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

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Caselles, 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

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  1. [1] F. Alter - V. Caselles - A. Chambolle, A characterization of convex calibrable sets in R N . Math. Ann., 332 (2) (2005), pp. 329–366. Zbl1108.35073MR2178065
  2. [2] L. Ambrosio, Corso introduttivo alla teoria geometrica della misura ed alle superfici minime. Scuola Normale Superiore, Pisa, 1997. MR1736268
  3. [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. [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. [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. [6] F. Andreu - V. Caselles - J. M. Mazón, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Birkhaüser Verlag, 2004. Zbl1053.35002MR2033382
  7. [7] G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl., 135 (1983), pp. 293–318. Zbl0572.46023MR750538
  8. [8] G. Bellettini - V. Caselles - M. Novaga, The total variation flow in R N . J. Differential Equations, 184 (2) (2002), pp. 475–525. Zbl1036.35099MR1929886
  9. [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. [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. [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. [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. [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. [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. [15] A. Chambolle, An algorithm for mean curvature motion. Interfaces Free Bound., 6 (2) (2004), pp. 195–218. Zbl1061.35147MR2079603
  16. [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. [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. [18] K. Jalalzai, Regularization of inverse problems in image processing. PhD Thesis, École Polytechnique, Palaiseau, Mars 2012. 
  19. [19] L. Rudin - S. Osher - E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D, 60 (1992), pp. 259–268. Zbl0780.49028
  20. [20] W. P. Ziemer, Weakly Differentiable Functions, GTM 120, Springer Verlag, 1989. MR1014685

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