},
year = {2013},
}
TY - JOUR
AU - Caselles, V.
AU - Jalalzai, K.
AU - Novaga, M.
TI - On the jump set of solutions of the total variation flow
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2013
PB - Seminario Matematico of the University of Padua
VL - 130
SP - 155
EP - 168
LA - eng
KW - total variation flow; jump set; image denoising; nonlinear parabolic equations; functions of bounded variation
UR - http://eudml.org/doc/275131
ER -
References
top- [1] F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in . Math. Ann., 332 (2) (2005), pp. 329–366. Zbl1108.35073MR2178065
- [2] L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime. Scuola Normale Superiore, Pisa, 1997. MR1736268
- [3] L. Ambrosio - N. Fusco - D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs XVIII, Clarendon Press, 2000. Zbl0957.49001MR1857292
- [4] F. Andreu - C. Ballester - V. Caselles - J. M. Mazón, Minimizing total variation flow. Differential Integral Equations, 14 (3) (2001), pp. 321–360. Zbl1020.35037MR1799898
- [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. Zbl0973.35109MR1814993
- [6] F. Andreu - V. Caselles - J. M. Mazón, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Birkhaüser Verlag, 2004. Zbl1053.35002MR2033382
- [7] G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl., 135 (1983), pp. 293–318. Zbl0572.46023MR750538
- [8] G. Bellettini - V. Caselles - M. Novaga, The total variation flow in . J. Differential Equations, 184 (2) (2002), pp. 475–525. Zbl1036.35099MR1929886
- [9] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam, 1973. Zbl0252.47055MR348562
- [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. Zbl1145.49024MR2368971
- [11] V. Caselles - A. Chambolle - M. Novaga, Total Variation in Imaging. Handbook of Mathematical Methods in Imaging, Springer Verlag, 2010, pp. 1016–1057. Zbl1259.68217
- [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. Zbl1209.94004MR2731599
- [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. Zbl1228.94005MR2815736
- [14] A. Chambolle - P.-L. Lions, Image recovery via total variation minimization and related problems. Numer. Math., 76 (1997), pp. 167–188. Zbl0874.68299MR1440119
- [15] A. Chambolle, An algorithm for mean curvature motion. Interfaces Free Bound., 6 (2) (2004), pp. 195–218. Zbl1061.35147MR2079603
- [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. Zbl0929.68118MR1694649
- [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. Zbl0226.47038MR287357
- [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. Zbl0780.49028
- [20] W. P. Ziemer, Weakly Differentiable Functions, GTM 120, Springer Verlag, 1989. MR1014685
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.